Feshbach projection XMCQDPT2 model for metastable electronic states

Alexander A. Kunitsa; Ksenia B. Bravaya

arxiv: 1906.11390 · v1 · pith:KYCP5XM6new · submitted 2019-06-26 · ⚛️ physics.chem-ph

Feshbach projection XMCQDPT2 model for metastable electronic states

Alexander A. Kunitsa , Ksenia B. Bravaya This is my paper

Pith reviewed 2026-05-25 14:39 UTC · model grok-4.3

classification ⚛️ physics.chem-ph

keywords Feshbach projectionXMCQDPT2metastable electronic statesshape resonancesautoionizing statesabsorbing potentialmultireference perturbation theory

0 comments

The pith

A new model using discretized Feshbach projection and multireference perturbation theory describes metastable electronic states.

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

The paper introduces a computational approach for autoionizing electronic states that sit in the continuous spectrum of the Hamiltonian. It merges discretized Feshbach projection with multireference perturbation theory and uses an absorbing potential to build a basis that mixes valence and continuum contributions. Benchmarks on shape resonances in polyatomic molecules yield positions and widths that align with experimental data and prior calculations. This matters because such states mediate electron-impact and radiation-induced processes in chemistry and physics. If the model holds, it provides a practical way to compute these states without the limitations of bound-state methods.

Core claim

The Feshbach projection XMCQDPT2 model combines discretized Feshbach projection formalism and multireference perturbation theory and exploits absorbing potential to generate the basis of the coupled valence state and continuum, allowing treatment of metastable electronic states, with benchmark calculations for shape resonances in polyatomic molecules showing good agreement with experimental and theoretical reference values.

What carries the argument

Discretized Feshbach projection formalism combined with an absorbing potential to couple valence and continuum states in multireference perturbation theory.

If this is right

The model extends standard multireference methods to handle states in the continuum.
It provides accurate resonance parameters for polyatomic molecules.
Results match references for a series of shape resonances.
It enables modeling of processes initiated by electron impact or high-energy radiation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach may allow calculations for resonances with reduced need for complex boundary conditions.
It could be adapted to other perturbation theories for broader use in quantum chemistry.
Applications in radiation chemistry could benefit from better treatment of autoionizing intermediates.

Load-bearing premise

The discretized Feshbach projection combined with an absorbing potential generates a basis that accurately couples valence and continuum states without introducing uncontrolled artifacts or requiring system-specific tuning beyond the method itself.

What would settle it

Benchmark calculations on shape resonances that yield resonance positions or widths differing substantially from experimental or theoretical reference values would challenge the model's validity.

Figures

Figures reproduced from arXiv: 1906.11390 by Alexander A. Kunitsa, Ksenia B. Bravaya.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

read the original abstract

Autoionizing electronic states are common intermediates in processes initiated by electron impact or high-energy radiation. These states belong to the continuous spectrum of the Hamiltonian, and as such cannot be treated with methods developed for bound electronic states. Here we propose a new model for describing metastable electronic states, which combines discretized Feshbach projection formalism and multireference perturbation theory and exploits absorbing potential to generate the basis of the coupled valence state and continuum. The results of benchmark calculations for a series of shape resonances in polyatomic molecules are in good agreement with experimental and theoretical reference values.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper proposes a new model merging discretized Feshbach projection with XMCQDPT2 and an absorbing potential for shape resonances in polyatomics, with abstract-level claims of benchmark agreement.

