CP2K: An electronic structure and molecular dynamics software package - Dynamics, Transport, and Spectroscopic Response

Anna-Sophia Hehn; Augustin Bussy; Beliz Sertcan G\"okmen; Benjamin Stamm; Bibek Samal; Chao Zhang; Christian S. Ahart; Christoph Schran; Clotilde S. Cucinotta; Dominik Marx

REVIEW 3 major objections 4 minor 300 references

CP2K: An electronic structure and molecular dynamics software package - Dynamics, Transport, and Spectroscopic Response

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read CP2K's modular perturbation–response machinery lets a single electronic-structure representation feed static response, thermal sampling, real-time propagation, and open-boundary transport alike.

desk verdict A solid, useful developer-side review that maps CP2K's finite-temperature spectroscopy and transport methods; two real soft spots—the in-sample alpha-COHSEX fit and the unverified GW supercell decay assumption—keep it from being as definitive as it claims. read the letter →

arxiv 2607.22916 v2 pith:VHLALAGK submitted 2026-07-24 physics.chem-ph cond-mat.dis-nncond-mat.mtrl-scicond-mat.stat-mechphysics.comp-ph

Jan Wilhelm , Anna-Sophia Hehn , Hossam Elgabarty , Beliz Sertcan Gökmen , Maximilian Graml , Stepan Marek , Ritaj Tyagi , Frederick Stein

show 34 more authors

Johann V. Potoschnig Augustin Bussy Christian S. Ahart Zehua Chen Linnea Andersson Zdenek Futera Filip Ivanovic Margherita Buraschi Christoph Schran Remi Pasquier Leonard Prokisch Bibek Samal Jelena Schmitz Shridhar Sanjay Shanbhag Harald Forbert Ole Schütt Franz Pöschl Sebastian Ehlert Stefano Battaglia Michele Nottoli Benjamin Stamm Vamsee Voora Rustam Z. Khaliullin Sergey K. Chulkov Matt B. Watkins Clotilde S. Cucinotta Jochen Blumberger Chao Zhang Yang Yang Dominik Marx Matthias Krack Jürg Hutter Marcella Iannuzzi Thomas D. Kühne

This is my paper · ORCID

classification physics.chem-phcond-mat.dis-nncond-mat.mtrl-scicond-mat.stat-mechphysics.comp-ph

keywords CP2KGaussianandplane-waveDFTDFPTTDDFTGW-BSEabinitiomoleculardynamicsKubotransportfinite-temperaturespectroscopy

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 CP2K has reached the point where one open-source electronic-structure platform can carry a calculation from a static, zero-temperature response property to an experimentally comparable observable that includes thermal motion, anharmonicity, and even explicit bias. The organizing idea is the perturbation–response relation: the same Gaussian and plane-wave electronic-structure representation can feed a density-functional perturbation theory, time-dependent density-functional theory, or GW-Bethe–Salpeter static response, an ab initio or path-integral molecular dynamics trajectory, a time-correlation spectrum, a Kubo conductivity, or an open-boundary nonequilibrium Green's function transport calculation. The paper's claim is that this unification is not just a matter of having many modules, but of a single architecture in which the same energy, force, state, and response machinery supports both static and dynamical observables. If true, a computational scientist can compute, in one package, spectra and transport coefficients that include thermal disorder, anharmonicity, and nuclear quantum effects, with benchmarked errors of tens of meV for band structures and couplings.

What carries the argument

The central object is the perturbation–response relation expressed through a Gaussian and plane-wave (GPW) dual representation of the electronic structure, augmented by the all-electron GAPW extension. The GPW representation expands Kohn–Sham orbitals in atom-centered Gaussians while representing the electron density on a plane-wave grid; GAPW decomposes the density into a smooth part and atom-centered hard components, removing the core density from the grid and suppressing force oscillations. This dual representation provides smooth, repeatable energies and forces, makes response tensors and trajectories share the same Hamiltonian and overlap matrices, and supplies the locality that low-sca

What would settle it

Compute GW quasiparticle band gaps of a metallic or narrow-gap three-dimensional supercell (for example, doped silicon or a small-gap semiconductor) at increasing supercell sizes, and compare the minimum-image reconstruction against a full k-point calculation; if the reconstructed gap does not converge to the full-k result before periodic images overlap, the central scalability claim for large-supercell GW fails.

