Multireference electron correlation methods: Journeys along potential energy surfaces

Bess Vlaisavljevich; Jae Woo Park; Matthew K. MacLeod; Rachael Al-Saadon; Toru Shiozaki

Multireference electron correlation methods: Journeys along potential energy surfaces

T0 review · 0 major / 8 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Analytical gradients make multireference photodynamics practical.

desk verdict A thorough, accurate review of multireference gradients and dynamics; the self-citation heavy narrative is a minor concern, not a flaw. read the letter →

arxiv 1911.06836 v1 pith:C3AWKXC7 submitted 2019-08-08 physics.chem-ph

Jae Woo Park , Rachael Al-Saadon , Matthew K. MacLeod , Toru Shiozaki , Bess Vlaisavljevich This is my paper · ORCID

classification physics.chem-ph

keywords multireferenceelectroncorrelationanalyticalnucleargradientsderivativecouplingsCASPT2conicalintersectionson-the-flyphotodynamicspotentialenergysurfacessurfacehopping

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review argues that multireference electron correlation methods have matured from single-point energy tools into workhorses for exploring potential energy surfaces, because analytical nuclear gradients and derivative couplings are now available for them. The central message is that geometry optimization, including excited-state minima and conical intersections, and on-the-fly photodynamics simulations are practical at correlated levels such as CASPT2, even when single-reference methods fail. The authors trace the theory from Hartree-Fock gradients through the Lagrangian approach that makes multireference gradient derivations tractable, and they catalog applications showing where dynamical correlation changes the picture qualitatively.

What carries the argument

The central object is the analytical nuclear gradient expressed through the Lagrangian and the Z-vector equation. Because the CASPT2 or multistate CASPT2 energy is not stationary with respect to orbital rotations or CI coefficients, the gradient is obtained by constructing a Lagrangian with constraints, solving the Z-vector response equations, and forming relaxed (effective) densities. The derivative couplings follow from the interstate coupling term, which for multistate CASPT2 comes from differentiating the effective Hamiltonian, plus a determinant term. For fully internally contracted CASPT2, automatic code generation is the mechanism that made the involved CI derivatives tractable.

What would settle it

Take a small photochemical system with a known conical intersection, such as ethylene or a protonated Schiff base model, and optimize the S1/S0 crossing with both XMS-CASPT2 and a high-level uncontracted MRCI reference using the same basis set; a qualitative mismatch in the branching-plane vectors and seam topology would show that the practical reliability asserted by the review does not transfer to that system.

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Extended reading notes

Core claim

The paper's central claim is that analytical nuclear gradients and derivative couplings for multireference electron correlation methods, above all for internally contracted CASPT2, have reached the point where they can be used routinely in geometry optimizations and nonadiabatic dynamics. The load-bearing development is the Lagrangian (response-function) formalism, which handles the fact that correlated multireference energies are not variational in the orbital and configuration-interaction coefficients by introducing Z-vector equations and effective densities; this is what makes the gradient evaluation practical. With fully internally contracted CASPT2, automatic code generation overcame the algebraic complexity of the CI derivative. The review documents that including dynamical correlation through these gradients changes conical intersection geometries, branching-plane topologies, and photodynamics lifetimes compared with CASSCF, often bringing calculations into agreement with experiment.

Load-bearing premise

The review's conclusion that these methods are practical workhorses rests on the correctness of the software implementations and on the selected applications being representative; if the implementations contain bugs or the highlighted systems are atypical, the claimed practicality would be overstated.

Editorial extensions

If this is right

Geometry optimization of excited states and conical intersections can be carried out at the CASPT2 and XMS-CASPT2 levels, not only at CASSCF.
On-the-fly surface-hopping and ab initio multiple spawning simulations with multireference perturbation theory now reproduce experimental lifetimes and branching qualitatively, including intersystem crossing when spin-orbit coupling is added.
Choosing XMS-CASPT2 avoids artifacts from state rotations in multistate perturbation theory, giving reliable potential-energy-surface topologies near crossings.
MRCI and CASPT2 gradient data provide references against which cheaper methods such as TDDFT, ADC(2), and semiempirical MRCI can be benchmarked for conical intersection geometries.
Further progress depends on reducing cost; explicitly correlated and local-correlation multireference gradients are named as the next step.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If analytical gradients stop being the bottleneck, the same Lagrangian-plus-automatic-derivation machinery could be carried over to other multireference methods such as NEVPT2 and multireference coupled cluster, and to higher-order properties like Hessians and spin-orbit couplings.
The systematic differences between CASSCF and CASPT2 conical intersections reported here suggest that CASSCF-based mechanistic conclusions in photochemistry should be rechecked with a correlated gradient method whenever the two states differ in dynamical correlation.
As implementations speed up, multireference on-the-fly dynamics may become a standard complement to time-resolved spectroscopy, turning simulation into an interpretive tool rather than a specialized calculation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Bottom line: this is a solid, genuinely useful review. It won't reshape the field, but it will orient people who need to choose among multireference methods and understand how the gradients are actually computed. The main claim—that analytic gradients make these methods practical—is well supported by the applications literature.

What's good: the theory sections are clear and historically accurate. The Lagrangian/Z-vector derivation is the right pedagogical backbone, and the coverage of internal contraction schemes (FIC vs PIC, XMS vs MS) is more explicit than most papers. I especially appreciate the candid note that the PIC-MS-CASPT2 gradient was never published; that kind of transparency is rare. The application tables are a useful quick reference, and the examples span organic photochemistry, nucleobases, transition metals, and actinides.

Where it's soft: the review leans heavily on the authors' own BAGEL FIC/XMS-CASPT2 work. That's not circularity in a damning sense—those papers are peer-reviewed and many applications come from independent groups—but a reader should know that the 'workhorse' label is partly a statement of faith in code that isn't independently benchmarked in this review. The stress-test note about a potential bug in the CI-derivative contractions is real as a verification gap, but it's not evidence of a bug, and it applies equally to any review that cites software results. I'd call that a minor limitation, not a load-bearing flaw.

Other soft spots: minor typos ('graidents' in Sec. V), and the numerical results are taken on faith from the original papers. For a review, that's normal.

Who this is for: graduate students and experimental collaborators who need to know when CASPT2 vs MRCISD vs XMS-CASPT2 is appropriate, and method developers who want a compact summary of gradient theory. It deserves a serious referee, and I'd accept it after minor revisions—mainly fixing typos and tempering a couple of 'workhorse' claims to acknowledge that the reliability rests on the underlying implementations.

Referee Report

0 major / 8 minor

Summary. This manuscript is a review of multireference (MR) electron correlation methods for computing potential energy surfaces, with an emphasis on analytical nuclear gradients and derivative couplings. It first surveys geometry optimizations and on-the-fly nonadiabatic dynamics applications (Tables I and II), then introduces the electronic structure background (CASSCF, MRCI, MRCC, MRPT), and then presents the gradient and derivative-coupling formalism, including the Hartree-Fock/MCSCF foundations, the Lagrangian approach, and its application to PIC-CASPT2, FIC-CASPT2, and (X)MS-CASPT2. It closes with conical intersection optimization and semiclassical dynamics interfaces. The central claim is that the availability of analytical gradients and derivative couplings has made MR methods practical tools for geometry optimizations and photodynamics, even where single-reference methods fail.

Significance. The paper is a useful, broad reference that connects historical developments in MR gradient theory to modern applications. Its main strengths are the coherent exposition of the Celani-Werner Lagrangian, the coverage of internal-contraction variants and zeroth-order Hamiltonian choices, the documentation of the automatic code-generation route (smith3) for FIC-CASPT2, and the extensive tables of applications. The manuscript also credits open-source software (BAGEL) and cites many applications by groups other than the authors. The verification-gap concern of the stress-test does not, on reading the manuscript, amount to a demonstrated flaw; the cited method papers are peer-reviewed and BAGEL is open source, so the concern is a scoping caveat rather than evidence of incorrectness. Nevertheless, the most recent pillar of the 'practical tool' claim rests on the authors' own BAGEL implementations, and a brief, explicit statement about the absence of new independent benchmarking would make the claim more precise.

minor comments (8)

[§VI.E, Eq. (106)] The printed expression for the derivative coupling, h^{PT2,QP} = 1/2 [<Q|dΨ_P/dX> + <Ψ_Q|dP/dX>], is not the standard definition; for normalized real wave functions the plus-sign form would vanish. Please replace it with h^{QP} = <Ψ_Q|dΨ_P/dX> (or an explicitly antisymmetrized expression with a minus sign).
[§VI.C, Eq. (79)] The stationarity condition is written as ∂L/∂U_rs - ∂L/∂U_rs = 0; the second term should be ∂L/∂U_sr.
[§IV.B] The clause 'several reviews ... on the CI and CC theories' cites Refs. 6, 77, 140, and 175; Ref. 140 is a nonadiabatic dynamics review and does not belong in that citation grouping. Please correct the citation list.
[Tables I and II] Many entries in the System column are blank and rely on footnote letters to identify the molecules; this makes the otherwise valuable survey difficult to scan. Please fill the System column directly or provide an explicit list of systems in the caption.
[§II.C and §III.B] The manuscript explicitly notes that the PIC-MS-CASPT2 nuclear gradient 'has never been published' even though it underlies several early MS-CASPT2 dynamics applications. This is an acknowledged reproducibility limitation; the review should state its consequences or explicitly point to the later published implementations that supersede it.
[§VI.D and §III.B] The recent FIC-CASPT2 and XMS-CASPT2 applications cited as evidence of practicality depend on the authors' BAGEL implementation, but the review does not state that no independent numerical validation is performed here. A one-sentence caveat, with pointers to finite-difference checks in Refs. 17, 19, 63, and 66, would make the scope of the claim precise.
[References 273–274] The entries for the NEVPT2 gradient papers give only a year and no journal or preprint identifier; since Ref. 274 is a self-reference, please supply full bibliographic data or label both as preprints.
[General] There are several typographical errors, including 'state-speficic' (§VI.F), 'graidents' (§V.B.2), 'earilest' (§III.A), 'unconvered' (§III.A), and 'some the studies' (§II.C). They should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity is found: the review's practical-tool claim is supported by external benchmark literature and peer-reviewed method papers, and the authors' self-citations do not function as derivation inputs.

full rationale

This manuscript is a review of established analytical-gradient and derivative-coupling theory for multireference electron correlation methods. It contains no fitted parameter that is later relabeled as a prediction, and no equation is shown to be equivalent to its own input by construction. The central claim, that analytical nuclear gradients and derivative couplings make multireference methods practical for geometry optimization and on-the-fly dynamics, is supported by a broad set of applications from independent groups, including MS-CASPT2 AIMS studies of ethylene, butadiene, and cyclohexadiene, XMS-CASPT2 dynamics of pyrrole, cyclohexadiene, and methanol dications, and comparisons with experimental lifetimes and quantum yields. The authors' own BAGEL FIC/XMS-CASPT2 gradient and derivative-coupling developments (Refs. 17, 19, 63, 66, 73, 74) are cited as prior peer-reviewed work rather than as an unexamined premise, and the review also points to independent implementations and users. The manuscript itself flags external-verification gaps, including the PIC-MS-CASPT2 gradient "which has never been published" (Sec. II.C) and the MCQDPT2 gradient whose implementation "has never been reported" (Introduction and Sec. II.B); these are reproducibility limitations, not circular reductions. Accordingly, no circularity step can be identified under the required standard of quoting a specific reduction or fitted-input-as-prediction.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The review rests on standard quantum chemistry assumptions and on the correctness of external implementations. No free parameters are fitted; no new entities are introduced.

assumptions (4)

standard math The electronic wave function is represented as a linear combination of Slater determinants (Eq. 1) and the Born-Oppenheimer approximation separates nuclear and electronic motion.
This is the foundational setup of quantum chemistry and is stated in Sec. IV.
standard math The Hellmann-Feynman theorem does not hold for finite-basis correlated methods, so derivative integrals and orbital response terms are needed.
Sec. V.A explains this and uses it to derive gradient expressions.
domain assumption The software packages (COLUMBUS, MOLPRO, MOLCAS, BAGEL) implement the methods as described and the results reported in the cited applications are correct.
The review's conclusions about the utility of the methods depend on the reliability of these implementations and the cited numerical results, e.g., Secs. II and III.
domain assumption Intruder-state shifts (real, imaginary, IPEA) are applied in the cited studies in a way that does not bias the comparisons.
Sec. IV.B.2 discusses shifts, and Secs. II.C and III.B rely on those results, assuming the shift parameters are appropriate.

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Cite this review

Pith. "Pith review of Multireference electron correlation methods: Journeys along potential energy surfaces." pith.science (2026). https://pith.science/paper/C3AWKXC7

@misc{pith2026191106836,
  author       = {Pith},
  title        = {Pith review of: Multireference electron correlation methods: Journeys along potential energy surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C3AWKXC7}},
  note         = {Machine review of arXiv:1911.06836}
}

read the original abstract

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way, and therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field (MCSCF) theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces (PES). This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections, and on-the-fly photodynamics simulations; both depend heavily on the ability of the method to properly explore the PES. Since such applications require the nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly improves the utility of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. To motivate the readers, we first summarize the notable applications of multireference electron correlation methods to mainstream chemistry, including geometry optimizations and on-the-fly dynamics. Subsequently, we review the analytical nuclear gradient and derivative coupling theories for these methods, and the software infrastructure that allows one to make use of these quantities in applications. The future prospects are discussed at the end of this review.