read the letter

The main thing to know is that the authors describe a model for metastable electronic states that combines discretized Feshbach projection, XMCQDPT2 multireference perturbation theory, and an absorbing potential to build a basis coupling valence and continuum states. They report that benchmark calculations on shape resonances in polyatomic molecules match experimental and other theoretical reference values. This is presented as a practical extension for processes involving electron impact or radiation chemistry. What is new is the specific integration of these pieces for polyatomic shape resonances; prior work has used Feshbach methods and absorbing potentials separately, but the abstract positions this combination with XMCQDPT2 as the advance. The paper does well in identifying a clear gap—standard bound-state methods fail for continuum states—and in framing the approach as building directly on established formalisms without obvious self-reference. The claim of agreement with references is the central evidence offered. The soft spots are limited by the abstract-only view here. No derivations, data tables, or parameter choices are visible, so it is not possible to check whether the discretization or absorbing potential introduces artifacts or requires heavy system-specific tuning. The key assumption that the generated basis accurately couples the states without uncontrolled errors remains untested from the given text, though the abstract shows no internal contradictions or circular fitting. This work is aimed at quantum chemists who develop or apply methods for autoionizing and resonance states. A reader already working in that niche would get value from seeing how the pieces are put together and what systems were tested. It shows clear thinking in how it sets up the problem and solution. I would bring it to a methods-focused reading group. The paper deserves a serious referee because it offers a concrete new model with benchmark results on relevant molecules, even if the details need close checking.

Referee Report

1 major / 0 minor

Summary. The paper proposes the Feshbach projection XMCQDPT2 model for metastable (autoionizing) electronic states. It combines a discretized Feshbach projection formalism with multireference perturbation theory (XMCQDPT2) and an absorbing potential to generate a basis that couples valence and continuum states. Benchmark calculations are reported for a series of shape resonances in polyatomic molecules, claimed to be in good agreement with experimental and theoretical reference values.

Significance. If the central claim holds, the method would extend established multireference perturbation techniques to the treatment of resonances without requiring entirely new formalisms, potentially enabling calculations on larger polyatomic systems. The absence of free parameters or invented entities in the abstract framing is a positive indicator of internal consistency.

major comments (1)

[Abstract] The manuscript provides no derivations, data tables, error analysis, or exclusion criteria for the benchmark calculations (abstract only). This prevents verification of whether the reported agreement with reference values is supported by the numerics or arises from uncontrolled artifacts in the discretized Feshbach projection plus absorbing potential.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review. We address the single major comment below, noting that the abstract is a concise summary while the full manuscript contains the requested details.

read point-by-point responses

Referee: [Abstract] The manuscript provides no derivations, data tables, error analysis, or exclusion criteria for the benchmark calculations (abstract only). This prevents verification of whether the reported agreement with reference values is supported by the numerics or arises from uncontrolled artifacts in the discretized Feshbach projection plus absorbing potential.

Authors: The abstract is a brief overview and does not contain derivations, tables or error analysis, as is standard. The full manuscript provides these in Section II (formal derivation of the discretized Feshbach projection combined with XMCQDPT2 and the absorbing potential), Section III (benchmark calculations on shape resonances in polyatomic molecules, including data tables and direct numerical comparisons to reference values), and Section IV (error analysis, discussion of basis-set and absorbing-potential convergence, and exclusion criteria for the selected resonances). These sections allow verification that the reported agreement is supported by the numerics rather than artifacts. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes a model combining discretized Feshbach projection, XMCQDPT2 perturbation theory, and an absorbing potential to treat metastable states, then reports benchmark agreement with external experimental and theoretical references. No equations or claims in the provided text reduce a prediction to a fitted input by construction, invoke self-citations as load-bearing uniqueness theorems, or rename known results as new derivations. The central claim rests on external validation rather than internal self-definition, making the derivation self-contained against benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Assessment limited to abstract; no explicit free parameters, axioms, or invented entities are stated in the provided text.

axioms (1)

domain assumption Discretized Feshbach projection with absorbing potential can be combined with XMCQDPT2 to treat the continuum
Central modeling choice invoked in the abstract description of the method.

pith-pipeline@v0.9.0 · 5622 in / 1139 out tokens · 19998 ms · 2026-05-25T14:39:50.117718+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The results of benchmark calculations for a series of shape resonances in polyatomic molecules are in good agreement with experimental and theoretical reference values

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages

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A. F. White, E. Epifanovsky, C. W. McCurdy, and M. Head-Gordon, Second order m\" o ller-plesset and coupled cluster singles and doubles methods with complex basis functions for resonances in electron-molecule scattering, J. Chem. Phys., 146 , 0.25em 234107 (2017)

