Dynamic Electron Correlation Effects Research Articles

Simulation of Vibrational Circular Dichroism Spectra Using Second-Order Møller-Plesset Perturbation Theory and Configuration Interaction Doubles.

We present the first single-reference calculations of the atomic axial tensors (AATs) with wave function-based methods including dynamic electron correlation effects using second-order Møller-Plesset perturbation theory (MP2) and configuration interaction doubles (CID). Our implementation involves computing the overlap of numerical derivatives of the correlated wave functions with respect to both nuclear displacement coordinates and the external magnetic field. Out test set included three small molecules, including the axially chiral hydrogen molecule dimer and (P)-hydrogen peroxide, and the achiral H2O. For our molecular test set, we observed deviations of the AATs for MP2 and CID from that of the Hartree-Fock (HF) method upward of 49%, varying with the choice of basis set. For (P)-hydrogen peroxide, electron correlation effects on the vibrational circular dichroism (VCD) rotatory strengths and corresponding spectra were particularly significant, with maximum deviations of the rotatory strengths of 62 and 49% for MP2 and CID, respectively, using our largest basis set. The inclusion of dynamic electron correlation to the computation of the AATs can have a significant impact on the resulting rotatory strengths and VCD spectra.

Dynamical Electron Correlation and the Chemical Bond. IV. Covalent Bonds in A2 Molecules (A = N-As and F-Br).

In a series of recent papers, we investigated the effect of dynamical electron correlation on the potential energy curves and spectroscopic constants of several diatomic molecules, including the simple diatomic hydrides (AH) and the more complex diatomic fluorides (AF) and homonuclear diatomic molecules (A2) with A = B-F (AF) or A = C-F (A2), respectively. Our goal was to understand the dependence of the dynamical electron correlation energy, EDEC, on the internuclear distance, R, and quantify how dynamical electron correlation influences the spectroscopic constants (De, Re, and ωe) of these molecules. At large R, we found that the magnitude of EDEC(R) had a simple dependence on R, with EDEC(R) increasing nearly exponentially with decreasing R. However, as R continued to decrease, there were significant variations in EDEC(R). These variations led to differing changes in the predicted spectroscopic constants of the molecules. In many molecules, the changes in EDEC(R) could be correlated with changes in the underlying spin-coupled generalized valence bond wave function, either in the orbitals or the spin-coupling coefficients. In the current paper, we extend these studies to higher main group elements, comparing the effects of EDEC(R) on P2 and As2 versus N2, and on Cl2 and Br2 versus F2. We find that there are significant differences between the effects of dynamical electron correlation on the molecules in the first and subsequent rows of the periodic table.

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory.

Coupled cluster methods based exclusively on double excitations are comparatively "cheap" and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

Quantum chemical calculations of electron affinities of alkaline earth metal atoms (Ca, Sr, Ba, and Ra)

We performed high-level ab initio quantum chemical calculations, incorporating higher-order excitations, spin–orbit coupling (SOC), and the Gaunt interaction, to calculate the electron affinities (EAs) of alkaline earth (AE) metal atoms (Ca, Sr, Ba, and Ra), which are notably small. The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is insufficient to accurately calculate the EAs of AE metal atoms. Higher-order excitations proved crucial, with the coupled-cluster singles, doubles, and triples with perturbative quadruples [CCSDT(2)Q] method effectively capturing dynamic electron correlation effects. The contributions of SOC (ΔESOs) to the EAs calculated using the multireference configuration interaction method with the Davidson correction, including SOC, positively enhance the EAs; however, these contributions are overestimated. The Dirac–Hartree–Fock (DHF)-CCSD(T) method addresses this overestimation and provides reasonable values for ΔESO (ΔESO−D). Employing additional sets of diffuse and core–valence correlation basis sets is critical for accurately calculating the EAs of AE metal atoms. The contributions of the Gaunt interaction (ΔEGaunt) to the EAs of AE metal atoms are negligible. Notably, the CCSDT(2)Q with the complete basis set limit + ΔESO−D + ΔEGaunt produced EA values for Ca, Sr, and Ba that closely aligned with experimental data and achieved accuracy exceeding the chemical accuracy. Based on our findings, the accurately proposed EA for Ra is 9.88 kJ/mol.