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Extended reading notes

Core claim

The central claim is that CP2K's response formalism unifies static and dynamical spectroscopy and transport. On the static side, the paper describes variational DFPT for electric, magnetic, and nuclear perturbations, linear-response TDDFT with Tamm–Dancoff and spin–orbit corrections, transition-potential and linear-response X-ray methods, GW and GW-BSE, and active-space embedding. On the dynamical side, the same electronic-structure layer feeds AIMD, path-integral MD, Ehrenfest and surface-hopping dynamics, real-time TDDFT, time-correlation spectra, Kubo transport, Hairy Probes open-boundary DFT, and DFT+NEGF. The paper's distinctive assertion is that a single electronic-structure representa

Load-bearing premise

The load-bearing premise is that the irreducible polarizability and self-energy of a large supercell decay in real space fast enough that the Γ-point-only minimum-image reconstruction of chi, W, and Sigma is accurate before periodic images overlap; the paper validates this only for gapped two-dimensional semiconductors in roughly 20-Angstrom cells, leaving metals, narrow-gap systems, and three-dimensional supercells without controlled error bounds.

Editorial extensions

If this is right

If the unified architecture holds, vibrational, electronic, X-ray, and magnetic spectra can be computed with thermal disorder and nuclear quantum effects in one package, rather than by stitching together separate codes.
Equilibrium conductivities from Kubo transport and biased currents from DFT+NEGF can be obtained from the same Hamiltonian, enabling operando comparison with experiment for disordered and driven systems.
GW quasiparticle band structures of large two-dimensional moiré systems become tractable: 984-atom cells are demonstrated, and the paper indicates that thousands of atoms are within reach.
Static approximations such as COHSEX yield smooth quasiparticle energy surfaces suitable for geometry optimization and molecular dynamics, avoiding the discontinuities that can plague perturbative GW.
Benchmarks in the paper put typical errors at roughly 20–50 meV for spin–orbit splittings and band gaps, and about 10 meV for charge-transfer couplings, making quantitative predictions plausible in those regimes.

Reading between the lines

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

Editorial inference: if the real-space decay of the polarizability and self-energy is the load-bearing premise for large-supercell GW, then the advertised scalability to several thousand atoms is conditional on that decay, and should be tested on metals, narrow-gap systems, and three-dimensional supercells where the decay is slower.
Editorial extension: the perturbation–response viewpoint suggests a design principle for future modules: every new static response capability should have a defined trajectory-based or ensemble-based counterpart, or the unification claim weakens.
Editorial extrapolation: a natural stress test of the unified claim is to compare, for the same system, a time-correlation infrared spectrum against a snapshot-averaged DFPT spectrum; agreement would validate that the static and dynamical routes are truly consistent within one representation.

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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

The useful thing here is the map: Tables I and II connect observables (IR, Raman, XAS, EPR, transport) to the specific CP2K modules and to whether you need static response, MD snapshots, time correlations, or real-time propagation. For someone new to CP2K or choosing a method for finite-temperature spectra, that is genuinely valuable. The augmented MOLOPT basis set, benchmarked against GW5000, is a concrete new deliverable, not just a survey. The st-COHSEX coupling benchmark on HAB79, with no empirical scaling, is also a clean result. And the paper is unusually transparent about boundaries: NMR is not for conductors, RT-BSE is molecular only, st-COHSEX overestimates absolute IPs/EAs. That honesty counts.

The soft spots are real but localized. The alpha-COHSEX claim needs a correction: the single scaling parameter is fitted to W12, and the reported 21 meV MAE is over a cluster set that includes W12. That is an in-sample error. The paper should separate the fitting point from the test set and report the leave-one-out or out-of-sample number. This does not break the method's usefulness, but it overstates transferability.

The bigger concern is the Gamma-point-only GW supercell machinery. The paper says the minimum-image reconstruction becomes exact in the large-cell limit and validates it on 8x8 TMD cells (about 20 Å, gapped 2D semiconductors). For metals, narrow-gap systems, or 3D cells, the real-space decay of chi and Sigma is algebraic or slow, so the reconstruction is uncontrolled. The paper does not flag this, and the 'possibly up to 10 000 atoms' claim is not supported for those material classes. That is a load-bearing limitation for a flagship capability, but it is confined to that section; the rest of the review does not depend on it.