Figures

Figures reproduced from arXiv: 1911.06836 by the authors.

**Figure 2.** FIG. 2. Geometries of organic molecules computed with various methods, including MRCISD, superimposed to demonstrate the accuracy of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Geometry and active orbitals of copper corrole complex op [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: FIG. 4. Optimized structures for the S [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Optimized structures for S [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: FIG. 6. Dynamics population of the T [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: FIG. 7. Dynamics trajectories with (solid) and without (dashed) solvent for the (a) [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: FIG. 8. Experimental (top) and computed (bottom) Dalitz plots of [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9. PES contour plots near the MECIs of PSB3 computed with [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]

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Works this paper leans on

300 extracted references · 80 canonical work pages

[1]

S., Hiberty, P

Shaik, S. S., Hiberty, P. C., Eds. A Chemist's Guide to Valence Bond Theory; Wiley-Interscience: Hoboken, NJ, 2007

2007
[2]

Bally, T.; Borden, W. T. In Reviews in Reviews in Computational Chemistry, Vol. 13; Lipkowitz, K. B., Boyd, D. B., Eds.; John Wiley & Sons, 1999

1999
[3]

Borden, W. T. In The Foundations of Physical Organic Chemistry: Fifty Years of the James Flack Norris Award; Mainz, E. T. S. V. V., Ed.; American Chemical Society, 2015; Chapter 11

2015
[4]

Singly Occupied MOs in Mono- and Diradical Conjugated Hydrocarbons: Comparison between Variational Single-Reference, -Fully Correlated and H \"u ckel Descriptions

Suaud, N.; Ruamps, R.; Malrieu, J.-P.; Guih \'e ry, N. Singly Occupied MOs in Mono- and Diradical Conjugated Hydrocarbons: Comparison between Variational Single-Reference, -Fully Correlated and H \"u ckel Descriptions. J. Phys. Chem. A 2014, 118, 5876--5884

2014
[5]

Kekul \'e versus Lewis: When Aromaticity Prevents Electron Pairing and Imposes Polyradical Character

Trinquier, G.; Malrieu, J.-P. Kekul \'e versus Lewis: When Aromaticity Prevents Electron Pairing and Imposes Polyradical Character. Chem. Eur. J. 2015, 21, 814--828

2015
[6]

Lischka, H.; Nachtigallov \'a , D.; Aquino, A. J. A.; Szalay, P. G.; Plasser, F.; Machado, F. B. C.; Barbatti, M. Multireference Approaches for Excited States of Molecules. Chem. Rev. 2018, 118, 7293--7361

2018
[7]

Le calcul non empirique des constantes de force et des d \'e riv \'e es du moment dipolaire

Brato z , S. Le calcul non empirique des constantes de force et des d \'e riv \'e es du moment dipolaire. Colloq. Int. C.N.R.S. 1958, 82, 287--301

1958
[8]

Gerratt, J.; Mills, I. M. Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree--Fock Calculations. I. J. Chem. Phys. 1968, 49, 1719--1730

1968

Show all 300 references

[9]

Ab initio Calculation of Force Constants and Equilibrium Geometries in Polyatomic Molecules

Pulay, P. Ab initio Calculation of Force Constants and Equilibrium Geometries in Polyatomic Molecules . Mol. Phys. 1969, 17, 197--204

1969
[10]

Energy Gradient in a Multi-Configurational SCF Formalism and its Application to Geometry Optimization of Trimethylene Diradicals

Kato, S.; Morokuma, K. Energy Gradient in a Multi-Configurational SCF Formalism and its Application to Geometry Optimization of Trimethylene Diradicals. Chem. Phys. Lett 1979, 65, 19--25

1979
[11]

In Applications of Electronic Structure Theory; Schaefer, III , H

Pulay, P. In Applications of Electronic Structure Theory; Schaefer, III , H. F., Ed.; Plenum Press: New York, 1977; Vol. 4; pp 153--185

1977
[12]

H., III; Saxe, P.; Yarkony, D

Lengsfield, B. H., III; Saxe, P.; Yarkony, D. R. On the Evaluation of Nonadiabatic Coupling Matrix Elements Using SA-MCSCF/CI Wave Functions and Analytic Gradient Methods. I. J. Chem. Phys. 1984, 81, 4549--4553

1984
[13]

Geometrical Energy Derivative Evaluation with MRCI Wave Functions

Shepard, R. Geometrical Energy Derivative Evaluation with MRCI Wave Functions. Int. J. Quantum Chem. 1987, 31, 33--44

1987
[14]

G.; Bartlett, R

Szalay, P. G.; Bartlett, R. J. Analytical Energy Gradients for the Two-Determinant Coupled Cluster Method with Application to Singlet Excited States of Butadiene and Ozone. J. Chem. Phys. 1994, 101, 4936--4944

1994
[15]

Nakano, H.; Hirao, K.; Gordon, M. S. Analytic Energy Gradients for Multiconfigurational Self-Consistent Field Second-Order Quasidegenerate Perturbation Theory (MC-QDPT). J. Chem. Phys. 1998, 108, 5660--5669

1998
[16]

Analytical Energy Gradients for Internally Contracted Second-Order Multireference Perturbation Theory

Celani, P.; Werner, H.-J. Analytical Energy Gradients for Internally Contracted Second-Order Multireference Perturbation Theory. J. Chem. Phys. 2003, 119, 5044--5057

2003
[17]

K.; Shiozaki, T

MacLeod, M. K.; Shiozaki, T. Automatic Code Generation Enables Nuclear Gradient Computations for Fully Internally Contracted Multireference Theory. J. Chem. Phys. 2015, 142, 051103

2015
[18]

Intersystem Crossing Pathways in the Noncanonical Nucleobase 2-Thiouracil: A Time-Dependent Picture

Mai, S.; Marquetand, P.; Gonz\' a lez , L. Intersystem Crossing Pathways in the Noncanonical Nucleobase 2-Thiouracil: A Time-Dependent Picture. J. Phys. Chem. Lett. 2016, 7, 1978--1983

2016
[19]

W.; Shiozaki, T

Park, J. W.; Shiozaki, T. On-the-fly CASPT2 Surface Hopping Dynamics. J. Chem. Theory Comput. 2017, 13, 3676--3683

2017
[20]

A XMS-CASPT2 Non-Adiabatic Dynamics Study on Pyrrole

Heindl, M.; Gonz \'a lez, L. A XMS-CASPT2 Non-Adiabatic Dynamics Study on Pyrrole. Comput. Theor. Chem. 2019, 1155, 38 -- 46

2019
[21]

Making Sense of Coulomb Explosion Imaging

Luzon, I.; Livshits, E.; Gope, K.; Baer, R.; Strasser, D. Making Sense of Coulomb Explosion Imaging. J. Phys. Chem. Lett. 2019, 10, 1361--1367

2019
[22]

Polyak, I.; Hutton, L.; Crespo-Otero, R.; Barbatti, M.; Knowles, P. J. Ultrafast Photo-Induced Dynamics of 1,3-Cyclohexadiene using XMS-CASPT2 Surface Hopping. J. Chem. Theory Comput. 2019, 15, 3929--3940

2019
[23]

M.; Gonz \'a lez, L

G \'o mez, S.; Ibele, L. M.; Gonz \'a lez, L. The 3s Rydberg State as a Doorway State in the Ultrafast Dynamics of 1,1-difluoroethylene. Phys. Chem. Chem. Phys. 2019, 21, 4871--4878

2019
[24]

F.; Lengsfield, III , B

Page, M.; Saxe, P.; Adams, G. F.; Lengsfield, III , B. H. Multireference CI Gradients and MCSCF Second Derivatives. J. Chem. Phys. 1984, 81, 434--450

1984
[25]

M.; Shavitt, I.; Dallos, M.; M \"u ller, T.; Szalay, P

Lischka, H.; Shepard, R.; Pitzer, R. M.; Shavitt, I.; Dallos, M.; M \"u ller, T.; Szalay, P. G.; Seth, M.; Kedziora, G. S.; Yabushita, S.; Zhang, Z. High-Level Multireference Methods in the Quantum-Chemistry Program System COLUMBUS: Analytic MR-CISD and MR-AQCC Gradients and M...

2001
[26]

G.; Shavitt, I.; Pitzer, R

Lischka, H.; M \"u ller, T.; Szalay, P. G.; Shavitt, I.; Pitzer, R. M.; Shepard, R. Columbus---A Program System for Advanced Multireference Theory Calculations. WIREs Comput. Mol. Sci. 2011, 1, 191--199

2011
[27]

u ller, T.; Szalay, P. G.; Brown, F. B.; Ahlrichs, R.; B \

Lischka, H.; Shepard, R.; Shavitt, I.; Pitzer, R. M.; Dallos, M.; M \"u ller, T.; Szalay, P. G.; Brown, F. B.; Ahlrichs, R.; B \"o hm, H. J.; Chang, A.; Comeau, D. C.; Gdanitz, R.; Dachsel, H.; Ehrhardt, C.; Ernzerhof, M.; H \"o chtl, P.; Irle, S.; Kedziora, G.; Kovar, T.; Par...

2017
[28]

Dallos, M.; M \"u ller, T.; Lischka, H.; Shepard, R. Geometry Optimization of Excited Valence States of Formaldehyde Using Analytical Multireference Configuration Interaction Singles and Doubles and Multireference Averaged Quadratic Coupled-Cluster Gradients, and the Conical I...

2001
[29]

Analytic MRCI Gradient for Excited States: Formalism and Application to the n - ^ * Valence- and n -(3 s ,3 p Rydberg States of Formaldehyde

Lischka, H.; Dallos, M.; Shepard, R. Analytic MRCI Gradient for Excited States: Formalism and Application to the n - ^ * Valence- and n -(3 s ,3 p Rydberg States of Formaldehyde. Mol. Phys. 2002, 100, 1647--1658

2002
[30]

K.; Chibotaru, L

Aquilante, F.; Autschbach, J.; Carlson, R. K.; Chibotaru, L. F.; Delcey, M. G.; De Vico, L.; Fdez. Galv \'a n, I.; Ferr \'e , N.; Frutos, L. M.; Gagliardi, L.; Garavelli, M.; Giussani, A.; Hoyer, C. E.; Li Manni, G.; Lischka, H.; Ma, D.; Malmqvist, P. .; M \"u ller, T.; Nenov,...

2016
[31]

S.; Olivucci, M

Page, C. S.; Olivucci, M. Ground and Excited State CASPT2 Geometry Optimizations of Small Organic Molecules. J. Comput. Chem. 2003, 24, 298--309

2003
[32]

u tz , M.; Celani, P.; Gy\

Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Sch\" u tz , M.; Celani, P.; Gy\"orffy, W.; Kats, D.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; Shamasundar, K. R.; Adler, T. B.; Amos, R. D.; Bennie, S. J.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deega...

2019
[33]

G.; Yarkony, D

Lischka, H.; Dallos, M.; Szalay, P. G.; Yarkony, D. R.; Shepard, R. Analytical Evaluation of Nonadiabatic Coupling Terms at the MR-CI Level. I. Formalism. J. Chem. Phys. 2004, 120, 7322--7329

2004
[34]

R.; Szalay, P

Dallos, M.; Lischka, H.; Shepard, R.; Yarkony, D. R.; Szalay, P. G. Analytic Evaluation of Nonadiabatic Coupling Terms at the MR-CI Level. II. Minima on the Crossing Seam: Formaldehyde and the Photodimerization of Ethylene. J. Chem. Phys. 2004, 120, 7330--7339

2004
[35]

Photochemistry of Ethylene: A Multireference Configuration Interaction Investigation of the Excited-State Energy Surfaces

Barbatti, M.; Paier, J.; Lischka, H. Photochemistry of Ethylene: A Multireference Configuration Interaction Investigation of the Excited-State Energy Surfaces. J. Chem. Phys. 2004, 121, 11614--11624

2004
[36]

Computation of Conical Intersections by Using Perturbation Techniques

Serrano-Andr\' e s , L.; Merch\'an , M.; Lindh, R. Computation of Conical Intersections by Using Perturbation Techniques. J. Chem. Phys. 2005, 122, 104107

2005
[37]

Three-State Conical Intersections in Nucleic Acid Bases

Matsika, S. Three-State Conical Intersections in Nucleic Acid Bases. J. Phys. Chem. A 2005, 109, 7538--7545

2005
[38]

G.; Ko, C.; Quenneville, J.; Mart\' i nez , T

Levine, B. G.; Ko, C.; Quenneville, J.; Mart\' i nez , T. J. Conical Intersections and Double Excitations in Time-Dependent Density Functional Theory. Mol. Phys. 2006, 104, 1039--1051

2006
[39]

W.; Lindh, R

De Vico , L.; Liu, Y.-J.; Krogh, J. W.; Lindh, R. Chemiluminescence of 1,2-Dioxetane. Reaction Mechanism Uncovered. J. Phys. Chem. A 2007, 111, 8013--8019

2007
[40]

G.; Coe, J

Levine, B. G.; Coe, J. D.; Mart\' i nez , T. J. Optimizing Conical Intersections without Derivative Coupling Vectors: Application to Multistate Multireference Second-Order Perturbation Theory (MS-CASPT2). J. Phys. Chem. B 2008, 112, 405--413

2008
[41]