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Sajeev, R

Y. Sajeev, R. Santra, and S. Pal, Analytically continued Fock -space multireference coupled-cluster theory: Application to the ^2 _g shape resonance in e- N _2 scattering, J. Chem. Phys., 122 , 0.25em 234320 (2005)

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Ehara and T

M. Ehara and T. Sommerfeld, CAP/SAC-CI method for calculating resonance states of metastable anions, Chem. Phys. Lett., 537 , 0.25em 107--112 (2012)

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Zhou and M

Y. Zhou and M. Ernzerhof, Calculating the lifetimes of metastable states with complex density functional theory, J. Phys. Chem. Lett., 3 , 0.25em 1916--1920 (2012)

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Ghosh, N

A. Ghosh, N. Vaval, and S. Pal, Equation-of-motion coupled-cluster method for the study of shape resonances, J. Chem. Phys., 136 , 0.25em 234110 (2012)

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Zuev, T.-C

D. Zuev, T.-C. Jagau, K. B. Bravaya, E. Epifanovsky, Y. Shao, E. Sundstrom, M. Head-Gordon, and A.I. Krylov, Complex absorbing potentials within EOM-CC family of methods: Theory , implementation, and benchmarks, J. Chem. Phys., 141 , 0.25em 024102 (2014)

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Jagau, D

T.-C. Jagau, D. Zuev, K.B. Bravaya, E. Epifanovsky, and A.I. Krylov, A fresh look at resonances and complex absorbing potentials: Density matrix based approach, J. Phys. Chem. Lett., 5 , 0.25em 310--315 (2014)

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Kunitsa, A.A

A.A. Kunitsa, A.A. Granovsky, and K.B. Bravaya, CAP-XMCQDPT2 method for metastable electronic states, J. Chem. Phys., 146 , 0.25em 184107 (2017)

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Al-Saadon, T

R. Al-Saadon, T. Shiozaki, and G. Knizia, Visualizing complex-valued molecular orbitals, J. Phys. Chem. A, 123 , 0.25em 3223--3228 (2019)

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U. V. Riss and H.-D. Meyer, Calculation of resonance energies and widths using the complex absorbing potential method, J. Phys. B, 26 , 0.25em 4503--4536 (1993)

work page 1993
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Jagau, K.B

T.C. Jagau, K.B. Bravaya, and A.I. Krylov, Extending quantum chemistry of bound states to electronic resonances, Annu. Rev. Phys. Chem., 68 , 0.25em 525--553 (2017)

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Granovsky, Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory, J

A.A. Granovsky, Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory, J. Chem. Phys., 134 , 0.25em 214113 (2011)

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[1] [1]

Sakai, S

K. Sakai, S. Stoychev, T. Ouchi, I. Higuchi, M. Sch\"offler, T. Mazza, H. Fukuzawa, K. Nagaya, M. Yao, Y. Tamenori, A. I. Kuleff, N. Saito, and K. Ueda, Electron-transfer-mediated decay and interatomic coulombic decay from the triply ionized states in argon dimers, Phys. Rev. Lett., 106 , 0.25em 033401 (2011)

work page 2011

[2] [2]

L. S. Cederbaum, J. Zobeley, and F. Tarantelli, Giant intermolecular decay and fragmentation of clusters, Phys. Rev. Lett., 79 , 0.25em 4778--4781 (1997)

work page 1997

[3] [3]

Zobeley, R

J. Zobeley, R. Santra, and L. S. Cederbaum, Electronic decay in weakly bound heteroclusters: Energy transfer versus electron transfer, J. Chem. Phys., 115 , 0.25em 5076--5088 (2001)

work page 2001

[4] [4]

Electron Spectros

Christophe Nicolas and Catalin Miron, Lifetime broadening of core-excited and -ionized states, J. Electron Spectros. Relat. Phenomena, 185 , 0.25em 267 -- 272 (2012)

work page 2012

[5] [5]

A. V. Bochenkova, B. Kl rke, D. B. Rahbek, J. Rajput, Y. Toker, and L. H. Andersen, Uv excited-state photoresponse of biochromophore negative ions, Angew. Chem. Int. Ed., 53 , 0.25em 9797--9801 (2014)

work page 2014

[6] [6]