The paper is self-citation heavy, but that is normal for a developer code review, and there are external anchors (WIEN2k, BerkeleyGW, ORCA, NEVPT2). The 'invented Hairy Probes' flag from the reader is wrong: Hairy Probes is a published method (Refs. 59, 271, 272), not a product of the review.

Who benefits: CP2K users planning finite-temperature spectroscopy or transport calculations, method developers looking for a gap map, and students wanting an entry point. The paper deserves a serious referee—it is a major public resource—but the referee should require the fit reporting to be fixed and the GW supercell claims to be scoped to systems where the decay assumption is checked. I would send it out.

Referee Report

3 major / 4 minor

Summary. This is a comprehensive code review of CP2K covering the methods that connect electronic structure to dynamics, transport, and spectroscopic response. The paper is organized around the perturbation–response idea: static response calculations (DFPT, TDDFT, RT-TDDFT, GW, GW-BSE, X-ray, NMR/EPR, etc.) are embedded in finite-temperature sampling, AIMD/PIMD, time-correlation functions, or nonequilibrium propagation, and the same electronic-structure representation is used for Kubo transport, Hairy Probes, and DFT+NEGF. The manuscript provides detailed equations, input-keyword guidance, benchmark data against external codes (WIEN2k, BerkeleyGW, ORCA, GW5000, HAB databases), and a supplement with implementation-level working equations. The central claim is that CP2K offers a uniquely integrated, modular platform that carries a user from ground-state DFT through response and transport to spectra that include thermal disorder, anharmonicity, and nuclear quantum effects.

Significance. If the claims hold, this is a valuable reference for the community because it demonstrates—with concrete benchmarks—that one open-source package can unify quantum chemistry with statistical mechanics and transport. The paper is particularly strong where it anchors accuracy to third-party codes: spin–orbit splittings against WIEN2k (MAE below 20 meV), GW band structures against BerkeleyGW (within about 50 meV), and excitation-energy basis-set convergence against GW5000. The modular architecture and the explicit tables of capabilities and finite-temperature strategies are genuinely useful. The main risk is that some headline scalability claims, especially the Γ-point-only supercell GW, rest on a narrow validation set and are stated more broadly than the evidence supports. This is a correctness concern for a flagship capability, not merely a presentation issue.

major comments (3)

[Section VI E] The Γ-point-only supercell GW implementation is advertised as being able to reach 'several thousand atoms, and possibly up to 10,000 atoms,' and the minimum-image reconstruction of χ and Σ is described as 'becoming exact in the limit of a large unit cell.' The only validation shown is for gapped 2D semiconductors: 8×8 TMD cells (about 20 Å lateral, convergence below 20 meV) and the 984-atom MoSe2/WS2 twisted bilayer. For metals, narrow-gap semiconductors, or 3D supercells, the real-space decay of G, χ, and Σ is algebraic or slow, so the microscopic reconstruction error is not controlled by the large-cell limit in any practical sense. This is load-bearing because the large-supercell GW capability and its accuracy at the advertised scale are part of the paper's central claim. Please either provide validation for a metallic or narrow-gap system and for a 3D supercell, or explicitly restrict
[Section IX D, Eq. (79)] The Kubo conductivity implemented in CP2K is evaluated on a finite supercell with a phenomenological dissipation parameter η. The paper states that this yields 'equilibrium transport coefficients,' but it does not discuss how results depend on η or how a meaningful η→0 limit should be taken (e.g., via system-size extrapolation or a Drude–Lorentzian analysis of the finite-size spectrum). For metallic or low-carrier-density systems, the computed conductivity can vary strongly with η, and without a convergence protocol the label 'transport coefficient' is ambiguous. The implementation may be perfectly usable in practice, but the review should state the recommended procedure and the accuracy envelope, or explicitly flag this as a model-dependent estimate requiring extrapolation.
[Section VI F, Eq. (58)] The α-COHSEX scheme uses an empirical scaling factor α that is fitted to the W12 water cluster and then transferred to other clusters. The paper does disclose this ('empirical scaling factor'), but the presentation may leave the impression that the resulting 21 meV MAE for electron affinities is a first-principles accuracy statement. Since α is a free parameter, the claim should be framed as a test of transferability rather than as an ab initio benchmark. Please add a sentence quantifying the sensitivity to α and clarifying that st-COHSEX is the parameter-free version, whereas α-COHSEX is a one-parameter model.