A.; Lin, J

Lu, Y.-J.; Lee, L.; Pan, J.-W.; Xie, T.; Witek, H. A.; Lin, J. J. Barrierless Reactions Between Two Closed-Shell Molecules. I. Dynamics of F_2 + CH_3 SCH_3 Reaction. J. Chem. Phys. 2008, 128, 104317

2008
[42]

Shao, H.-C.; Xie, T.; Lu, Y.-J.; Chang, C.-H.; Pan, J.-W.; Lin, J. J. Barrierless Reactions Between Two Closed-Shell Molecules. II. Dynamics of F_2+CH_3 SSCH_3 Reaction. J. Chem. Phys. 2009, 130, 014301

2009
[43]

Dynamic Electron Correlation Effect on Conical Intersections in Photochemical Ring-Opening Reaction of Cyclohexadiene: MS-CASPT2 Study

Mori, T.; Kato, S. Dynamic Electron Correlation Effect on Conical Intersections in Photochemical Ring-Opening Reaction of Cyclohexadiene: MS-CASPT2 Study. Chem. Phys. Lett. 2009, 476, 97--100

2009
[44]

Eisfeld, W.; Francisco, J. S. Structure, Spectroscopic Properties, and Photochemistry of the Hydroxymethoxy Radical. J. Chem. Phys. 2009, 131, 134313

2009
[45]

Conical Intersections of Free Energy Surfaces in Solution: Effect of Electron Correlation on a Protonated Schiff Base in Methanol Solution

Mori, T.; Nakano, K.; Kato, S. Conical Intersections of Free Energy Surfaces in Solution: Effect of Electron Correlation on a Protonated Schiff Base in Methanol Solution. J. Chem. Phys. 2010, 133, 064107

2010
[46]

L.; Mart \'i nez, T

Thompson, A. L.; Mart \'i nez, T. J. Time-Resolved Photoelectron Spectroscopy from First Principles: Excited State Dynamics of Benzene. Faraday Discuss. 2011, 150, 293--311

2011
[47]

Extended Multi-State Complete Active Space Second-Order Perturbation Theory: Energy and Nuclear Gradients

Shiozaki, T.; Gy o rffy , W.; Celani, P.; Werner, H.-J. Extended Multi-State Complete Active Space Second-Order Perturbation Theory: Energy and Nuclear Gradients. J. Chem. Phys. 2011, 135, 081106

2011
[48]

A.; Angeli, C.; Olivucci, M

Gozem, S.; Huntress, M.; Schapiro, I.; Lindh, R.; Granovsky, A. A.; Angeli, C.; Olivucci, M. Dynamic Electron Correlation Effects on the Ground State Potential Energy Surface of a Retinal Chromophore Model. J. Chem. Theory Comput. 2012, 8, 4069--4080

2012
[49]

Nonradiative Deactivation Mechanisms of Uracil, Thymine, and 5-Fluorouracil: A Comparative Ab Initio Study

Yamazaki, S.; Taketsugu, T. Nonradiative Deactivation Mechanisms of Uracil, Thymine, and 5-Fluorouracil: A Comparative Ab Initio Study. J. Phys. Chem. A 2012, 116, 491--503

2012
[50]

Granovsky, A. A. Firefly , http://classic.chem.msu.su/gran/firefly/index.html (accessed )
[51]

N.; Granovsky, A

Ioffe, I. N.; Granovsky, A. A. Photoisomerization of Stilbene: The Detailed XMCQDPT2 Treatment. J. Chem. Theory Comput. 2013, 9, 4973--4990

2013
[52]

Theoretical Study of the Photochemical Generation of Triplet Acetophenone

Huix-Rollant, M.; Siri, D.; Ferr \'e , N. Theoretical Study of the Photochemical Generation of Triplet Acetophenone. Phys. Chem. Chem. Phys. 2013, 15, 19293--19300

2013
[53]

Mori, T.; Mart \'i nez, T. J. Exploring the Conical Intersection Seam: The Seam Space Nudged Elastic Band Method. J. Chem. Theory Comput. 2013, 9, 1155--1163

2013
[54]

Pyrazine Excited States Revisited Using the Extended Multi-State Complete Active Space Second-Order Perturbation Method

Shiozaki, T.; Woywod, C.; Werner, H.-J. Pyrazine Excited States Revisited Using the Extended Multi-State Complete Active Space Second-Order Perturbation Method. Phys. Chem. Chem. Phys. 2013, 15, 262--269

2013
[55]

Geometries and Vertical Excitation Energies in Retinal Analogues Resolved at the CASPT2 Level of Theory: Critical Assessment of the Performance of CASSCF, CC2, and DFT Methods

Walczak, E.; Szefczyk, B.; Andruni \'o w, T. Geometries and Vertical Excitation Energies in Retinal Analogues Resolved at the CASPT2 Level of Theory: Critical Assessment of the Performance of CASSCF, CC2, and DFT Methods. J. Chem. Theory Comput. 2013, 9, 4915--4927

2013
[56]

A.; Thiel, W.; Hoix-Rollant, M.; Filatov, M

Nikiforov, A.; Gomez, J. A.; Thiel, W.; Hoix-Rollant, M.; Filatov, M. Assessment of Approximate Computational Methods for Conical Intersections and Branching Plane Vectors in Organic Molecules. J. Chem. Phys. 2014, 141, 124122

2014
[57]

J.; Suits, A

Joalland, B.; Mori, T.; Mart \'i nez, T. J.; Suits, A. G. Photochemical Dynamics of Ethylene Cation C_2H_4^+ . J. Phys. Chem. Lett. 2014, 5, 1467--1471

2014
[58]

D.; Molina, A

Chien, A. D.; Molina, A. R.; Abeyasinghe, N.; Varnavski, O. P.; Goodson, III , T.; Zimmerman, P. M. Structure and Dynamics of the 1(TT) State in a Quinoidal Bithiophene: Characterizing a Promising Intramolecular Singlet Fission Candidate. J. Phys. Chem. C 2015, 119, 28258--28268

2015
[59]

A.; Bravaya, K

Mironov, V. A.; Bravaya, K. B.; Nemukhin, A. V. Role of Zwitterions in Kindling Fluorescent Protein Photochemistry. J. Phys. Chem. B 2015, 119, 2467--2474

2015
[60]

Assessment of the Potential Energy Hypersurfaces in Thymine within Multiconfigurational Theory: CASSCF vs

Segarra-Mart \'i , J.; Franc \'e s-Monerris, A.; Roca-Sanju \'a n, D.; Merchan, M. Assessment of the Potential Energy Hypersurfaces in Thymine within Multiconfigurational Theory: CASSCF vs. CASPT2. Molecules 2016, 21, 1666

2016
[61]

F.; Bettinger, H

Edel, K.; Fink, R. F.; Bettinger, H. F. Isomerization and Fragmentation Pathways of 1,2-azaborine. J. Comput. Chem. 2016, 37, 110--116

2016
[62]

BAGEL: Brilliantly Advanced General Electronic‐structure Library

Shiozaki, T. BAGEL: Brilliantly Advanced General Electronic‐structure Library. WIREs Comput. Mol. Sci. 2018, 8, e1331

2018
[63]

Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions

Vlaisavljevich, B.; Shiozaki, T. Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions. J. Chem. Theory Comput. 2016, 12, 3781--3787

2016
[64]

F.; Sobolewski, A

Hu, D.; Liu, Y. F.; Sobolewski, A. L.; Lan, Z. Nonadiabatic Dynamics Simulation of Keto-Isocytosine: A Comparison of Dynamical Performance of Different Electronic-Structure Methods. Phys. Chem. Chem. Phys. 2017, 19, 19168--19177

2017
[65]

M.; Weingart, O

Dokukina, I.; Marian, C. M.; Weingart, O. New Perspectives on an Old Issue: A Comparative MS-CASPT2 and OM2-MRCI Study of Polyenes and Protonated Schiff Bases. Photochem. Photobiol. 2017, 93, 1345--1355

2017
[66]

W.; Shiozaki, T

Park, J. W.; Shiozaki, T. Analytical Derivative Coupling for Multistate CASPT2 Theory. J. Chem. Theory Comput. 2017, 13, 2561--2570

2017
[67]

Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

Budz \'a k, S .; Scalmani, G.; Jacquemin, D. Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules. J. Chem. Theory Comput. 2017, 13, 6237--6252

2017
[68]

W.; Shiozaki, T

Park, J. W.; Shiozaki, T. On the Accuracy of Retinal Protonated Schiff Base Models. Mol. Phys. 2018, 116, 2583--2590

2018
[69]

A Comprehensive Benchmark of the XMS-CASPT2 Method for the Photochemistry of a Retinal Chromophore Model

Sen, S.; Schapiro, I. A Comprehensive Benchmark of the XMS-CASPT2 Method for the Photochemistry of a Retinal Chromophore Model. Mol. Phys. 2018, 116, 2571--2582

2018
[70]

Segarra-Mart \'i , J.; Tran, T.; Bearpark, M. J. Ultrafast and Radiationless Electronic Excited State Decay of Uracil and Thymine Cations: Computing the Effects of Dynamic Electron Correlation. Phys. Chem. Chem. Phys 2019, 21, 14322--14330

2019
[71]

Segarra-Mart \'i , J.; Tran, T.; Bearpark, M. J. Computing the Ultrafast and Radiationless Electronic Excited State Decay of Cytosine and 5‐methyl‐cytosine Cations: Uncovering the Role of Dynamic Electron Correlation. ChemPhotoChem 2019, in press

2019
[72]

Curious Case of 2-Selenouracil: Efficient Population of Triplet States and Yet Photostable

Mai, S.; Wolf, A.-P.; Gonz \'a lez, L. Curious Case of 2-Selenouracil: Efficient Population of Triplet States and Yet Photostable. J. Chem. Theory Comput. 2019, 15, 3730--3742

2019
[73]

W.; Al-Saadon, R.; Strand, N

Park, J. W.; Al-Saadon, R.; Strand, N. E.; Shiozaki, T. Imaginary Shift in CASPT2 Nuclear Gradient and Derivative Coupling Tfheory. J. Chem. Theory Comput. 2019, 15, 4088--4098

2019
[74]

Park, J. W. Single-State Single-Reference and Multistate Multireference Zeroth-Order Hamiltonians in MS-CASPT2 and Conical Intersections. J. Chem. Theory Comput. 2019, 15, 3960--3973

2019
[75]

Osamura, Y.; Yamaguchi, Y.; Schaefer III , H. F. Generalization of Analytic Configuration Interaction (CI) Gradient Techniques for Potential Energy Hypersurfaces, Including a Solution to the Coupled Perturbed Hartree--Fock Equations for Multiconfiguration SCF Molecular Wave Fu...

1982
[76]

G.; Kovar, T.; Ernzerhof, M

Shepard, R.; Lischka, H.; Szalay, P. G.; Kovar, T.; Ernzerhof, M. A General Multireference Configuration Interaction Gradient Program. J. Chem. Phys. 1992, 96, 2085--2098

1992
[77]

I.; Musia , M.; Lotrich, V

Lyakh, D. I.; Musia , M.; Lotrich, V. F.; Bartlett, R. J. Multireference Nature of Chemistry: The Coupled-Cluster View. Chem. Rev. 2012, 112, 182--243

2012
[78]

Hachey, M. R. J.; Bruna, P. J.; Grein, F. The Spectroscopy of Formaldehyde: III. Out-of-Plane Potentials and Geometry Optimizations for Singlet States. J. Mol. Spectroscopy 1996, 176, 375--384

1996
[79]

Merch \'a n, M.; Roos, B. O. A Theoretical Determination of the Electronic Spectrum of Formaldehyde. Theor. Chim. Acta 1995, 92, 227--239

1995
[80]

Ben-Nun, M.; Mart\'inez , T. J. Photodynamics of Ethylene: Ab Initio Studies of Conical Intersections. Chem. Phys. 2000, 259, 237--248

2000
[81]

J.; Klene, M.; Robb, M

Boggio-Pasqua, M.; Bearpark, M. J.; Klene, M.; Robb, M. A. A Computational Strategy for Geometry Optimization of Ionic and Covalent Excited States, Applied to Butadiene and Hexatriene. J. Chem. Phys. 2004, 120, 7849

2004
[82]

Nonadiabatic Deactivation of 9H-Adenine: A Comprehensive Picture Based on Mixed Quantum-Classical Dynamics

Barbatti, M.; Lischka, H. Nonadiabatic Deactivation of 9H-Adenine: A Comprehensive Picture Based on Mixed Quantum-Classical Dynamics. J. Am. Chem. Soc. 2008, 130, 6831--6839

2008
[83]

Barbatti, M.; Aquino, A. J. A.; Szymczak, J. J.; Nachtigallov\' a , D.; Hobza, P.; Lischka, H. Relaxation Mechanisms of UV-Photoexcited DNA and RNA Nucleobases. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 21453--21458

2010
[84]

J.; Aquino, A

Barbatti, M.; Szymczak, J. J.; Aquino, A. J. A.; Nachtigallov\' a , D.; Lischka, H. The Decay Mechanism of Photoexcited Guanine -- A Nonadiabatic Dynamics Study. J. Chem. Phys. 2011, 134, 014304

2011
[85]

J.; Lischka, H.; Thiel, W

Barbatti, M.; Lan, Z.; Crespo-Otero, R.; Szymczak, J. J.; Lischka, H.; Thiel, W. Critical Appraisal of Excited State Nonadiabatic Dynamics Simulations of 9H-Adenine. J. Chem. Phys. 2012, 137, 22A503