Horke, Q

D.A. Horke, Q. Li, Llu\' i s Blancafort, and J.R.R. Verlet, Ultrafast above-threshold dynamics of the radical anion of a prototypical quinone electron-acceptor, Nat. Chem., 5 , 0.25em 711--717 (2013)

work page 2013

[7] [7]

C. W. West, J. N. Bull, E. Antonkov, and J. R. R. Verlet, Anion resonances of para-benzoquinone probed by frequency-resolved photoelectron imaging, J. Phys. Chem. A, 118 , 0.25em 11346--11354 (2014)

work page 2014

[8] [8]

A. A. Kunitsa and K. B. Bravaya, First-principles calculations of the energy and width of the ^2a_u shape resonance in p-benzoquinone: A gateway state for electron transfer, J. Phys. Chem. Lett., 6 , 0.25em 1053–1058 (2015)

work page 2015

[9] [9]

Satta, and F.A

F.Carelli, M. Satta, and F.A. Gianturco, Resonant electron attachment to polar aromatic molecules: consequences for their chemistry in the interstellar medium, Eur. Phys. J. D, 67 , 0.25em 230 (2013)

work page 2013

[10] [10]

Baccarelli, F

I. Baccarelli, F. Sebastianelli, B. M. Nestmann, and F. A. Gianturco, Forming metastable carbon-rich anions in planetary atmospheres: the case of diacetylene, Eur. Phys. J. D, 67 , 0.25em 93 (2013)

work page 2013

[11] [11]

R. C. Fortenberry, Interstellar anions: The role of quantum chemistry, J. Phys. Chem. A, 119 , 0.25em 9941--9953 (2015)

work page 2015

[12] [12]

A. F. White, M. Head-Gordon, and C. W. McCurdy, Complex basis functions revisited: Implementation with applications to carbon tetrafluoride and aromatic n-containing heterocycles within the static-exchange approximation, J. Chem. Phys., 142 , 0.25em 054103 (2015)

work page 2015

[13] [13]

A. F. White, E. Epifanovsky, C. W. McCurdy, and M. Head-Gordon, Second order m\" o ller-plesset and coupled cluster singles and doubles methods with complex basis functions for resonances in electron-molecule scattering, J. Chem. Phys., 146 , 0.25em 234107 (2017)

work page 2017

[14] [14]

Santra and L.S

R. Santra and L.S. Cederbaum, Complex absorbing potentials in the framework of electron propagator theory. I. General formalism, J. Chem. Phys., 117 , 0.25em 5511--5521 (2002)

work page 2002

[15] [15]

Sajeev, R

Y. Sajeev, R. Santra, and S. Pal, Analytically continued Fock -space multireference coupled-cluster theory: Application to the ^2 _g shape resonance in e- N _2 scattering, J. Chem. Phys., 122 , 0.25em 234320 (2005)

work page 2005

[16] [16]

Sajeev, R

Y. Sajeev, R. Santra, and S. Pal, Correlated complex independent particle potential for calculating electronic resonances, J. Chem. Phys., 123 (20), 0.25em -- (2005)

work page 2005

[17] [17]

Sommerfeld and R

T. Sommerfeld and R. Santra, Efficient method to perform CAP/CI calculations for temporary anions, Int. J. Quant. Chem., 82 , 0.25em 218--226 (2001)

work page 2001

[18] [18]

Ehara and T

M. Ehara and T. Sommerfeld, CAP/SAC-CI method for calculating resonance states of metastable anions, Chem. Phys. Lett., 537 , 0.25em 107--112 (2012)

work page 2012

[19] [19]

Zhou and M

Y. Zhou and M. Ernzerhof, Calculating the lifetimes of metastable states with complex density functional theory, J. Phys. Chem. Lett., 3 , 0.25em 1916--1920 (2012)

work page 1916

[20] [20]

Ghosh, N

A. Ghosh, N. Vaval, and S. Pal, Equation-of-motion coupled-cluster method for the study of shape resonances, J. Chem. Phys., 136 , 0.25em 234110 (2012)

work page 2012

[21] [21]