minor comments (4)

[Throughout] The review relies heavily on the same author group's publications for method validation. While this is common in code reviews, the independence of the evidence would be strengthened by explicitly marking which benchmarks are third-party and which are author-generated. Some figures (e.g., Figs. 11, 12) are already labeled 'unpublished results by the authors'; please make the same distinction consistently for all benchmark claims.
[Section VI E] The phrase 'possibly up to 10,000 atoms' should be accompanied by a note that tractability does not imply accuracy. Even for tractable supercells, the minimum-image reconstruction error must be separately converged for each material class.
[Table I / Section VII A] Table I lists BSE optical absorption among CP2K capabilities, while Section VII A states that linear-response GW-BSE is currently implemented only for finite systems. Please add a qualifier in the table row (e.g., 'molecular systems') so that the table does not imply periodic BSE is available.
[Section IX E] The term 'Hairy Probes' is introduced as a CP2K-specific device. It may be helpful to note explicitly that this is a method name unique to the present implementation and to define the physical content at first use: a set of weakly coupled reservoir-like orbitals that impose local Fermi-level control. This would improve readability for readers outside the CP2K developer community.

Circularity Check

1 steps flagged · score 3.0 of 10

Mostly self-contained developer review; one fitted benchmark (α-COHSEX) partially reduces to its own fit parameter.

fitted input called prediction [Section VI F (Coulomb-hole and Screened-Exchange), Fig. 12 and surrounding text]
"A single scaling parameter fitted to the W12 reference is transferred without refitting across surface- and interior-bound clusters. The cluster set, reference data, and fitted value are specified in Section V E in the SI. The α-COHSEX method has an MAE of 21 meV, which is much smaller than the st-COHSEX error of 270 meV."

The α parameter in α-COHSEX is an empirical scaling of the static screened interaction. It is explicitly fitted to the W12 cluster ('W12 is used for parametrization of α-COHSEX'), and the reported 21 meV MAE is over the water-cluster set that includes W12. Thus the headline accuracy claim is partially forced by construction: the fitted point contributes a near-zero error by design, lowering the aggregate MAE. The transfer to other clusters is a genuine prediction, so this is a partial reduction rather than full circularity.

full rationale

The review is a developer-code overview, so self-citation is pervasive; however, the central capability claims are anchored outside the author network by open-source code, external benchmarks (WIEN2k, BerkeleyGW, ORCA, NEVPT2/HAB79, GW5000), and parameter-free validation. The GW supercell MIC reconstruction is an approximation with stated assumptions and convergence tests, not a self-referential prediction. The spin-orbit, basis-set, GW-BSE, and transport benchmarks use independent references. The only concrete case where a 'prediction' reduces by construction is the α-COHSEX water-cluster MAE, because the scaling parameter is fitted to one of the reported clusters and the MAE includes that cluster. This is disclosed and the transfer to other clusters is legitimate, so it is a minor partial circularity, not a collapse of the paper's derivation chain.

Assumptions & free parameters 4 free parameters · 8 assumptions · 1 invented entities

The review's central claim — that CP2K's architecture turns electronic structure into dynamics, transport, and spectra with quantified accuracy — rests on the accuracy and transferability of the underlying DFT layer, on method-specific domain assumptions (many explicitly acknowledged), on one disclosed empirical fit (alpha-COHSEX, alpha=0.72), and on the generalizability of developer-selected benchmark sets. Standard machinery (Bloch, Sternheimer, Kubo, Landauer) is invoked without proof; the domain assumptions delimit applicability (insulators for magnetic response; large cells for MIC-GW; molecules for RT-BSE). No new physical particles or forces are postulated; Hairy Probes is a computational construct with external validation anchors.