Reassessing the Composition of Hybrid Orbitals in Contemporary VB Calculations.

Large variations in the ratios between the p and s components of individual hybrid orbitals that have been observed in contemporary ab initio VB calculations are reassessed, and links are established to specific energy terms that drive bond formation. It is demonstrated that the ratios between the p and s components for individual hybrid orbitals are not indicative of the overall hybridization status of the relevant atom, which exhibits only relatively small variations with the level of theory, irrespective of whether or not non-dynamical and dynamical electron correlation effects are accounted for. An alternative orbital representation that turns out to be far more consistent with the overall hybridization of the relevant atom is examined. The chosen test cases, which can be compared with the classical sp3, sp2, and sp hybridization models for a central carbon atom, are CH4 (Td), trigonal CH3 (D3h), and triplet CH2 distorted from its ground state geometry so as to be linear (D∞h).

Unraveling effects of electron correlation in two-dimensional FenGeTe2 (n = 3, 4, 5) by dynamical mean field theory

The FenGeTe2 systems are recently discovered two-dimensional van-der-Waals materials, exhibiting magnetism at room temperature. The sub-systems belonging to FenGeTe2 class are special because they show site-dependent magnetic behavior. We focus on the critical evaluation of magnetic properties and electron correlation effects in FenGeTe2 (n = 3, 4, 5) (FGT) systems performing first-principles calculations. Three different ab initio approaches have been used primarily, viz., (i) standard density functional theory (GGA), (ii) incorporating static electron correlation (GGA + U) and (iii) inclusion of dynamic electron correlation effect (GGA + DMFT). Our results show that GGA + DMFT is the more accurate technique to correctly reproduce the magnetic interactions, experimentally observed transition temperatures and electronic properties. The inaccurate values of magnetic moments, exchange interactions obtained from GGA + U make this method inapplicable for the FGT family. Correct determination of magnetic properties for this class of materials is important since they are promising candidates for spin transport and spintronic applications at room temperature.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy.

Obtaining the atomistic structure and dynamics of disordered condensed-phase systems from first-principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure and provide a data-efficient approach to obtain machine-learned condensed-phase potential energy surfaces using AFQMC, CCSD, and CCSD(T) from a very small number (≤200) of energies by leveraging a transfer learning scheme starting from lower-tier electronic structure methods. We demonstrate the effectiveness of this approach for liquid water by performing both classical and path integral molecular dynamics simulations on these machine-learned potential energy surfaces. By doing this, we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed-phase systems.

On the role of dynamic electron correlation in non-orthogonal configuration interaction with fragments.

Two different approaches have been implemented to include the effect of dynamic electron correlation in the Non-Orthogonal Configuration Interaction for Fragments (NOCI-F) method. The first is based on shifting the diagonal matrix elements of the NOCI matrix, while the second incorporates the dynamic correlation explicitly in the fragment wave functions used to construct the many-electron basis functions of the NOCI. The two approaches are illustrated for the calculation of the electronic coupling relevant in singlet fission and the coupling of spin moments in organic radicals. Comparison of the calculated diabatic couplings, the NOCI energies and wave functions shows that dynamic electron correlation is not only efficiently but also effectively incorporated by the shifting approach and can largely affect the coupling between electronic states. Also, it brings the NOCI coupling of the spin moments in close agreement with benchmark calculations.

Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost.

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N2, F2, C2, CN+, CO, BN, BO+, and Cr2) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

Electronic Structure and Electron Delocalization in Bare and Dressed Boron Pentamer Clusters.