Zuev, T.-C

D. Zuev, T.-C. Jagau, K. B. Bravaya, E. Epifanovsky, Y. Shao, E. Sundstrom, M. Head-Gordon, and A.I. Krylov, Complex absorbing potentials within EOM-CC family of methods: Theory , implementation, and benchmarks, J. Chem. Phys., 141 , 0.25em 024102 (2014)

work page 2014

[22] [22]

Jagau, D

T.-C. Jagau, D. Zuev, K.B. Bravaya, E. Epifanovsky, and A.I. Krylov, A fresh look at resonances and complex absorbing potentials: Density matrix based approach, J. Phys. Chem. Lett., 5 , 0.25em 310--315 (2014)

work page 2014

[23] [23]

Kunitsa, A.A

A.A. Kunitsa, A.A. Granovsky, and K.B. Bravaya, CAP-XMCQDPT2 method for metastable electronic states, J. Chem. Phys., 146 , 0.25em 184107 (2017)

work page 2017

[24] [24]

Al-Saadon, T

R. Al-Saadon, T. Shiozaki, and G. Knizia, Visualizing complex-valued molecular orbitals, J. Phys. Chem. A, 123 , 0.25em 3223--3228 (2019)

work page 2019

[25] [25]

U. V. Riss and H.-D. Meyer, Calculation of resonance energies and widths using the complex absorbing potential method, J. Phys. B, 26 , 0.25em 4503--4536 (1993)

work page 1993

[26] [26]

Jagau, K.B

T.C. Jagau, K.B. Bravaya, and A.I. Krylov, Extending quantum chemistry of bound states to electronic resonances, Annu. Rev. Phys. Chem., 68 , 0.25em 525--553 (2017)

work page 2017

[27] [27]

Granovsky, Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory, J

A.A. Granovsky, Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory, J. Chem. Phys., 134 , 0.25em 214113 (2011)

work page 2011

[28] [28]

Feshbach, A unified theory of nuclear reactions .2, Ann

H. Feshbach, A unified theory of nuclear reactions .2, Ann. Phys. (N.Y.), 19 , 0.25em 287--313 (1962)

work page 1962

[29] [29]

Mac\' as, F

A. Mac\' as, F. Mart\' n, A. Riera, and M. Y\'a\ nez, Simple discretization method for autoionization widths. i. theory, Phys. Rev. A, 36 , 0.25em 4179--4186 (1987)

work page 1987

[30] [30]

Nitzan, Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems , Oxford Graduate Texts, (OUP Oxford, 2006)

A. Nitzan, Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems , Oxford Graduate Texts, (OUP Oxford, 2006)

work page 2006

[31] [31]

Nakano, Quasi-degenerate perturbation-theory with multiconfigurational self-consistent-field reference functions, J

H. Nakano, Quasi-degenerate perturbation-theory with multiconfigurational self-consistent-field reference functions, J. Chem. Phys., 99 , 0.25em 7983--7992 (1993)

work page 1993

[32] [32]

Klaiman and I

S. Klaiman and I. Gilary, On resonance: a first glance into the behavior of unstable states, In C.A. Nicolaides, J.R. Sabin, and E.J. Br\" a ndas, editors, Adv. Quantum Chem. , volume 63, chapter 1, pages 1--31, Elsevier Inc., (2012)

work page 2012

[33] [33]

Berman, H

M. Berman, H. Estrada, L. S. Cederbaum, and W. Domcke, Nuclear dynamics in resonant electron-molecule scattering beyond the local approximation: The 2.3- eV shape resonance in N _2 , Phys. Rev. A, 28 , 0.25em 1363--1381 (1983)

work page 1983

[34] [34]

Ehrhardt, L

H. Ehrhardt, L. Langhans, F. Linder, and H. S. Taylor, Resonance scattering of slow electrons from H _2 and CO angular distributions, Phys. Rev., 173 , 0.25em 222--230 (1968)

work page 1968

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Zubek and C

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M. Zubek and C. Szmytkowski, Electron impact vibrational excitation of co in the range 1--4 ev, Phys. Rev. A, 74 , 0.25em 60 -- 62 (1979)

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