2012
[86]

Radiationless Decay of Excited States of Uracil through Conical Intersections

Matsika, S. Radiationless Decay of Excited States of Uracil through Conical Intersections. J. Phys. Chem. A 2004, 109, 7584--7590

2004
[87]

A.; Matsika, S

Kistler, K. A.; Matsika, S. Radiationless Decay Mechanism of Cytosine: An Ab Initio Study with Comparisons to the Fluorescent Analogue 5-Methyl-2-pyrimidinone. J. Phys. Chem. A 2007, 111, 2650--2661

2007
[88]

A.; Matsika, S

Kistler, K. A.; Matsika, S. Three-State Conical Intersections in Cytosine and Pyrimidinone Bases. J. Chem. Phys. 2008, 128, 215102

2008
[89]

Nonadiabatic Events and Conical Intersections

Matsika, S.; Krause, P. Nonadiabatic Events and Conical Intersections. Annu. Rev. Phys. Chem. 2011, 62, 621--643

2011
[90]

Marquetand, M. R. P.; Gonz \'a lez-V \'a zquez, J.; Sola, I.; Gonz \'a lez, L. Femtosecond Intersystem Crossing in the DNA Nucleobase Cytosine. J. Phys. Chem. Lett. 2012, 3, 3090--3094

2012
[91]

Semiempirical Quantumchemical Methods

Thiel, W. Semiempirical Quantumchemical Methods. WIREs Comput. Mol. Sci. 2014, 4, 145--157

2014
[92]

Shao, Y.; Head-Gordon, M.; Krylov, A. I. The Spin-Flip Approach within Time-Dependent Density Functional Theory: Theory and Applications to Diradicals. J. Chem. Phys. 2003, 118, 4807--4818

2003
[93]

Assessment of Density Functional Methods for Obtaining Geometries at Conical Intersections in Organic Molecules

Filatov, M. Assessment of Density Functional Methods for Obtaining Geometries at Conical Intersections in Organic Molecules. J. Chem. Theory Comput. 2013, 9, 4526--4541

2013
[94]

Andersson, K.; Malmqvist, P.- .; Roos, B. O. Second-Order Perturbation Theory with a Complete Active Space Self-Consistent Field Reference Function. J. Chem. Phys. 1992, 96, 1218--1226

1992
[95]

Quasidegenerate Perturbation Theory with Multiconfigurational Self-Consistent Field Reference Functions

Nakano, H. Quasidegenerate Perturbation Theory with Multiconfigurational Self-Consistent Field Reference Functions. J. Chem. Phys. 1993, 99, 7983--7992

1993
[96]

Granovsky, A. A. Extended Multi-Configuration Quasi-Degenerate Perturbation Theory: The New Approach to Multi-State Multi-Reference Perturbation Theory. J. Chem. Phys. 2011, 134, 214113

2011
[97]

L.; Ioffe, I.; Granovsky, A

Doryakov, A. L.; Ioffe, I.; Granovsky, A. A.; Ernsting, N. P.; Kovalenko, S. A. Femtosecond Raman Spectra of cis-Stilbene and trans-Stilbene with Isotopomers in Solution. J. Chem. Phys. 2012, 137, 244505

2012
[98]

Andrews, L.; Wang, X.; Lindh, R.; Roos, B.; Marsden, C. J. Simple N U F_3 and P U F_3 Molecules with Triple Bonds to Uranium. Angew. Chem. Int. Ed. 2008, 47, 5366--5370

2008
[99]

Infrared Spectra of Small Insertion and Methylidene Complexes in Reactions of Laser-Ablated Nickel Atoms with Halomethanes

Cho, H.-G.; Andrews, L.; Vlaisavljevich, B.; Gagliardi, L. Infrared Spectra of Small Insertion and Methylidene Complexes in Reactions of Laser-Ablated Nickel Atoms with Halomethanes. Organometallics 2009, 28, 5623--5632

2009
[100]

Infrared Spectra of Small Insertion and Methylidene Complexes in Reactions of Laser-Ablated Palladium Atoms with Halomethanes

Cho, H.-G.; Andrews, L.; Vlaisavljevich, B.; Gagliardi, L. Infrared Spectra of Small Insertion and Methylidene Complexes in Reactions of Laser-Ablated Palladium Atoms with Halomethanes. Organometallics 2009, 28, 6871--6879

2009
[101]

O.; Andrews, L

Wang, X.; Roos, B. O.; Andrews, L. Matrix Infrared Spectra and Electronic Structure Calculations of the First Actinide Borylene: FB=Th F_2 . Chem. Commun. 2010, 46, 1946--1948

2010
[102]

Combined Triple and Double Bonds to Uranium: The N U=N--H Uranimine Nitride Molecule Prepared in Solid Argon

Wang, X.; Andrews, L.; Vlaisavljevich, B.; Gagliardi, L. Combined Triple and Double Bonds to Uranium: The N U=N--H Uranimine Nitride Molecule Prepared in Solid Argon. Inorg. Chem. 2011, 50, 3826--3831

2011
[103]

D.; Ibers, J

Andrews, L.; Wang, X.; Liang, B.; Ruip \'e rez, F.; Infante, I.; Raw, A. D.; Ibers, J. A. Matrix Infrared Spectroscopy and a Theoretical Investigation of SUO and US_2 . Eur. J. Inorg. Chem. 2011, 2011, 4457--4463

2011
[104]

A.; Andrews, L.; Gong, Y

Wei, R.; Fang, Z.; Vasiliu, M.; Dixon, D. A.; Andrews, L.; Gong, Y. Infrared Spectroscopic and Theoretical Studies of the 3d Transition Metal Oxyfluoride Molecules. Inorg. Chem. 2019, in press

2019
[105]

Analytical Energy Gradients for Second-Order Multireference Perturbation Theory Using Density Fitting

Gy orffy , W.; Shiozaki, T.; Knizia, G.; Werner, H.-J. Analytical Energy Gradients for Second-Order Multireference Perturbation Theory Using Density Fitting. J. Chem. Phys. 2013, 138, 104104

2013
[106]

http://www.nubakery.org under the GNU General Public License

bagel , Brilliantly Advanced General Electronic-structure Library. http://www.nubakery.org under the GNU General Public License
[107]

O.; Malmqvist, P.- .; Molina, V.; Serrano-Andr \'e s, L.; Merch \'an , M

Roos, B. O.; Malmqvist, P.- .; Molina, V.; Serrano-Andr \'e s, L.; Merch \'an , M. Theoretical Characterization of the Lowest Energy Absorption Band of Pyrrole. J. Chem. Phys. 2002, 116, 7526--7536

2002
[108]

G.; Mart\' i nez , T

Tao, H.; Levine, B. G.; Mart\' i nez , T. J. Ab Initio Multiple Spawning Dynamics Using Multi-State Second-Order Perturbation Theory. J. Phys. Chem. A 2009, 113, 13656--13662

2009
[109]

J.; Robb, M

Bearpark, M. J.; Robb, M. A.; Schlegel, H. B. A Direct Method for the Location of the Lowest Energy Point on a Potential Surface Crossing. Chem. Phys. Lett. 1994, 223, 269--274

1994
[110]

Analytical Energy Gradient for the Reference Interaction Site Model Multiconfigurational Self-Consistent-Field Method: Application to 1,2-difluoroethylene in Aqueous Solution

Sato, H.; Hirata, F.; Kato, S. Analytical Energy Gradient for the Reference Interaction Site Model Multiconfigurational Self-Consistent-Field Method: Application to 1,2-difluoroethylene in Aqueous Solution. J. Chem. Phys. 1996, 105, 1546--1551

1996
[111]

Reference Interaction Site Model Self-Consistent-Field Study for Solvation Effect on Carbonyl Compounds in Aqueous Solution

Ten-no, S.; Hirata, F.; Kato, S. Reference Interaction Site Model Self-Consistent-Field Study for Solvation Effect on Carbonyl Compounds in Aqueous Solution. J. Chem. Phys. 1994, 100, 7443--7453

1994
[112]

Locating the Lowest Free-Energy Point on Conical Intersection in Polar Solvent: Reference Interaction Site Model Self-Consistent Field Study of Ethylene and CH_2 NH_2^+

Yamazaki, S.; Kato, S. Locating the Lowest Free-Energy Point on Conical Intersection in Polar Solvent: Reference Interaction Site Model Self-Consistent Field Study of Ethylene and CH_2 NH_2^+ . J. Chem. Phys. 2005, 123, 114510

2005
[113]

Multiple Pathways in the Photodynamics of a Polar -Bond: A Case Study of Silaethylene

Zechmann, G.; Barbatti, M.; Lischka, H.; Pittner, J.; Bona c i \'c -Kouteck \'y , V. Multiple Pathways in the Photodynamics of a Polar -Bond: A Case Study of Silaethylene. Chem. Phys. Lett. 2006, 418, 377--382

2006
[114]

G.; Mart\' i nez , T

Coe, J.; Levine, B. G.; Mart\' i nez , T. J. Ab Initio Molecular Dynamics of Excited-State Intramolecular Proton Transfer Using Multireference Perturbation Theory. J. Phys. Chem. A 2007, 111, 11302

2007
[115]

Newton-X: A Surface-Hopping Program for Nonadiabatic Molecular Dynamics

Barbatti, M.; Ruckenbauer, M.; Plasser, F.; Pittner, J.; Granucci, G.; Persico, M.; Lischka, H. Newton-X: A Surface-Hopping Program for Nonadiabatic Molecular Dynamics. WIREs Comput. Mol. Sci. 2014, 4, 26--33

2014
[116]

2016; Newton-X : A Package for Newtonian Dynamics Close to the Crossing Seam, Version 2

Barbatti, M.; Granucci, G.; Ruckenbauer, M.; Plasser, F.; Crespo-Otero, R.; Pittner, J.; Persico, M.; Lischka, H. 2016; Newton-X : A Package for Newtonian Dynamics Close to the Crossing Seam, Version 2

2016
[117]

The On-the-Fly Surface-Hopping Program System Newton-X: Application to Ab Initio Simulation of the Nonadiabatic Photodynamics of Benchmark Systems

Barbatti, M.; Granucci, G.; Persico, M.; Ruckenbauer, M.; Vazdar, M.; Eckert-Maksi \'c , M.; Lischka, H. The On-the-Fly Surface-Hopping Program System Newton-X: Application to Ab Initio Simulation of the Nonadiabatic Photodynamics of Benchmark Systems. J. Photochem. Photobiol....

2007
[118]

Excited-State Non-Adiabatic Dynamics Simulations of Pyrrole

Vazdar, M.; Eckert-Maksi \'c , M.; Barbatti, M.; Lischka, H. Excited-State Non-Adiabatic Dynamics Simulations of Pyrrole. Mol. Phys. 2009, 107, 845--854

2009
[119]

K.; Wright, T

Tao, H.; Allison, T. K.; Wright, T. W.; Stooke, A. M.; Khurmi, C.; van Tilborg , J.; Liu, Y.; Falcone, R. W.; Belkacem, A.; Mart \'i nez, T. J. Ultrafast Internal Conversion in Ethylene. I. The Excited State Lifetime. J. Chem. Phys. 2011, 134, 244306

2011
[120]

K.; Tao, H.; Glover, W

Allison, T. K.; Tao, H.; Glover, W. J.; Wright, T. W.; Stooke, A. M.; Khurmi, C.; van Tilborg , J.; Liu, Y.; Falcone, R. W.; Mart \'i nez, T. J.; Belkacem, A. Ultrafast Internal Conversion in Ethylene. II. Mechanisms and Pathways for Quenching and Hydrogen Elimination. J. Chem...

2012
[121]

J.; Schuurman, M

Mori, T.; Glover, W. J.; Schuurman, M. S.; Mart\' i nez , T. J. Role of Rydberg States in the Photochemical Dynamics of Ethylene. J. Phys. Chem. A 2012, 116, 2808--2818

2012
[122]

S.; Glover, W

Kuhlman, T. S.; Glover, W. J.; Mori, T.; M ller, K. B.; Mart \'i nez, T. J. Between Ethylene and Polyenes --- The Non-Adiabatic Dynamics of cis-Dienes. Faraday Discuss. 2012, 157, 193--212

2012
[123]

Zelen \'y , T.; Ruckenbauer, M.; Aquino, A. J. A.; M \"u ller, T.; Lanka s , F.; Dr s ata, T.; Hase, W. L.; Nachtigallova, D.; Lischka, H. Strikingly Different Effects of Hydrogen Bonding on the Photodynamics of Individual Nucleobases in DNA: Comparison of Guanine and Cytosine...

