arXiv subjects

Kevin Carter-Fenk

Publications and source records attributed to Kevin Carter-Fenk.

10 recordsLinked to original sources

arXiv2026

Information-Theoretic Appraisal of Electron Densities

We present an information-theoretic assessment of atomic and molecular densities in the ground state and under a range of physical scenarios--excitation, confinement, and ensemblization. Comparisons across densities obtained from single-reference methods are facilitated through information entropy measures evaluated in position space. We demonstrate that the J-divergence serves as a key metric for benchmarking electron densities against coupled cluster and configuration interaction references. Mean-field orbital information is further compared with that of Brueckner and Dyson orbitals, and informational changes in multiple self-consistent-field solutions are examined under various symmetry-breaking conditions. We also explore the relationship between entropic measures of electron delocalization and the accuracy of the CO dipole moment computed with different methods. Our work offers insights into the selection of optimal reference determinants for a given chemical application and highlights potential benefits of incorporating information-entropy concepts in the development of new density functionals.

physics.chem-ph↗

arXiv2026

Kohn-Sham density encoding rescues coupled cluster theory for strongly correlated molecules

Coupled cluster theory with a Kohn-Sham reference (KS-CC) can dramatically outperform its Hartree-Fock counterpart for strongly correlated systems, but the origin of these improvements has remained unclear. Here we demonstrate that these improvements arise from differences in the one-particle density matrix that are encoded into the non-canonical Fock matrix and not from the nature of the KS orbitals, as is commonly assumed. Equipped with this insight, KS-CCSD(T) can be leveraged to achieve near-chemical-accuracy for electronic and thermochemical properties of transition-metal dimers and main-group compounds. Most strikingly, KS-CCSD(T) qualitatively recovers the entire Cr$_2$ potential energy surface, a notorious failure case for HF-CCSD(T) and single-reference density functional theory. We further introduce a density difference diagnostic that identifies multireference character and guides practitioners toward rational selections of optimal references at mean-field cost. These results establish KS-CCSD(T) as a practical route to treat strong correlation within the "gold standard" framework, and this has immediate implications for machine learning potential development and materials research, areas that heavily rely on KS-DFT for model-parameter fitting.

physics.chem-ph↗

arXiv2026

The Dose Makes the Poison: Perturbative Steps Toward the Ultimate Linearized Coupled Cluster Method

"Addition-by-subtraction" coupled cluster (CC) approaches provide a promising approach to treating the difficult strong correlation problem by simplifying the standard CC equations. In a separate vein, linearized CC methods have drawn interest for their lower computational cost, increased parallelizability, and favorable properties for extension to the excited state--but the inclusion of ring/crossed-ring terms causes singularities even for single bond breaking. A linearized, addition-by-subtraction CC method called linearized ladder CCD (linLCCD) removes these terms to avoid divergences, but linLCCD under-estimates dynamical correlation. Herein we resolve this deficiency of linLCCD by introducing a linearized external coupled cluster perturbation theory that adds a second-order ring/crossed-ring correction back into a linLCCD reference wave function. Our resultant xlinCCD(2) method is regular and yields comparable results to linearized CCD in weakly-correlated regimes.

cond-mat.str-el↗

arXiv2025

Diagrammatic Simplification of Linearized Coupled Cluster Theory

Linearized Coupled Cluster Doubles (LinCCD) often provides near-singular energies in small-gap systems that exhibit static correlation. This has been attributed to the lack of quadratic $T_2^2$ terms that typically balance out small energy denominators in the CCD amplitude equations. Herein, I show that exchange contributions to ring and crossed-ring contractions (not small denominators per se) cause the divergent behavior of LinCC(S)D approaches. Rather than omitting exchange terms, I recommend a regular and size-consistent method that retains only linear ladder diagrams. As LinCCD and configuration interaction doubles (CID) equations are isomorphic, this also implies that simplification (rather than quadratic extensions) of CID amplitude equations can lead to a size-consistent theory. Linearized ladder CCD (LinLCCD) is robust in statically-correlated systems and can be made $O(n_{\text{occ}}^4n_{\text{vir}}^2)$ with a hole-hole approximation. The results presented here show that LinLCCD and its hole-hole approximation can accurately capture energy differences, even outperforming full CCD and CCSD for non-covalent interactions in small-to-medium sized molecules, setting the stage for further adaptations of these approaches that incorporate more dynamical correlation.

physics.chem-ph↗

arXiv2025

Towards ab initio Realizations of Collins' Conjecture

An ab initio approach formulated under an entropy-inspired repartitioning of the electronic Hamiltonian is presented. This ansatz produces orbital eigenvalues each shifted by entropic contributions expressed as subsets of scaled pair correlation energy terms present in second-order Moller-Plesset (MP) perturbation theory. Under the auspices of Collins' conjecture, which suggests that the electron correlation energy is approximately proportional to the Jaynes entropy of the one-electron density matrix, we introduce a parameter that controls the accuracy of the resultant one-electron density at the MP2 level. By tuning the density in a somewhat automated way, we achieve one-electron densities on par with those from full configuration interaction for single-bond dissociation. This parameter can then be used to add a Collins'-like static correlation correction to the energy functional, capturing both dynamical and nondynamical correlation effects in many-electron systems. The performance of the proposed method and its related variants approaches the accuracy of generalized valence bond theory for estimating single bond dissociation energies (BDEs) for set of small, closed-shell molecules composed of first and second row elements. Our results hold implications for reincorporating the missing (static) correlation energy in regularized perturbation theories that is typically discarded. Finally, we propose generic BDE parameters (accurate to within 7% on average) that could be used for strongly-correlated systems in general.