free parameters (4)

alpha_COHSEX = 0.72
Empirical scaling applied to the static screened exchange in Eq. (58); fitted to the W12 water-cluster electron affinity and transferred to the other clusters in Fig. 12 (Section V E in the SI). The reported MAE of 21 meV appears to include the W12 fit point.
Kubo_dissipation_eta = system-dependent (not stated)
Phenomenological dissipation eta in Eq. (79) broadens the conductivity; no convergence protocol or validation of sigma vs. eta or supercell size is given in Section IX D.
HP_solution_probe_alpha = alpha << 1
Dimensionless weight of the solution-probe Fermi functions in Eq. (82), chosen by hand to prevent unphysical depopulation of states weakly coupled to the electrode probes (Section IX E).
VM_TIDFT_penalty_C_P = increased adaptively
Penalty strength C_P in Eq. (39) enforcing interstate orthogonality; a numerical-schedule control reported as increased until the orthogonality deviation falls below threshold (Section IV C).

assumptions (8)

domain assumption Kohn-Sham DFT with the implemented XC functionals (PBE, PBE0, HSE06, Skala-1.1) provides an accurate electronic-structure layer for all downstream response, spectroscopy, and transport properties.
The entire review is built on the GPW/GAPW KS layer (Section II A); no cross-cutting accuracy audit is provided, so errors in this layer inherit into every predicted spectrum and coefficient.
domain assumption GTH pseudopotentials (and GAPW augmentation) faithfully represent core-valence interactions across the periodic table for response properties.
GPW 'rests primarily on' GTH pseudopotentials (Section II A); spin-orbit splittings are benchmarked only over alkali halides, elemental crystals, and compound semiconductors (Fig. 1).
domain assumption The Sebastiani-Parrinello magnetic-response machinery requires exponentially localized Wannier functions, i.e., insulating systems.
Section III C states the core assumption that 'each Wannier function is contained entirely within the simulation cell once it is centered' and explicitly: 'this implementation is not suitable for conductors.'
domain assumption The one-electron excitation approximation with a strongly localized core hole is valid for K-edge XAS/XES (transition potential method).
Section V A: the core hole is 'strongly localized on a single atomic site, and the problem can often be approximated within a single-particle framework, in particular for K-edges of light elements.'
domain assumption Core-valence separation and the sudden approximation hold for core-level LR-TDDFT.
Section V B introduces CVS and the sudden approximation as the two enablers that make core LR-TDDFT tractable for large systems.
domain assumption G, chi, and Sigma decay in real space before periodic images overlap, making the Gamma-point minimum-image reconstruction of the GW self-energy exact in the large-cell limit.
Section VI E: reconstruction 'becomes exact in the limit of a large unit cell'; validated only on 8x8 TMD cells (~20 A lateral, convergence below 20 meV).
domain assumption The finite-volume Kubo formula with a minimum-image position-Hamiltonian commutator kernel (Eq. 80) reproduces the velocity operator, and conductivity is insensitive to the chosen dissipation eta.
Section IX D presents no convergence study of sigma(eta) or sigma(supercell) in this paper; reliability rests on prior work (Refs. 56-58).
standard math Standard machinery: Bloch's theorem; Sternheimer linear response; Kadanoff-Baym to von Neumann EOM; Landauer-Buttiker formula for NEGF currents.
Invoked in Sections II A 2 (Eqs. 12-14), III (Eq. 25), VII B (Eq. 62), and IX F (Eqs. 84-89) without proof.

invented entities (1)

Hairy Probes (virtual atomically thin reservoirs attached to AO subspaces) independent evidence
purpose: Impose local Fermi-level / electrochemical-potential control in periodic DFT without explicit electrodes or steady current, enabling potential-controlled AIMD of electrified interfaces (Section IX E).
A computational construct (wide-band reservoirs in the Gamma_p -> 0 limit), not a physical entity. It carries independent falsifiable handles: validation on the Pt(111) parallel-plate capacitor reproduces the classical C=Q/Delta-mu value and the linear Hartree-potential drop (Fig. 18a), and its predictions about interfacial charge transfer under bias are testable experimentally.