2012
[124]

Nonadiabatic Photodynamics of a Retinal Model in Polar and Nonpolar Environment

Ruckenbauer, M.; Barbatti, M.; M\"uller , T.; Lischka, H. Nonadiabatic Photodynamics of a Retinal Model in Polar and Nonpolar Environment. J. Phys. Chem. A 2013, 117, 2790--2799

2013
[125]

Nonadiabatic Dynamics: The SHARC Approach

Mai, S.; Marquetand, P.; Gonz \'a lez, L. Nonadiabatic Dynamics: The SHARC Approach. WIREs Comput. Mol. Sci. 2018, 8, e1370

2018
[126]

Mai, S.; Richter, M.; Heindl, M.; Menger, M. F. S. J.; Atkins, A.; Ruckenbauer, M.; Plasser, F.; Oppel, M.; Marquetand, P.; Gonz\'alez, L. SHARC2.0: Surface Hopping Including Arbitrary Couplings — Program Package for Non-Adiabatic Dynamics. 2018

2018
[127]

Non-Adiabatic and Intersystem Crossing Dynamics in SO _2

Mai, S.; Marquetand, P.; Gonz \'a lez, L. Non-Adiabatic and Intersystem Crossing Dynamics in SO _2 . II. The Role of Triplet States in the Bound State Dynamics Studied by Surface-Hopping Simulations. J. Chem. Phys. 2014, 140, 204302

2014
[128]

Wolf, T. J. A.; Kuhlman, T. S.; Schalk, O.; Mart \'i nez, T. J.; M ller, K. B.; Stolow, A.; Unterreiner, A.-N. Hexamethylcyclopentadiene: Time-Resolved Photoelectron Spectroscopy and Ab Initio Multiple Spawning Simulations. Phys. Chem. Chem. Phys. 2014, 16, 11770--11779

2014
[129]

O.; Nanbu, S

Ohta, A.; Kobayashi, O.; Danielache, S. O.; Nanbu, S. Nonadiabatic Ab Initio Molecular Dynamics of Photoisomerization Reaction Between 1,3-cyclohexadiene and 1,3,5-cis-hexatriene. Chem. Phys. 2015, 459, 45--53

2015
[130]

Mignolet, B.; Curchod, B. F. E.; Mart \'i nez, T. J. Rich Athermal Ground‐State Chemistry Triggered by Dynamics through a Conical Intersection. Angew. Chem. Int. Ed. 2016, 55, 14993--14996

2016
[131]

Liu, L.; Liu, J.; Mart\' i nez , T. J. Dynamical Correlation Effects on Photoisomerization: Ab Initio Multiple Spawning Dynamics with MS-CASPT2 for a Model trans-Protonated Schiff Base. J. Phys. Chem. B 2016, 120, 1940--1949

2016
[132]

E.; Gonz\' a lez , L

Mai, S.; ; Pollum, M.; Mart\' i nez-Fern\' a ndez, L.; Dunn, N.; Marquetand, P.; Corral, I.; Crespo-Hern\' a ndez, C. E.; Gonz\' a lez , L. The Origin of Efficient Triplet State Population in Sulfur-Substituted Nucleobases. Nat. Commun. 2016, 7, 13077

2016
[133]

QM/MM Nonadiabatic Dynamics Simulations on Photoinduced Wolff Rearrangements of 1,2,3-Thiadiazole

Liu, X.-Y.; Fang, Y.-G.; Xie, B.-B.; Fang, W.-H.; Cui, G. QM/MM Nonadiabatic Dynamics Simulations on Photoinduced Wolff Rearrangements of 1,2,3-Thiadiazole. J. Chem. Phys. 2017, 146, 224302

2017
[134]

Molecular Dynamics and Metadynamics Simulations of [2 + 2] Photocycloaddition

Muchov \'a , E.; Bezek, M.; Suchan, J.; Cibulka, R.; Slav \'i c ek , P. Molecular Dynamics and Metadynamics Simulations of [2 + 2] Photocycloaddition. Int. J. Quantum Chem. 2017, 118, e25534

2017
[135]

C.; Mai, S.; Marquetand, P.; Gonz\' a lez , L

Borin, A. C.; Mai, S.; Marquetand, P.; Gonz\' a lez , L. Ab Initio Molecular Dynamics Relaxation and Intersystem Crossing Mechanisms of 5-azacytosine. Phys. Chem. Chem. Phys. 2017, 19, 5888--5894

2017
[136]

Insights into the Deactivation of 5-bromouracil after Ultraviolet Excitation

Peccati, F.; Mai, S.; Gonz\' a lez , L. Insights into the Deactivation of 5-bromouracil after Ultraviolet Excitation. Phil. Trans. R. Soc. A 2017, 375, 20160202

2017
[137]

J.; Mori, T.; Schuurman, M

Glover, W. J.; Mori, T.; Schuurman, M. S.; Boguslavskiy, A. E.; Schalk, O.; Stolow, A.; Mart \'i nez, T. J. Excited State Non-Adiabatic Dynamics of the Smallest Polyene, trans-1,3-butadiene. II. Ab Initio Multiple Spawning Simulations. J. Chem. Phys. 2018, 148, 164303

2018
[138]

J.; Plasser, F.; Gonz \'a lez, L

Mai, S.; Atkins, A. J.; Plasser, F.; Gonz \'a lez, L. The Influence of the Electronic Structure Method on Intersystem Crossing Dynamics. The Case of Thioformaldehyde. J. Chem. Theory Comput. 2019, 15, 3470--3480

2019
[139]

Curchod, B. F. E.; Mart \'i nez, T. J. Ab Initio Nonadiabatic Quantum Molecular Dynamics. Chem. Rev. 2018, 118, 3305--3336

2018
[140]

Recent Advances and Perspectives on Nonadiabatic Mixed Quantum-Classical Dynamics

Crespo-Otero, R.; Barbatti, M. Recent Advances and Perspectives on Nonadiabatic Mixed Quantum-Classical Dynamics. Chem. Rev. 2018, 118, 7026--7068

2018
[141]

Critical Appraisal of the Fewest Switches Algorithm for Surface Hopping

Granucci, G.; Persico, M. Critical Appraisal of the Fewest Switches Algorithm for Surface Hopping. J. Chem. Phys. 2007, 126, 134114

2007
[142]

A General Method to Describe Intersystem Crossing Dynamics in Trajectory Surface Hopping

Mai, S.; Marquetand, P.; Gonz\'alez, L. A General Method to Describe Intersystem Crossing Dynamics in Trajectory Surface Hopping. Int. J. Quantum Chem. 2015, 115, 1215--1231

2015
[143]

SHARC : Ab Initio Molecular Dynamics with Surface Hopping in the Adiabatic Representation Including Arbitrary Couplings

Richter, M.; Marquetand, P.; Gonz\'alez-V\'azquez, J.; Sola, I.; Gonz\'alez, L. SHARC : Ab Initio Molecular Dynamics with Surface Hopping in the Adiabatic Representation Including Arbitrary Couplings. J. Chem. Theory Comput. 2011, 7, 1253--1258

2011
[144]

E.; Mikosch, J.; Bertrand, J

Wilkinson, I.; Boguslavskiy, A. E.; Mikosch, J.; Bertrand, J. B.; W \"o rner, H. J.; Villeneuve, D. M.; Spanner, M.; Patchkovskii, S.; Stolow, A. Excited State Dynamics in SO_2 . I. Bound State Relaxation Studied by Time-Resolved Photoelectron-Photoion Coincidence Spectroscopy...

2014
[145]

E.; Stolow, A

Schalk, O.; Boguslavskiy, A. E.; Stolow, A. Substituent Effects on Dynamics at Conical Intersections: Cyclopentadienes. J. Phys. Chem. A 2010, 114, 4058--4064

2010
[146]

J.; Ramsay, D

Clouthier, D. J.; Ramsay, D. A. The Spectroscopy of Formaldehyde and Thioformaldehyde. Annu. Rev. Phys. Chem. 1983, 34, 31--58

1983
[147]

Spectra and Emission Lifetimes of H_2 CS ( A ^1 A_2)

Kawasaki, M.; Kasatani, K.; Ogawa, Y.; Sato, H. Spectra and Emission Lifetimes of H_2 CS ( A ^1 A_2) . Chem. Phys. 1983, 74, 83--88

1983
[148]

C.; Lim, E

Moule, D. C.; Lim, E. C. Highly Varying Photophysical Properties of Thiocarbonyls: Validation of Fundamental Theoretical Concepts of Electronic Radiationless Transitions. J. Phys. Chem. A 2002, 106, 3072--3076

2002
[149]

Olsen, S.; Lamothe, K.; Mart\' i nez , T. J. Protonic Gating of Excited-State Twisting and Charge Localization in GFP Chromophores: A Mechanistic Hypothesis for Reversible Photoswitching. J. Am. Chem. Soc. 2010, 132, 1192 -- 1193

2010
[150]

Non-Adiabatic Dynamics of Isolated Green Fluorescent Protein Chromophore Anion

Zhao, L.; Zhou, P.-W.; Li, B.; Gao, A.-H.; Han, K.-L. Non-Adiabatic Dynamics of Isolated Green Fluorescent Protein Chromophore Anion. J. Chem. Phys. 2014, 141, 235101

2014
[151]

L.; Petrovi \'c , V

Kim, J.; Tao, H.; White, J. L.; Petrovi \'c , V. S.; Mart \'i nez, T. J.; Bucksbaum, P. H. Control of 1,3-Cyclohexadiene Photoisomerization Using Light-Induced Conical Intersections. J. Phys. Chem. B 2012, 116, 2758--2763

2012
[152]

Photo-Induced 1,3-cyclohexadiene Ring Opening Reaction: Ab Initio On-the-Fly Nonadiabatic Molecular Dynamics Simulation

Lei, Y.; Wu, H.; Zhang, X.; Zhai, G.; Zhu, C. Photo-Induced 1,3-cyclohexadiene Ring Opening Reaction: Ab Initio On-the-Fly Nonadiabatic Molecular Dynamics Simulation. J. Photochem. Photobiol. A 2016, 317, 39--49

2016
[153]

P.; Budarz, J

Minitti, M. P.; Budarz, J. M.; Kirrander, A.; Robinson, J. S.; Ratner, D.; Lane, T. J.; Zhu, D.; Glownia, J. M.; Kozina, M.; Lemke, H. T.; Sikorski, M.; Feng, Y.; Nelson, S.; Saita, K.; Stankus, B.; Northey, T.; Hastings, J. B.; Weber, P. M. Imaging Molecular Motion: Femtoseco...

2015
[154]

R.; Bhattacherjee, A.; Pemmaraju, C

Attar, A. R.; Bhattacherjee, A.; Pemmaraju, C. D.; Schnorr, K.; Closser, K. D.; Prendergast, D.; Leone, S. R. Femtosecond X-Ray Spectroscopy of an Electrocyclic Ring-Opening Reaction. Science 2017, 356, 54--59

2017
[155]

Wolf, T. J. A.; Sanchez, D. M.; Yang, J.; Parrish, R. M.; Nunes, J. P. F.; Centurion, M.; Coffee, R.; Cryan, J. P.; G \"u hr, M.; Hegazy, K.; Kirrander, A.; Li, R. K.; Ruddock, J.; Shen, X.; Vecchione, T.; Weathersby, S. P.; Weber, P. M.; Wilkin, K.; Yong, H.; Zheng, Q.; Wang,...

2019
[156]

Direct Observation of Ground-State Product Formation in a 1,3-Cyclohexadiene Ring-Opening Reaction

Adachi, S.; Sato, M.; Suzuki, T. Direct Observation of Ground-State Product Formation in a 1,3-Cyclohexadiene Ring-Opening Reaction. J. Phys. Chem. Lett 2015, 6, 343--346

2015
[157]

A.; de Vivie-Riedle, R

Nenov, A.; K \"o lle, P.; Robb, M. A.; de Vivie-Riedle, R. Beyond the van der Lugt/Oosterhoff Model: When the Conical Intersection Seam and the S_1 Minimum Energy Path Do Not Cross. J. Org. Chem. 2010, 75, 123--129

2010
[158]

M.; Williams, C

Roberts, G. M.; Williams, C. A.; Yu, H.; Chatterley, A. S.; Young, J. D.; Ullrich, S.; Stavros, V. G. Probing Ultrafast Dynamics in Photoexcited Pyrrole: Timescales for ^1 ^* Mediated H-atom Elimination. Faraday Discuss. 2013, 163, 95--116

2013
[159]

Non-Adiabatic Dynamics of Pyrrole: Dependence of Deactivation Mechanisms on the Excitation Energy

Barbatti, M.; Pittner, J.; Pederzoli, M.; Werner, U.; Mitri \'c , R.; Bona c i \'c -Kouteck \'y , V.; Lischka, H. Non-Adiabatic Dynamics of Pyrrole: Dependence of Deactivation Mechanisms on the Excitation Energy. Chem. Phys. 2010, 375, 26--34

2010
[160]

Timescales of N--H Bond Dissociation in Pyrrole: A Nonadiabatic Dynamics Study

Sapunar, M.; Ponzin, A.; Chaiwongwattana, S.; Mali s , M.; Prlj, A.; Decleva, P.; Do s li \'c , N. Timescales of N--H Bond Dissociation in Pyrrole: A Nonadiabatic Dynamics Study. Phys. Chem. Chem. Phys. 2015, 17, 19012--19020

2015
[161]

Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory; McGraw-Hill: New York, 1989

1989
[162]

J.; Handy, N

Knowles, P. J.; Handy, N. C. A New Determinant-Based Full Configuration Interaction Method. Chem. Phys. Lett. 1984, 111, 315--321

1984
[163]

J.; Zarrabian, S

Harrison, R. J.; Zarrabian, S. An Efficient Implementation of the Full-CI Method Using an (n-2)-electron Projection Space. Chem. Phys. Lett. 1989, 158, 393 -- 398

1989
[164]

Siegbahn, P. E. M.; Heiberg, A.; Roos, B. O.; Levy, B. A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method. Physica Scripta 1980, 21, 323--327

1980
[165]

O.; Taylor, P

Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M. A Complete Active Space SCF Method (CASSCF) Using a Density Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48, 157--173

1980
[166]