physics.chem-ph↗

arXiv2025

Optimal-Reference Excited State Methods: Static Correlation at Polynomial Cost with Single-Reference Coupled-Cluster Approaches

Accurate yet efficient modeling of chemical systems with pronounced static correlation in their excited states remains a significant challenge in quantum chemistry, as most electronic structure methods that can adequately capture static correlation scale factorially with system size. Researchers are often left with no option but to use more affordable methods that may lack the accuracy required to model critical processes in photochemistry such as photolysis, photocatalysis, and non-adiabatic relaxation. A great deal of work has been dedicated to refining single-reference descriptions of static correlation in the ground state via ``addition-by-subtraction'' coupled cluster methods such as pair coupled cluster with double substitutions (pCCD), singlet-paired CCD (CCD0), triplet-paired CCD (CCD1), and CCD with frozen singlet- or triplet-paired amplitudes (CCDf0/CCDf1). By combining wave functions derived from these methods with the intermediate state representation (ISR), we gain insights into the extensibility of single-reference coupled cluster theory's coverage of static correlation to the excited state problem. Our CCDf1-ISR(2) approach is robust in the face of static correlation and provides enough dynamical correlation to accurately predict excitation energies to within about 0.2~eV in small organic molecules. We also highlight distinct advantages of the Hermitian ISR construction, such as the avoidance of pathological failures of equation-of-motion methods for excited state potential energy surface topology. Our results prompt us to continue exploring optimal single-reference theories (excited state approaches that leverage dependence on the initial reference wave function) as a potentially economical approach to the excited state static correlation problem.

physics.chem-ph↗

arXiv2023

Optimizing the Regularization in Size-Consistent Second-Order Brillouin-Wigner Perturbation Theory

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ($α$) was set to recover the exact dissociation limit of H2 in a minimal basis set. Alternatively $α$ can be viewed as a regularization parameter, where each value of $α$ represents a valid variant of BW-s2, which we denote as BW-s2($α$). In this work, we semi-empirically optimize $α$ for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the $\textit{ab initio}$ parameterization of BW-s2 and MP2. We demonstrate that the optimal $α$ parameter ($α = 4$) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2($α$) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2($α$) is iterative $O(N^5)$, this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

physics.chem-ph↗

arXiv2023

Repartitioned Brillouin-Wigner Perturbation Theory with a Size-Consistent Second-Order Correlation Energy

Second-order Møller-Plesset perturbation theory (MP2) often breaks down catastrophically in small-gap systems, leaving much to be desired in its performance for myriad chemical applications such as noncovalent interactions, thermochemistry, and dative bonding in transition metal complexes. This divergence problem has reignited interest in Brillouin-Wigner perturbation theory (BWPT), which is regular at all orders but lacks size-consistency and extensivity, severely limiting its application to chemistry. In this work, we propose an alternative partitioning of the Hamiltonian that leads to a regular BWPT perturbation series that, through second order, is size-extensive, size-consistent (provided its Hartree-Fock reference is also), and orbital invariant. Our second-order size-consistent Brillouin-Wigner (BW-s2) approach is capable of describing the exact dissociation limit of H$_2$ in a minimal basis set regardless of the spin-polarization of the reference orbitals. More broadly, we find that BW-s2 offers improvements relative to MP2 for covalent bond breaking, noncovalent interaction energies, and metal/organic reaction energies, while rivaling coupled-cluster with single and double substitutions (CCSD) for thermochemical properties.

physics.chem-ph↗

arXiv2022

Electron-Affinity Time-Dependent Density Functional Theory: Formalism and Applications to Core-Excited States

The particle-hole interaction problem is longstanding within time-dependent density functional theory (TDDFT) and leads to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n-1-electron system as reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems.

physics.chem-ph↗

arXiv2022

Computing X-ray absorption spectra from linear-response particles atop optimized holes

State specific orbital optimized density functional theory (OO-DFT) methods like restricted open-shell Kohn-Sham (ROKS) can attain semiquantitative accuracy for predicting X-ray absorption spectra of closed-shell molecules. OO-DFT methods however require that each state be individually optimized. In this work, we present an approach to generate an approximate core-excited state density for use with the ROKS energy ansatz, that is capable of giving reasonable accuracy without requiring state-specific optimization. This is achieved by fully optimizing the core-hole through the core-ionized state, followed by use of electron-addition configuration interaction singles (EA-CIS) to obtain the particle level. This hybrid approach can be viewed as a DFT generalization of the static-exchange (STEX) method, and can attain $\sim 0.6$ eV RMS error for the K-edges of C-F through the use of local functionals like PBE and OLYP. This ROKS(STEX) approach can also be used to identify important transitions for full OO ROKS treatment, and can thus help reduce the computational cost for obtaining OO-DFT quality spectra. ROKS(STEX) therefore appears to be a useful technique for efficient prediction of X-ray absorption spectra.

physics.chem-ph↗