The electronic structures of the lowest energy spin-states of the cationic, neutral and anionic bare boron pentamer clusters have been investigated by means of high level multiconfigurational type calculations, in view of the large static and dynamical electron correlation effects for these species. We found that resembles a singlet spin-state perfect pentagon, which bears no intra-annular chemical bonding interactions, as shown by our analysis of the electron delocalization carried out in terms of the normalized Giambiagi ring-current index, and the total and adjacent atom-pair delocalization indices. However, its lowest-energy triplet and quintet spin-state isomers have C2v symmetry, with large intra-annular chemical bonding interactions. This geometrical feature extends to both the neutral and the anionic species. Namely, the lowest-energy isomers of boron pentamer neutral and anionic clusters have peripheral and intra-annular sizable bonding interactions reflected in the delocalization of both π- and σ-type valence natural orbitals over the whole molecular plane, which impart large structural stability. In accordance to our calculations, the lowest energy triplet spin-state isomer of the anionic boron pentamer cluster has C2 symmetry, and consequently, it should show optical activity. Finally, we have studied the change of the geometrical structure of the boron pentamer clusters from planar to compact three-dimensional structures caused by the bonding of ligands to the boron atoms. Our explicit all-electron calculations have been rationalized in terms of the shell-closure of the delocalized valence orbitals of the clusters as predicted by the jellium model extended to nonspherical confinement potentials, circumscribing the role of the ligand to modulate the total number of valence electrons assigned to the core cluster.

Edge-state-induced correlation effects in two-color pump-probe high-order harmonic generation

We show that two-color high-harmonic spectroscopy can reveal finite-size and edge-state-induced dynamic electron correlation effects in a generic nanostructured band-gap material. Compared to the response of a bulk sample, we demonstrate a significant correlation-induced increase in the efficiency of the generated signal over a wide range of frequencies by harnessing the power of these ultrafast many-electron dynamics.

Multireference configuration interaction and coupled cluster study of Gold monosulfide (AuS) including spin–orbit coupling

A multireference configuration interaction with the Davidson correction (MRCI + Q) method, including spin–orbit coupling (SOC), was used to calculate the full potential energy curves of the various Ω states of AuS. The spectroscopic constants of the Ω states of AuS were also calculated and compared with the available experimental results. In general, the MRCI + Q+SOC gives qualitatively correct results but does not provide quantitatively accurate results. The unrestricted coupled cluster singles and doubles with perturbative triples (UCCSD(T)) with SOC describe well the molecular properties (bond lengths, vibrational frequencies, and Te values) of the Ω states. In particular, the bond length of the ground state (Ω = 3/2(2Π3/2(1)) (2.158 Å) calculated using the UCCSD(T)+SOC is in excellent agreement with the experimental values (2.156 ± 0.002 Å). Both the dynamic electron correlation effect and SOC are crucial to obtain accurate results. We correctly assigned the atomic asymptotes that are correlated with the Ω states and calculated the bond dissociation energies of various Ω states of AuS.

Modification and Validation of the DREIDING Force Field for Molecular Liquid Simulations (DREIDING-UT)

In this study, we modified Lennard-Jones (LJ) parameters and point-charge parameters of the DREIDING force field (the modified force-field model is named DREIDING-UT). While the original LJ parameters of DREIDING were derived through an analytical formula to reproduce the potential depths and the equilibrium lengths of the Buckingham potentials of DREIDING/X6, the modified LJ parameters were derived through the least square fitting of the Buckingham potentials. Because the Gasteiger-Marsili (GM) charges of the original DREIDING underestimated electrostatic interactions, we replaced it with the restrained electrostatic potential (RESP) charges calculated from the ab initio wavefunctions, taking the dynamic electron correlation and solvation effects into account. To confirm how the modified force field works, we conducted molecular dynamics (MD) simulations of typical liquids. It was found that the densities and self-diffusion coefficients of the DREIDING-UT model agreed with the experimental ones much better than those of the original model.

Ab Initio Nonadiabatic Molecular Dynamics with Hole-Hole Tamm-Dancoff Approximated Density Functional Theory.