Siegbahn, P. E. M.; Alml \"o f, J.; Heiberg, A.; Roos, B. O. The Complete Active Space SCF (CASSCF) Method in a Newton--Raphson Formulation with Application to the HNO Molecule. J. Chem. Phys. 1981, 74, 2384--2396

1981
[167]

A Quadratically Convergent MCSCF Method for the Simultaneous Optimizations of Several States

Werner, H.-J.; Meyer, W. A Quadratically Convergent MCSCF Method for the Simultaneous Optimizations of Several States. J. Chem. Phys. 1981, 74, 5794--5801

1981
[168]

K.; Hinze, J

Docken, K. K.; Hinze, J. LiH Potential Curves and Wavefunctions for X ^1 ^+ , A ^1 ^+ , B ^1 , ^3 ^+ , and ^3 ^* . J. Chem. Phys. 1972, 57, 4928--4936

1972
[169]

P.; Nesbitt, D

Deskevich, M. P.; Nesbitt, D. J.; Werner, H.-J. Dynamically Weighted Multiconfiguration Self-Consistent Field: Multistate Calculations for F + H_2 O HF + OH Reaction Paths. J. Chem. Phys. 2004, 120, 7281--7289

2004
[170]

Glover, W. J. Communication: Smoothing out Excited-State Dynamics: Analytical Gradients for Dynamically Weighted Complete Active Space Self-Consistent Field. J. Chem. Phys. 2014, 141, 171102

2014
[171]

Olsen, S. Canonical-Ensemble State-Averaged Complete Active Space Self-Consistent Field (SA-CASSCF) Strategy for Problems with More Diabatic than Adiabatic States: Charge-Bond Resonance in Monomethine Cyanines. J. Chem. Phys. 2015, 142, 044116

2015
[172]

O.; J rgensen, P.; Aa

Olsen, J.; Roos, B. O.; J rgensen, P.; Aa. Jensen , H. J. Determinant Based Configuration Interaction Algorithms for Complete and Restricted Configuration Interaction Spaces. J. Chem. Phys. 1988, 89, 2185--2192

1988
[173]

Malmqvist, P.- .; Rendell, A.; Roos, B. O. The Restricted Active Space Self-Consistent-Field Method, Implemented with a Split Graph Unitary Group Approach. J. Phys. Chem. 1990, 94, 5477--5482

1990
[174]

The Generalized Active Space Concept in Multiconfigurational Self-Consistent Field Methods

Ma, D.; Li Manni , G.; Gagliardi, L. The Generalized Active Space Concept in Multiconfigurational Self-Consistent Field Methods. J. Chem. Phys. 2011, 135, 044128

2011
[175]

G.; M \"u ller, T.; Gidofalvi, G.; Lischka, H.; Shepard, R

Szalay, P. G.; M \"u ller, T.; Gidofalvi, G.; Lischka, H.; Shepard, R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chem. Rev 2012, 112, 108--181

2012
[176]

J.; Peyerimhoff, S

Buenker, R. J.; Peyerimhoff, S. D. Individualized Configuration Selection in CI Calculations with Subsequent Energy Extrapolation. Theor. Chim. Act. 1974, 35, 33--58

1974
[177]

R.; Davidson, E

Langhoff, S. R.; Davidson, E. R. Configuration Interaction Calculations on the Nitrogen Molecule. Int. J. Quantum Chem. 1974, 8, 61--72

1974
[178]

Multireference Self-Consistent Size-Consistent Singles and Doubles Configuration Interaction for Ground and Excited States

Malrieu, J.-P.; Daudey, J.-P.; Caballol, R. Multireference Self-Consistent Size-Consistent Singles and Doubles Configuration Interaction for Ground and Excited States. J. Chem. Phys. 1994, 101, 8908--8921

1994
[179]

Size-Consistent Self-Consistent Truncated or Selected Configuration Interaction

Daudey, J.-P.; Heully, J.-L.; Malrieu, J.-P. Size-Consistent Self-Consistent Truncated or Selected Configuration Interaction. J. Chem. Phys 1993, 99, 1240--1254

1993
[180]

State-Specific Coupled Cluster-Type Dressing of Multireference Singles and Doubles Configuration Interaction Matrix

Meller, J.; Malrieu, J.-P.; Caballol, R. State-Specific Coupled Cluster-Type Dressing of Multireference Singles and Doubles Configuration Interaction Matrix. J. Chem. Phys. 1996, 104, 4068--4076

1996
[181]

Multireference Self-Consistent Size-Extensive State-Selective Configuration Interaction

Adamowicz, L.; Malrieu, J.-P. Multireference Self-Consistent Size-Extensive State-Selective Configuration Interaction. J. Chem. Phys. 1996, 105, 9240--9247

1996
[182]

Size-Consistent Multireference Configuration Interaction Method Through the Dressing of the Norm of Determinants

Meller, J.; Malrieu, J.-P.; Heully, J.-L. Size-Consistent Multireference Configuration Interaction Method Through the Dressing of the Norm of Determinants. Mol. Phys. 2003, 101, 2029--2041

2003
[183]

J.; Ahlrichs, R

Gdanitz, R. J.; Ahlrichs, R. The Averaged Coupled-Pair Functional (ACPF): A Size-Extensive Modification of MR-CI(SD). Chem. Phys. Lett. 1988, 143, 413--420

1988
[184]

Gdanitz, R. J. A New Version of the Multireference Averaged Coupled-Pair Functional (MR-ACPF-2). Int. J. Quantum Chem. 2001, 85, 281--300

2001
[185]

G.; Bartlett, R

Szalay, P. G.; Bartlett, R. J. Multi-reference Averaged Quadratic Coupled-Cluster Method: A Size-Extensive Modification of Multi-reference CI. Chem. Phys. Lett. 1993, 214, 481--488

1993
[186]

G.; Bartlett, R

Szalay, P. G.; Bartlett, R. J. Approximately Extensive Modifications of the Multireference Configuration Interaction Method: A Theoretical and Practical Analysis. J. Chem. Phys. 1995, 103, 3600--3612

1995
[187]

In Methods of Electronic Structure Theory; Schaefer, III , H

Meyer, W. In Methods of Electronic Structure Theory; Schaefer, III , H. F., Ed.; Springer: Boston, MA, 1977; Vol. 3; pp 413--446

1977
[188]

The Self-Consistent Electron Pairs Method for Multiconfigurational Reference State Functions

Werner, H.-J.; Reinsch, E.-A. The Self-Consistent Electron Pairs Method for Multiconfigurational Reference State Functions. J. Chem. Phys. 1982, 76, 3144--3156

1982
[189]

Werner, H.-J.; Knowles, P. J. An Efficient Internally Contracted Multiconfiguration-Reference Configuration Interaction Method. J. Chem. Phys. 1988, 89, 5803--5814

1988
[190]

Multi-state Multireference Rayleigh–Schr \"o dinger Perturbation Theory for Mixed Electronic States: Second and Third Order

Shavitt, I. Multi-state Multireference Rayleigh–Schr \"o dinger Perturbation Theory for Mixed Electronic States: Second and Third Order. Int. J. Mol. Sci. 2002, 3, 639--655

2002
[191]

Matrix-Formulated Direct Multiconfiguration Self-Consistent Field and Multiconfiguration Reference Configuration-Interaction Methods

Werner, H.-J. Matrix-Formulated Direct Multiconfiguration Self-Consistent Field and Multiconfiguration Reference Configuration-Interaction Methods. Adv. Chem. Phys. 1987, 49, 1--62

1987
[192]

A.; Kendall, R

Peterson, K. A.; Kendall, R. A.; Dunning, Jr. , T. H. Benchmark Calculations with Correlated Molecular Wave Functions. II. Configuration Interaction Calculations on First Row Diatomic Hydrides. J. Chem. Phys. 1993, 99, 1930--1944

1993
[193]

A.; Kendall, R

Peterson, K. A.; Kendall, R. A.; Dunning, Jr. , T. H. Benchmark Calculations with Correlated Molecular Wave Functions. III. Configuration Interaction Calculations on First Row Homonuclear Diatomics. J. Chem. Phys. 1993, 99, 9790--9805

1993
[194]

A Comparison of Various Approaches in Internally Contracted Multireference Configuration Interaction: the Carbon Dimer as a Test Case

Angeli, C.; Cimiraglia, R.; Pastore, M. A Comparison of Various Approaches in Internally Contracted Multireference Configuration Interaction: the Carbon Dimer as a Test Case. Mol. Phys. 2012, 110, 2963--2968

2012
[195]

J.; Szalewicz, K.; Zabolitzky, J

Jeziorski, B.; Monkhorst, H. J.; Szalewicz, K.; Zabolitzky, J. G. J.\ Chem.\ Phys. 1984, 81, 368

1984
[196]

Multireference Brillouin--Wigner Coupled-Cluster Theory

M \'a s ik, J.; Huba c , I. Multireference Brillouin--Wigner Coupled-Cluster Theory. Single-Root Approach. Adv. Quantum Chem. 1998, 31, 75--104

1998
[197]

Single-Root Multireference Brillouin--Wigner Coupled-Cluster Theory: Applicability to the F_2 Molecule

M \'a s ik, J.; Huba c , I.; Mach, P. Single-Root Multireference Brillouin--Wigner Coupled-Cluster Theory: Applicability to the F_2 Molecule. J. Chem. Phys. 1998, 108, 6571--6579

1998
[198]

S.; Datta, B.; Mukherjee, D

Mahapatra, U. S.; Datta, B.; Mukherjee, D. A Size-Consistent State-Specific Multireference Coupled Cluster Theory: Formal Developments and Molecular Applications. J. Chem. Phys. 1999, 110, 6171--6188

1999
[199]

Connection Between a Few Jeziorski--Monkhorst Ansatz-Based Methods

Kong, L. Connection Between a Few Jeziorski--Monkhorst Ansatz-Based Methods. Int. J. Quantum Chem. 2009, 109, 441--447

2009
[200]

A.; Gauss, J

Evangelista, F. A.; Gauss, J. An Orbital-Invariant Internally Contracted Multireference Coupled Cluster Approach. J. Chem. Phys. 2011, 134, 114102

2011
[201]

Pilot Applications of Internally Contracted Multireference Coupled Cluster Theory, and How to Choose the Cluster Operator Properly

Hanauer, M.; K\"ohn , A. Pilot Applications of Internally Contracted Multireference Coupled Cluster Theory, and How to Choose the Cluster Operator Properly. J. Chem. Phys. 2011, 134, 204111

2011
[202]

A Perspective on the CASPT2 Method

Pulay, P. A Perspective on the CASPT2 Method. Int. J. Quantum Chem. 2011, 111, 3273--3279

2011
[203]

B.; Messmer, R

Murphy, R. B.; Messmer, R. P. Generalized M ller--Plesset Perturbation Theory Applied to General MCSCF Reference Wave Functions. Chem. Phys. Lett. 1991, 183, 443--448

1991
[204]

B.; Messmer, R

Murphy, R. B.; Messmer, R. P. Generalized M ller--Plesset Perturbation Theory Applied to Multiply Bonded Molecules. J. Chem. Phys. 1992, 97, 4170--4185

1992
[205]

M.; Davidson, E

Kozlowski, P. M.; Davidson, E. R. Considerations in Constructing a Multireference Second-Order Perturbation Theory. J. Chem. Phys. 1994, 100, 3672--3682

1994
[206]

Multireference M ller--Plesset Method

Hirao, K. Multireference M ller--Plesset Method. Chem. Phys. Lett. 1992, 190, 374--380

1992
[207]

Multireference M ller--Plesset Perturbation Theory for High-Spin Open-Shell Systems

Hirao, K. Multireference M ller--Plesset Perturbation Theory for High-Spin Open-Shell Systems. Chem. Phys. Lett. 1992, 196, 397--403

1992
[208]

State-Specific Multireference M ller--Plesset Perturbation Treatment for Singlet and Triplet Excited States, Ionized States and Electron Attached States of H_2O

Hirao, K. State-Specific Multireference M ller--Plesset Perturbation Treatment for Singlet and Triplet Excited States, Ionized States and Electron Attached States of H_2O . Chem. Phys. Lett. 1993, 201, 59--66

1993
[209]

Introduction of n -electron Valence States for Multireference Perturbation Theory

Angeli, C.; Cimiraglia, R.; Evangelisti, S.; Leininger, T.; Malrieu, J.-P. Introduction of n -electron Valence States for Multireference Perturbation Theory. J. Chem. Phys. 2001, 114, 10252--10264

2001
[210]

n -electron Valence State Perturbation Theory: A Spinless Formulation and an Efficient Implementation of the Strongly Contracted and of the Partially Contracted Variants

Angeli, C.; Cimiraglia, R.; Malrieu, J.-P. n -electron Valence State Perturbation Theory: A Spinless Formulation and an Efficient Implementation of the Strongly Contracted and of the Partially Contracted Variants. J. Chem. Phys. 2002, 117, 9138--9153

2002
[211]

O.; Linse, P.; Siegbahn, P

Roos, B. O.; Linse, P.; Siegbahn, P. E. M.; Blomberg, M. R. A. A Simple Method for the Evaluation of the Second-Order-Perturbation Energy from External Double-Excitations with a CASSCF Reference Wavefunction. Chem. Phys. 1982, 66, 197--207

1982
[212]