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Cite this review

Pith. "Pith review of CP2K: An electronic structure and molecular dynamics software package - Dynamics, Transport, and Spectroscopic Response." pith.science (2026). https://pith.science/paper/VHLALAGK

@misc{pith2026260722916,
  author       = {Pith},
  title        = {Pith review of: CP2K: An electronic structure and molecular dynamics software package - Dynamics, Transport, and Spectroscopic Response},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VHLALAGK}},
  note         = {Machine review of arXiv:2607.22916}
}

read the original abstract

One of the distinguishing aspects of CP2K is its seamless integration of diverse structural and transition-state optimization techniques with advanced sampling approaches including Monte Carlo, molecular dynamics, and metadynamics, enabling the efficient exploration of complex potential- and free-energy landscapes, including rare events. These capabilities are combined with a broad hierarchy of energy and force evaluation methods, ranging from classical and machine-learned interaction potentials and mixed quantum-classical multiscale and semiempirical schemes, to highly accurate quantum-mechanical electronic-structure approaches. At the heart of the latter lies the Gaussian and plane-wave framework, along with its augmented all-electron generalization, which have been described in detail in our previous code review [T. D. K\"uhne et al., J. Chem. Phys. 152, 194103 (2020)]. Building on this foundation, the present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response. Particular emphasis is placed on the coupling between static response calculations and nuclear motion: spectra may be evaluated at optimized structures, averaged over thermally sampled configurations, obtained from time-correlation functions along ab-initio or path integral molecular trajectories, or followed in real time together with electronic and nuclear dynamics. The same modular structure also enables equilibrium and biased transport simulations, from Kubo-type linear response to open-boundary approaches under external potentials, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.

Figures

Figures reproduced from arXiv: 2607.22916 by the authors.

**Figure 1.** FIG. 1. Accuracy of spin–orbit-coupling splittings in the electronic band structure computed using PBE with HGH spin– [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

**Figure 2.** FIG. 2. Magnitude of the transition-dipole matrix element [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗

Figures from the paper (41 more)

**Figure 3.** Figure 3: FIG. 3. Benchmarking the new augmented MOLOPT basis sets. (a) shows the basis set convergence of the first ten excitation [PITH_FULL_IMAGE:figures/full_fig_p017_3.png]

**Figure 4.** Figure 4: FIG. 4. Size of an excitation in quasi-one-dimensional [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]

**Figure 5.** Figure 5: FIG. 5. RT-TDDFT simulation of the dianion of cysteine [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]

**Figure 6.** Figure 6: FIG. 6. S 1s (K-edge) XAS spectra of aqueous cysteine in the [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]

**Figure 7.** Figure 7: FIG. 7. RIXS from the O 1s (K-edge) for one configuration [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]

**Figure 8.** Figure 8: FIG. 8. Overview of the observables obtained from the [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]

**Figure 8.** Figure 8: FIG. 8. Overview of the observables obtained from the [PITH_FULL_IMAGE:figures/full_fig_p022_8.png]

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p025_9.png]

**Figure 11.** Figure 11: FIG. 11. Error in electronic couplings for cofacial molec [PITH_FULL_IMAGE:figures/full_fig_p026_11.png]

**Figure 12.** Figure 12: FIG. 12. Electron affinity of water cluster computed using [PITH_FULL_IMAGE:figures/full_fig_p027_12.png]

**Figure 13.** Figure 13: FIG. 13. Imaginary part of the polarizability of furan and [PITH_FULL_IMAGE:figures/full_fig_p028_13.png]

**Figure 14.** Figure 14: FIG. 14. Field-normalized spectrum of the dipole-moment [PITH_FULL_IMAGE:figures/full_fig_p030_14.png]

**Figure 15.** Figure 15: FIG. 15. Active-space embedding workflow in CP2K, adapted from the CP2K–Qiskit Nature interface of Ref. [PITH_FULL_IMAGE:figures/full_fig_p032_15.png]

**Figure 16.** Figure 16: FIG. 16. Representative applications of POD electronic cou [PITH_FULL_IMAGE:figures/full_fig_p034_16.png]

**Figure 17.** Figure 17: FIG. 17. Hairy Probes DFT concept and CP2K implementation workflow. (a) Hairy Probes connect selected AOs to [PITH_FULL_IMAGE:figures/full_fig_p036_17.png]

**Figure 18.** Figure 18: FIG. 18. Validation and application of Hairy Probes DFT under potential control. (a) Pt(111) parallel-plate capacitor: at [PITH_FULL_IMAGE:figures/full_fig_p038_18.png]