The study of photoinduced dynamics in chemical systems necessitates accurate and computationally efficient electronic structure methods, especially as the systems of interest grow larger. The linear response hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory method was recently proposed to satisfy such demands. The N-electron electronic states are obtained by means of double annihilations on a doubly anionic (N + 2)-electron reference state, allowing for the ground and excited states to be formed on the same footing and thus enabling the correct description of conical intersections. Dynamic electron correlation effects are incorporated by means of the exchange-correlation functional. The accuracy afforded by the simultaneous treatment of static and dynamic correlation in addition to the relatively low computational cost, comparable to that of time-dependent density functional theory (TDDFT), makes it a promising ab initio electronic structure method for on-the-fly generation of potential energy surfaces in nonadiabatic dynamics simulations of photochemical systems, particularly those for which the nπ* and ππ* electronic excitations are most relevant. Here, we apply the hh-TDA method to nonadiabatic dynamics simulations of prototypical photochemical processes. First, we demonstrate the ability of hh-TDA to adequately describe conical intersection geometries. We next examine its ability to describe the ultrafast excited state dynamics of photoexcited ethylene through an ab initio multiple spawning (AIMS) dynamics simulation. Finally, we present an alternative variant of the hh-TDA method, which uses orbitals from a fractional occupation number Kohn-Sham (FON-KS) calculation applied to an ensemble with N-electrons. The resulting method is termed floating occupation molecular orbital hh-TDA (FOMO-hh-TDA). This scheme allows us to combine hh-TDA with global hybrid functionals and allows us to avoid unbound valence orbitals that may result from an (N + 2)-electron self-consistent field (SCF) procedure. FOMO-hh-TDA-BHLYP faithfully reproduces the nonadiabatic dynamics of trans-azobenzene (TAB) and is used to characterize the excited state decay pathways from the first (nπ*) excited state.

Hole-hole Tamm-Dancoff-approximated density functional theory: A highly efficient electronic structure method incorporating dynamic and static correlation.

The study of photochemical reaction dynamics requires accurate as well as computationally efficient electronic structure methods for the ground and excited states. While time-dependent density functional theory (TDDFT) is not able to capture static correlation, complete active space self-consistent field methods neglect much of the dynamic correlation. Hence, inexpensive methods that encompass both static and dynamic electron correlation effects are of high interest. Here, we revisit hole-hole Tamm-Dancoff approximated (hh-TDA) density functional theory for this purpose. The hh-TDA method is the hole-hole counterpart to the more established particle-particle TDA (pp-TDA) method, both of which are derived from the particle-particle random phase approximation (pp-RPA). In hh-TDA, the N-electron electronic states are obtained through double annihilations starting from a doubly anionic (N+2 electron) reference state. In this way, hh-TDA treats ground and excited states on equal footing, thus allowing for conical intersections to be correctly described. The treatment of dynamic correlation is introduced through the use of commonly employed density functional approximations to the exchange-correlation potential. We show that hh-TDA is a promising candidate to efficiently treat the photochemistry of organic and biochemical systems that involve several low-lying excited states-particularly those with both low-lying ππ* and nπ* states where inclusion of dynamic correlation is essential to describe the relative energetics. In contrast to the existing literature on pp-TDA and pp-RPA, we employ a functional-dependent choice for the response kernel in pp- and hh-TDA, which closely resembles the response kernels occurring in linear response and collinear spin-flip TDDFT.

Reduced Density Matrix-Driven Complete Active Apace Self-Consistent Field Corrected for Dynamic Correlation from the Adiabatic Connection.

The recently proposed multireference adiabatic connection (AC) formalism [Pernal, Phys. Rev. Lett. 120, 013001 (2018)] is applied to recover dynamic electron correlation effects lacking in variational two-electron reduced density matrix (v2RDM)-driven complete active space self-consistent field theory (CASSCF). The AC approach is validated by computing potential energy curves for the dissociation of molecular nitrogen and the symmetric double dissociation of H2O while enforcing two sets of approximate N-representability conditions in the underlying v2RDM-driven CASSCF calculations (either two-particle or two-particle plus partial three-particle conditions). The AC yields smaller absolute errors than second-order N-electron perturbation theory (NEVPT2) at all molecular geometries for both sets of the N-representability conditions considered. The efficacy of the approach for thermochemistry is also assessed for a set of 31 small-molecule reactions. When imposing partial three-particle N-representability conditions, mean and maximum unsigned errors in reaction energies from the AC are superior to those from NEVPT2.

Theoretical Investigation of Excited-State Intramolecular Proton Transfer and Photoisomerization of 2-(Iminomethyl)phenol.