L.; Pulay, P

Wolinski, K.; Sellers, H. L.; Pulay, P. Consistent Generalization of the M ller--Plesset Partitioning to Open-Shell and Multiconfigurational SCF Reference States in Many-Body Perturbation Theory. Chem. Phys. Lett. 1987, 140, 225--231

1987
[213]

Generalized M ller--Plesset Perturbation Theory: Second Order Results for Two-Configuration, Open-Shell Excited Singlet, and Doublet Wave Functions

Wolinski, K.; Pulay, P. Generalized M ller--Plesset Perturbation Theory: Second Order Results for Two-Configuration, Open-Shell Excited Singlet, and Doublet Wave Functions. J. Chem. Phys. 1989, 90, 3647--3659

1989
[214]

O.; Sadlej, A

Andersson, K.; Malmqvist, P.- .; Roos, B. O.; Sadlej, A. J.; Wolinski, K. Second-Order Perturbation Theory with a CASSCF Reference Function. J. Phys. Chem. 1990, 94, 5483--5488

1990
[215]

Dyall, K. G. The Choice of a Zeroth-Order Hamiltonian for Second-Order Perturbation Theory with a Complete Active Space Self-Consistent-Field Reference Function. J. Chem. Phys. 1995, 102, 4909--4918

1995
[216]

A.; Neese, F

Sivalingam, K.; Krupicka, M.; Auer, A. A.; Neese, F. Comparison of Fully Internally and Strongly Contracted Multireference Configuration Interaction Procedures. J. Chem. Phys. 2016, 145, 054104

2016
[217]

Third-Order Multireference Perturbation Theory --- The CASPT3 Method

Werner, H.-J. Third-Order Multireference Perturbation Theory --- The CASPT3 Method. Mol. Phys. 1996, 89, 645

1996
[218]

O.; Serrano-Andr \' e s , L

Finley, J.; Malmqvist, P.- .; Roos, B. O.; Serrano-Andr \' e s , L. The Multi-State CASPT2 Method. Chem. Phys. Lett. 1998, 288, 299--306

1998
[219]

A Quasidegenerate Formulation of the Second Order n -electron Valence State Perturbation Theory Approach

Angeli, C.; Borini, S.; Cestari, M.; Cimiraglia, R. A Quasidegenerate Formulation of the Second Order n -electron Valence State Perturbation Theory Approach. J. Chem. Phys. 2004, 121, 4043--4050

2004
[220]

Multi-Partitioning Quasidegenerate Perturbation Theory

Zaitsevskii, A.; Malrieu, J.-P. Multi-Partitioning Quasidegenerate Perturbation Theory. A New Approach to Multireference M ller--Plesset Perturbation Theory. Chem. Phys. Lett 1995, 233, 597--604

1995
[221]

O.; Andersson, K

Roos, B. O.; Andersson, K. Multiconfigurational Perturbation Theory with Level Shift --- The Cr _2 Potential Revisited. Chem. Phys. Lett. 1995, 245, 215--223

1995
[222]

Multiconfiguration Perturbation Theory with Imaginary Level Shift

Forsberg, N.; Malmqvist, P.- . Multiconfiguration Perturbation Theory with Imaginary Level Shift. Chem. Phys. Lett 1997, 274, 196--204

1997
[223]

A.; Choe, Y.-K.; Finley, J

Witek, H. A.; Choe, Y.-K.; Finley, J. P.; Hirao, K. Intruder State Avoidance Multireference M ller--Plesset Perturbation Theory. J. Comput. Chem. 2002, 23, 957--965

2002
[224]

O.; Malmqvist, P.-

Ghigo, G.; Roos, B. O.; Malmqvist, P.- . A Modified Definition of the Zeroth-Order Hamiltonian in Multiconfigurational Perturbation Theory (CASPT2). Chem. Phys. Lett. 2004, 396, 142

2004
[225]

Different Forms of the Zeroth-Order Hamiltonian in Second-Order Perturbation Theory with a Complete Active Space Self-Consistent Field Reference Function

Andersson, K. Different Forms of the Zeroth-Order Hamiltonian in Second-Order Perturbation Theory with a Complete Active Space Self-Consistent Field Reference Function. Theor. Chim. Acta. 1995, 91, 31--46

1995
[226]

What Zeroth-Order Hamiltonian for CASPT2 Adiabatic Energetics of Fe(II) N_6 Architectures? J

Kepenekian, M.; Robert, V.; Le Guennic , B. What Zeroth-Order Hamiltonian for CASPT2 Adiabatic Energetics of Fe(II) N_6 Architectures? J. Chem. Phys. 2009, 131, 114702

2009
[227]

Rudavskyi, A.; Sousa, C.; de Graaf , C.; Havenith, R. W. A.; Broer, R. Computational Approach to the Study of Thermal Spin Crossover Phenomena. J. Chem. Phys. 2014, 140, 184318

2014
[228]

Energetics of [Fe(NCH)_6]^ 2+ via CASPT2 calculations: A Spin-Crossover Perspective

Kepenekian, M.; Robert, V.; Le Guennic , B.; De Graaf , C. Energetics of [Fe(NCH)_6]^ 2+ via CASPT2 calculations: A Spin-Crossover Perspective. J. Comput. Chem. 2009, 30, 2327--2333

2009
[229]

Light-Induced Excited Spin State Trapping: Ab Initio Study of the Physics at the Molecular Level

Suaud, N.; Bonnet, M.-L.; Boilleau, C.; Lab \`e guerie, P.; Guih \'e ry, N. Light-Induced Excited Spin State Trapping: Ab Initio Study of the Physics at the Molecular Level. J. Am. Chem. Soc. 2009, 131, 715--722

2009
[230]

On the Zeroth-Order Hamiltonian for CASPT2 Calculations of Spin Crossover Compounds

Vela, S.; Fumanal, M.; Ribas-Ari \ n o, J.; Robert, V. On the Zeroth-Order Hamiltonian for CASPT2 Calculations of Spin Crossover Compounds. J. Comput. Chem. 2016, 37, 947--953

2016
[231]

M.; Aquilante, F.; Robinson, T

Lawson Daku , L. M.; Aquilante, F.; Robinson, T. W.; Hauser, A. Accurate Spin-State Energetics of Transition Metal Complexes. 1. CCSD(T), CASPT2, and DFT Study of [M(NCH)_6]^ 2+ (M = Fe, Co). J. Chem. Theory Comput. 2012, 8, 4216--4231

2012
[232]

P.; Nogueira, J

Zobel, J. P.; Nogueira, J. J.; Gonz \'a lez, L. The IPEA dilemma in CASPT2. Chem. Sci. 2017, 8, 1482--1499

2017
[233]

Analytical Derivatives, Forces, Force Constants, Molecular Geometries, and Related Response Properties in Electronic Structure Theory

Pulay, P. Analytical Derivatives, Forces, Force Constants, Molecular Geometries, and Related Response Properties in Electronic Structure Theory. WIREs Comput. Mol. Sci. 2014, 4, 169--181

2014
[234]

Einf \"u rung in die Quantanchemie ; Deuticke: Leipzig and Vienna, 1937; pp 285--286

Hellmann, H. Einf \"u rung in die Quantanchemie ; Deuticke: Leipzig and Vienna, 1937; pp 285--286

1937
[235]

Feynman, R. P. Forces in Molecules. Chem. Rev. 1939, 56, 340--343

1939
[236]

McIver Jr. , J. W.; Komornicki, A. Rapid Geometry Optimization for Semi-Empirical Molecular Orbital Methods. Chem. Phys. Lett. 1971, 10, 303--306

1971
[237]

A.; Krishnan, R.; Schlegel, H

Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Derivative Studies in Hartree--Fock and M ller--Plesset Theories. Int. J. Quantum Chem. Symp. 1979, 13, 225--241

1979
[238]

R.; Laidig, W

Brooks, B. R.; Laidig, W. D.; Saxe, P.; Goddard, J. D.; Yamaguchi, Y.; Schaefer III , H. F. Analytic Gradients from Correlated Wave Functions Via the Two?Particle Density Matrix and the Unitary Group Approach. J. Chem. Phys. 1980, 72, 4652--4653

1980
[239]

Some Recent Advances in Density Matrix Theory

McWeeny, R. Some Recent Advances in Density Matrix Theory. Rev. Mod. Phys. 1960, 32, 335--369

1960
[240]

Perturbation Theory for the Fock--Dirac Density Matrix

McWeeny, R. Perturbation Theory for the Fock--Dirac Density Matrix. Phys. Rev. 1962, 126, 1028--1034

1962
[241]

M.; Pitzer, R

Stevens, R. M.; Pitzer, R. M.; Lipscomb, W. N. Perturbed Hartree--Fock Calculations. I. Magnetic Susceptibility and Shielding in the LiH Molecule. J. Chem. Phys. 1963, 38, 550--560

1963
[242]

C.; Karplus, M

Caves, T. C.; Karplus, M. Perturbed Hartree--Fock Theory. I. Diagrammatic Double-Perturbation Analysis. J. Chem. Phys. 1969, 50, 3649--3661

1969
[243]

B.; Pople, J

Krishnan, R.; Schlegel, H. B.; Pople, J. A. Derivative Studies in Configuration-Interaction Theory. J. Chem. Phys. 1980, 72, 4654--4656

1980
[244]

C.; Schaefer, H

Handy, N. C.; Schaefer, H. F. On the Evaluation of Analytic Energy Derivatives for Correlated Wave Functions. J. Chem. Phys. 1984, 81, 5031--5033

1984
[245]

Orbital-Invariant Formulation and Second-Order Gradient Evaluation in M ller--Plesset Perturbation Theory

Pulay, P.; Saeb , S. Orbital-Invariant Formulation and Second-Order Gradient Evaluation in M ller--Plesset Perturbation Theory. Theor. Chim. Acta. 1986, 69, 357--368

1986
[246]

C.; Amos, R

Handy, N. C.; Amos, R. D.; Gaw, J. F.; Rice, J. E.; Simandiras, E. D. The Elimination of Singularities in Derivative Calculations. Chem. Phys. Lett. 1985, 120, 151--158

1985
[247]

D.; Bartlett, R

Adamowicz, L.; Laidig, W. D.; Bartlett, R. J. Analytical Gradient for the Coupled-Cluster Method. Int. J. Quantum Chem. Symp. 1984, 18, 245--254

1984
[248]

R.; Simons, J

Hoffmann, M. R.; Simons, J. Analytical Energy Gradients for a Unitary Coupled-Cluster Theory. Chem. Phys. Lett. 1987, 142, 451--454

1987
[249]

E.; Scheiner, A

Scuseria, G. E.; Scheiner, A. C.; Rice, J. E.; Lee, T. J.; Schaefer, III , H. F. Analytical Evaluation of Energy Gradients for the Single and Double Excitation Coupled Cluster (CCSD) Wave Function: A Comparison with Configuration Interaction (CISD, CISDT, CISDTQ) Results for t...

1987
[250]

E.; Amos, R

Rice, J. E.; Amos, R. D. On the Efficient Evaluation of Analytic Energy Gradients. Chem. Phys. Lett. 1985, 122, 585--590

1985
[251]

A.; Trucks, G

Salter, E. A.; Trucks, G. W.; Fitzgerald, G.; Bartlett, R. J. Theory and Application of MBPT(3) Gradients: The Density Approach. Chem. Phys. Lett. 1987, 141, 61--70

1987
[252]

J.; Head-Gordon, M.; Pople, J

Frisch, M. J.; Head-Gordon, M.; Pople, J. A. A Direct MP2 Gradient Method. Chem. Phys. Lett. 1990, 166, 275--280

1990
[253]

F.; Gauss, J

Stanton, J. F.; Gauss, J. Analytic Second Derivatives in High-Order Many-Body Perturbation and Coupled-Cluster Theories: Computational Considerations and Applications. Int. Rev. Phys. Chem. 2000, 19, 61--95

2000
[254]

In Modern Electronic Structure Theory; Yarkony, D

Pulay, P. In Modern Electronic Structure Theory; Yarkony, D. R., Ed.; World Scientific: Singapore, 1995; Vol. 2; pp 1191--1240

1995
[255]

Energy Derivatives for Configuration Interaction Wave Functions

Dupuis, M. Energy Derivatives for Configuration Interaction Wave Functions. J. Chem. Phys. 1981, 74, 5758--5765

1981
[256]

Kumanova, M. D. First and Second Derivatives of the Eigenvalues of the Hamiltonian. Mol. Phys. 1972, 23, 407--412

1972
[257]

Granovsky, A. A. An Efficient Approach to Compute State-Specific Nuclear Gradient for a Generic State-Averaged Multi-Configuration Self Consistent Field Wavefunction,. J. Chem. Phys. 2015, 143, 231101

2015
[258]

H., III; Yarkony, D

Lengsfield, B. H., III; Yarkony, D. R. Nonadiabatic Interactions Between Potential Energy Surfaces: Theory and Applications. Adv. Chem. Phys. 1992, 82, 1--71

1992
[259]

F.; Delcey, M

Galvan, I. F.; Delcey, M. G.; Pedersen, T. B.; Aquilante, F.; Lindh, R. Analytical State-Average Complete-Active-Space Self-Consistent Field Nonadiabatic Coupling Vectors: Implementation with Density-Fitted Two-Electron Integrals and Application to Conical Intersections. J. Ch...