**Figure 19.** Figure 19: FIG. 19. Physical and computational structure of CP2K+SMEAGOL. (a) Two-terminal DFT+NEGF partitioning into left [PITH_FULL_IMAGE:figures/full_fig_p040_19.png]

**Figure 20.** Figure 20: FIG. 20. Representative CP2K+SMEAGOL validation [PITH_FULL_IMAGE:figures/full_fig_p041_20.png]

**Figure 20.** Figure 20: FIG. 20. Representative CP2K+SMEAGOL validation [PITH_FULL_IMAGE:figures/full_fig_p040_20.png]

**Figure 21.** Figure 21: FIG. 21. Overview of the workflow for FOB-SH, FE-SH, and X-SH. Methods for calculating the electronic Hamiltonian matrix [PITH_FULL_IMAGE:figures/full_fig_p043_21.png]

**Figure 22.** Figure 22: FIG. 22. Representative applications of FOB-SH, FE-SH, and X-SH. (a) FOB-SH simulation of thermoelectric hole transport [PITH_FULL_IMAGE:figures/full_fig_p044_22.png]

**Figure 23.** Figure 23: FIG. 23. Conceptual representation of Grassmann wavefunc [PITH_FULL_IMAGE:figures/full_fig_p044_23.png]

**Figure 6.3.** Figure 6.3: Glycine(aq): (6.3a) zwitterionic structure indicating the labeling scheme. (6.3b) H↵’s convergence: floating average of H↵2,H↵3 and their average during an MD trajectory (upper panel), difference between the average and their individual H↵’s floating average (lower …

**Figure 6.7.** Figure 6.7: Classical MD of tyrosine(aq): example of a multi–state structure. In Fig. (6.7c) is monitored the value of the C–C↵–C–H?3 dihedral angle (bold blue lines in Fig. (6.7a)). Fig. (6.7b) displays incremental average chemical shift for H?2 and H?3 atoms while sampling …

**Figure 25.** Figure 25: FIG. 25. Infrared spectra of CH [PITH_FULL_IMAGE:figures/full_fig_p053_25.png]

**Figure 25.** Figure 25: FIG. 25. Infrared spectra of CH [PITH_FULL_IMAGE:figures/full_fig_p052_25.png]

**Figure 26.** Figure 26: FIG. 26. Ultraviolet–visible absorption spectra of indole [PITH_FULL_IMAGE:figures/full_fig_p054_26.png]

**Figure 26.** Figure 26: FIG. 26. Ultraviolet–visible absorption spectra of indole [PITH_FULL_IMAGE:figures/full_fig_p053_26.png]

**Figure 27.** Figure 27: FIG. 27. Schematic of the CP2K–Newton-X interface for trajectory surface hopping and nuclear-ensemble spectroscopy. [PITH_FULL_IMAGE:figures/full_fig_p055_27.png]

**Figure 1.** Figure 1: FIG. 1. Scaling of the imaginary-time density-response con [PITH_FULL_IMAGE:figures/full_fig_p082_1.png]

**Figure 1.** Figure 1: FIG. 1. Scaling of the imaginary-time density-response con [PITH_FULL_IMAGE:figures/full_fig_p084_1.png]

**Figure 2.** Figure 2: FIG. 2. Computation time for a [PITH_FULL_IMAGE:figures/full_fig_p083_2.png]

**Figure 2.** Figure 2: FIG. 2. Computation time for a [PITH_FULL_IMAGE:figures/full_fig_p084_2.png]

**Figure 3.** Figure 3: FIG. 3. Scaling of the [PITH_FULL_IMAGE:figures/full_fig_p084_3.png]

**Figure 3.** Figure 3: FIG. 3. Scaling of the [PITH_FULL_IMAGE:figures/full_fig_p085_3.png]

**Figure 4.** Figure 4: FIG. 4. Flow chart of the finite-field module in CP2K. [PITH_FULL_IMAGE:figures/full_fig_p091_4.png]

**Figure 4.** Figure 4: FIG. 4. Flow chart of the finite-field module in CP2K. [PITH_FULL_IMAGE:figures/full_fig_p093_4.png]

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