2016
[260]

Density-Matrix Representation of Nonadiabatic Couplings in Time-Dependent Density Functional (TDDFT) Theories

Chernyak, V.; Mukamel, S. Density-Matrix Representation of Nonadiabatic Couplings in Time-Dependent Density Functional (TDDFT) Theories. J. Chem. Phys. 2000, 112, 3572--3579

2000
[261]

R.; Yarkony, D

Manaa, M. R.; Yarkony, D. R. On the Intersection of Two Potential Energy Surfaces of the Same Symmetry. Systematic Characterization Using a Lagrange Multiplier Constrained Procedure. J. Chem. Phys. 1993, 99, 5251--5256

1993
[262]

Toniolo, A.; Ben-Nun, M.; Mart\'inez , T. J. Optimization of Conical Intersections with Floating Occupation Semiempirical Configuration Interaction Wave Functions. J. Phys. Chem. A 2002, 106, 4679--4689

2002
[263]

Toniolo, A.; Granucci, G.; Mart\' i nez , T. J. Conical Intersections in Solution: A QM/MM Study Using Floating Occupation Semiempirical Configuration Interaction Wave Functions. J. Phys. Chem. A 2003, 107, 3822--3830

2003
[264]

W.; Thiel, W

Fabiano, E.; Keal, T. W.; Thiel, W. Implementation of Surface Hopping Molecular Dynamics Using Semiempirical Methods. Chem. Phys. 2008, 349, 334--347

2008
[265]

Snyder, Jr. , J. W.; Hohenstein, E. G.; Luehr, N.; Mart \'i nez, T. J. An Atomic-Orbital Based Formulation of Analytical Gradients and Nonadiabatic Coupling Vector Elements for the State-Averaged Complete Active Space Self-Consistent Field Method on Graphical Processing Units....

2015
[266]

Snyder, Jr. , J. W.; Fales, B. S.; Hohenstein, E. G.; Levine, B. G.; Mart \'i nez, T. J. A Direct-Compatible Formulation of the Coupled Perturbed Complete Active Space Self-Consistent Field Equations on Graphical Processing Units. J. Chem. Phys. 2017, 146, 174113

2017
[267]

Second and Third Derivatives of Variational Energy Expressions: Application to Multiconfigurational Self-Consistent Field Wave Functions

Pulay, P. Second and Third Derivatives of Variational Energy Expressions: Application to Multiconfigurational Self-Consistent Field Wave Functions. J. Chem. Phys. 1983, 78, 5043--5051

1983
[268]

F.; Komornicki, A

King, H. F.; Komornicki, A. Analytic Computation of Energy Derivatives. Relationships Among Partial Derivatives of a Variationally Determined Function. J. Chem. Phys. 1986, 84, 5645--5650

1986
[269]

Jensen , H

Koch, H.; Aa. Jensen , H. J.; J rgensen, P.; Helgaker, T.; Scuseria, G. E.; Schaefer III , H. F. Coupled Cluster Energy Derivatives. Analytic Hessian for the Closed-Shell Coupled Cluster Singles and Doubles Wave Function: Theory and Applications. J. Chem. Phys. 1990, 92, 4924--4940

1990
[270]

M ller--Plesset Energy Derivatives

J rgensen, P.; Helgaker, T. M ller--Plesset Energy Derivatives. J. Chem. Phys. 1988, 89, 1560--1570

1988
[271]

H.; Yarkony, D

Saxe, P.; Lengfield III , B. H.; Yarkony, D. R. On the Evaluation of Non-Adiabatic Coupling Matrix Elements for Large Scale CI Wavefunctions. Chem. Phys. Lett. 1985, 113, 159--164

1985
[272]

G.; Theis, D.; Hoffmann, M

Khait, Y. G.; Theis, D.; Hoffmann, M. R. Lagrangian Approach for Geometrical Derivatives and Nonadiabatic Coupling Terms in MRCISD. Mol. Phys. 2010, 108, 2703--2716

2010
[273]

Analytic First-Order Derivatives of Partially Contracted n-electron Valence State Second-Order Perturbation Theory (PC-NEVPT2)

Nishimoto, Y. Analytic First-Order Derivatives of Partially Contracted n-electron Valence State Second-Order Perturbation Theory (PC-NEVPT2). 2019,

2019
[274]

Park, J. W. Analytical Gradient Theory for Strongly Contracted (SC-) and Partially Contracted (PC-) N-Electron Valence State Perturbation Theory (NEVPT2). 2019,

2019
[275]

Symbolic Algebra in Quantum Chemistry

Hirata, S. Symbolic Algebra in Quantum Chemistry. Theor. Chem. Acc. 2006, 116, 2

2006
[276]

K\'allay , M.; Surj\'an , P. R. Higher Excitations in Coupled-Cluster Theory. J.\ Chem.\ Phys. 2001, 115, 2945

2001
[277]

Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories

Hirata, S. Tensor Contraction Engine: Abstraction and Automated Parallel Implementation of Configuration-Interaction, Coupled-Cluster, and Many-Body Perturbation Theories. J.\ Phys.\ Chem.\ A 2003, 107, 9887

2003
[278]

Higher-Order Equation-of-Motion Coupled-Cluster Methods

Hirata, S. Higher-Order Equation-of-Motion Coupled-Cluster Methods. J.\ Chem.\ Phys. 2004, 121, 51--59

2004
[279]

An Efficient Matrix-Matrix Multiplication Based Antisymmetric Tensor Contraction Engine for General Order Coupled Cluster

Hanrath, M.; Engels-Putzka, A. An Efficient Matrix-Matrix Multiplication Based Antisymmetric Tensor Contraction Engine for General Order Coupled Cluster. J. Chem. Phys. 2010 , 133 , 064108

2010
[280]

A Fully Simultaneously Optimizing Genetic Approach to the Highly Excited Coupled-Cluster Factorization Problem

Engels-Putzka, A.; Hanrath, M. A Fully Simultaneously Optimizing Genetic Approach to the Highly Excited Coupled-Cluster Factorization Problem. J. Chem. Phys. 2011 , 134 , 124106

2011
[281]

Shiozaki, T.; Kamiya, M.; Hirata, S.; Valeev, E. F. Phys.\ Chem.\ Chem.\ Phys. 2008, 10, 3358

2008
[282]

Shiozaki, T.; Kamiya, M.; Hirata, S.; Valeev, E. F. Explicitly Correlated Coupled-Cluster Singles and Doubles Method Based on Complete Diagrammatic Equations. J.\ Chem.\ Phys. 2008, 129, 071101

2008
[283]

W.; Tew, D

K\"ohn , A.; Richings, G. W.; Tew, D. P. Implementation of the Full Explicitly Correlated Coupled-Cluster Singles and Doubles Model CCSD-F12 with Optimally Reduced Auxiliary Basis Dependence. J. Chem. Phys. 2008, 129, 201103

2008
[284]

Shiozaki, T.; Kamiya, M.; Hirata, S.; Valeev, E. F. Higher-Order Explicitly Correlated Coupled-Cluster Methods. J.\ Chem.\ Phys. 2009, 130, 054101

2009
[285]

S.; K\'allay , M.; Visscher, L

Nataraj, H. S.; K\'allay , M.; Visscher, L. General Implementation of the Relativistic Coupled-Cluster Method. J. Chem. Phys. 2010, 133, 234109

2010
[286]

A General-Order Local Coupled-Cluster Method Based on the Cluster-in-Molecule Approach

Rolik, Z.; K\'allay , M. A General-Order Local Coupled-Cluster Method Based on the Cluster-in-Molecule Approach. J. Chem. Phys. 2011, 135, 104111

2011
[287]

Kats, D.; Manby, F. R. Sparse Tensor Framework for Implementation of General Local Correlation Methods. J. Chem. Phys. 2013, 138, 144101

2013
[288]

A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches

Datta, D.; Gauss, J. A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches. J. Chem. Theory Comput. 2013, 9, 2639--2653

2013
[289]

Analytic First Derivatives for a Spin-Adapted Open-Shell Coupled Cluster Theory: Evaluation of First-Order Electrical Properties

Datta, D.; Gauss, J. Analytic First Derivatives for a Spin-Adapted Open-Shell Coupled Cluster Theory: Evaluation of First-Order Electrical Properties. J. Chem. Phys. 2014, 141, 104102

2014
[290]

Wladyslawski, M.; Nooijen, M. Analytical Energy Gradients for Excited-State Coupled-Cluster Methods: Automated Algebraic Derivation of First Derivatives for Equation-of-Motion Coupled-Cluster and Similarity Transformed Equation-of-Motion Coupled-Cluster Theories. Adv. Quantum ...

2005
[291]

Neuscamman, E.; Yanai, T.; Chan, G. K.-L. Quadratic Canonical Transformation Theory and Higher Order Density Matrices. J. Chem. Phys. 2009, 130, 124102

2009
[292]

A.; Lawler, K.; Head-Gordon, M

Parkhill, J. A.; Lawler, K.; Head-Gordon, M. The Perfect Quadruples Model for Electron Correlation in a Valence Active Space. J. Chem. Phys. 2009, 130, 084101

2009
[293]

A.; Head-Gordon, M

Parkhill, J. A.; Head-Gordon, M. A Sparse Framework for the Derivation and Implementation of Fermion Algebra. Mol. Phys. 2010, 108, 513--522

2010
[294]

Multireference Configuration Interaction Theory Using Cumulant Reconstruction with Internal Contraction of Density Matrix Renormalization Group Wave Function

Saitow, M.; Kurashige, Y.; Yanai, T. Multireference Configuration Interaction Theory Using Cumulant Reconstruction with Internal Contraction of Density Matrix Renormalization Group Wave Function. J. Chem. Phys. 2013, 139, 044118

2013
[295]

Song, C.; Wang, L.-P.; Mart\'inez, T. J. Automated Code Engine for Graphical Processing Units: Application to the Effective Core Potential Integrals and Gradients. J. Chem. Theory Comput. 2016, 12, 92--106

2016
[296]

Liu, F.; Filatov, M.; Mart \'i nez, T. J. Analytical Derivatives of the Individual State Energies in Ensemble Density Functional Theory Method: II. Implementation on Graphical Processing Units (GPUs). 2019,

2019
[297]

Configuration-Interaction Energy Derivatives in a Fully Variational Formulation

Helgaker, T.; J rgensen, P. Configuration-Interaction Energy Derivatives in a Fully Variational Formulation. Theor. Chim. Acta 1989, 75, 111--127

1989
[298]

G.; Hoffmann, M

Theis, D.; Khait, Y. G.; Hoffmann, M. R. GVVPT2 Energy Gradient Using a Lagrangian Formulation. J. Chem. Phys. 2011, 135, 044117

2011
[299]

G.; Theis, D.; Hoffmann, M

Khait, Y. G.; Theis, D.; Hoffmann, M. R. Nonadiabatic Coupling Terms for the GVVPT2 Variant of Multireference Perturbation Theory. Chem. Phys. 2012, 401, 88--94

2012
[300]

Analytical Gradient for the Multireference Brillouin--Wigner Coupled Cluster Method and for the State-Universal Multireference Coupled Cluster Method

Pittner, J.; S mydke, J. Analytical Gradient for the Multireference Brillouin--Wigner Coupled Cluster Method and for the State-Universal Multireference Coupled Cluster Method. J. Chem. Phys. 2007, 127, 114103

2007

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

S., Hiberty, P

Shaik, S. S., Hiberty, P. C., Eds. A Chemist's Guide to Valence Bond Theory; Wiley-Interscience: Hoboken, NJ, 2007

2007

[2] [2]

Bally, T.; Borden, W. T. In Reviews in Reviews in Computational Chemistry, Vol. 13; Lipkowitz, K. B., Boyd, D. B., Eds.; John Wiley & Sons, 1999

1999

[3] [3]

Borden, W. T. In The Foundations of Physical Organic Chemistry: Fifty Years of the James Flack Norris Award; Mainz, E. T. S. V. V., Ed.; American Chemical Society, 2015; Chapter 11

2015

[4] [4]

Singly Occupied MOs in Mono- and Diradical Conjugated Hydrocarbons: Comparison between Variational Single-Reference, -Fully Correlated and H \"u ckel Descriptions

Suaud, N.; Ruamps, R.; Malrieu, J.-P.; Guih \'e ry, N. Singly Occupied MOs in Mono- and Diradical Conjugated Hydrocarbons: Comparison between Variational Single-Reference, -Fully Correlated and H \"u ckel Descriptions. J. Phys. Chem. A 2014, 118, 5876--5884

2014

[5] [5]

Kekul \'e versus Lewis: When Aromaticity Prevents Electron Pairing and Imposes Polyradical Character

Trinquier, G.; Malrieu, J.-P. Kekul \'e versus Lewis: When Aromaticity Prevents Electron Pairing and Imposes Polyradical Character. Chem. Eur. J. 2015, 21, 814--828

2015

[6] [6]

Lischka, H.; Nachtigallov \'a , D.; Aquino, A. J. A.; Szalay, P. G.; Plasser, F.; Machado, F. B. C.; Barbatti, M. Multireference Approaches for Excited States of Molecules. Chem. Rev. 2018, 118, 7293--7361

2018

[7] [7]

Le calcul non empirique des constantes de force et des d \'e riv \'e es du moment dipolaire

Brato z , S. Le calcul non empirique des constantes de force et des d \'e riv \'e es du moment dipolaire. Colloq. Int. C.N.R.S. 1958, 82, 287--301

1958

[8] [8]

Gerratt, J.; Mills, I. M. Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree--Fock Calculations. I. J. Chem. Phys. 1968, 49, 1719--1730

1968