Time-dependent density functional theory and high-level ab initio calculations were performed to investigate the excited-state intramolecular proton transfer (ESIPT) and subsequent isomerization of 2-(iminomethyl)phenol (IMP). According to the results of the correlated theoretical methods, ESIPT is a barrierless process; subsequently, the isomerization (rotation of the torsion angle) of IMP also readily occurs. Fictitious intermediates are found due to an insufficient theoretical level. The molecular structure of the conical intersection (CI) during the isomerization process is optimized, and its branching plane is characterized. Both the gradient difference vector and the derivative coupling vector are significantly correlated to the C═O and H2N-C antiparallel stretching coordinates, and the dynamic electron correlation effect is crucial to optimize the molecular structure of the real CI of IMP. The relaxation pathway from the CI in the S0 state was examined; the dominant pathway proceeds to the trans-keto form of IMP. However, if the C═O and H2N-C antiparallel stretching mode is sufficiently populated, then the reaction proceeds to the cis-keto form of IMP and can eventually recover to the cis-enol form.

Computing the Ultrafast and Radiationless Electronic Excited State Decay of Cytosine and 5‐methyl‐cytosine Cations: Uncovering the Role of Dynamic Electron Correlation

AbstractPhotoionisation in DNA, i. e. the process of photoinduced electron removal from the chromophoric species – the nucleobases – leading to their cationic form, has been scarcely studied despite being considered to be responsible for significant damaging instances in our genetic material. In this contribution we theoretically characterise the electronic ground and excited state decay pathways of cationic DNA nucleobase cytosine+ and its epigenetic derivative 5‐methyl‐cytosine+, including the effects of dynamic electron correlation on energies and geometries of minima and conical intersections. We do this by comparing the results of XMS‐CASPT2 calculations with CASSCF estimates and we find some significant differences between the results of these two methods. In particular, including dynamic electron correlation is found to significantly reduce the barrier to access the conical intersection. We find notable similarities in both cytosine and 5‐methyl‐cytosine cations, and accessible conical intersections in the vicinity of the Franck‐Condon region are found. This points towards an ultrafast depopulation of their electronic excited states. Moreover, the shape of the ground state potential energy surface strongly directs the decaying excited state population towards the cationic ground state minimum on ultrafast timescales, preventing photo‐fragmentation and thus explaining their photostability. To better compare our calculations with the available experimental data we compute the UV (ground and excited state) and IR absorptions.

Benchmarking the Accuracy of Seniority-Zero Wave Function Methods for Noncovalent Interactions.

In this paper, we scrutinize the ability of seniority-zero wave function-based methods to model different types of noncovalent interactions, such as hydrogen bonds, dispersion, and mixed noncovalent interactions as well as prototypical model systems with various contributions of dynamic and static electron correlation effects. Specifically, we focus on the pair Coupled Cluster Doubles (pCCD) ansatz combined with two different flavors of dynamic energy corrections, (i) based on a perturbation theory correction and (ii) on a linearized coupled cluster ansatz on top of pCCD. We benchmark these approaches against the A24 data set [ Řezáč and Hobza J. Chem. Theory Comput. 2013 , 9 , 2151 - 2155 .] extrapolated to the basis set limit and some model noncovalent complexes that feature covalent bond breaking. By dissecting different types of interactions in the A24 data set within the Symmetry-Adapted Perturbation Theory (SAPT) framework, we demonstrate that pCCD can be classified as a dispersion-free method. Furthermore, we found that both flavors of post-pCCD approaches represent encouraging and computationally more efficient alternatives to standard electronic structure methods to model weakly bound systems, resulting in small statistical errors. Finally, a linearized coupled cluster correction on top of pCCD proved to be most reliable for the majority of investigated systems, featuring smaller nonparallelity errors compared to perturbation-theory-based approaches.

Ultrafast and radiationless electronic excited state decay of uracil and thymine cations: computing the effects of dynamic electron correlation.

In this article we characterise the radiationless decay of the first few electronic excited states of the cations of DNA/RNA nucleobases uracil and thymine, including the effects of dynamic electron correlation on energies and geometries (optimised with XMS-CASPT2). In both systems, we find that one state of 2n and another two of 2π+ character can be populated following photoionisation, and their different minima and interstate crossings are located. We find strong similarities between uracil and thymine cations: with accessible conical intersections suggesting that depopulation of their electronic excited states takes place on ultrafast timescales in both systems, suggesting that they are photostable in agreement with previous theoretical (uracil+) evidence. We find that dynamic electron correlation separates the energy levels of the "3-state" conical intersection (D2/D1/D0)CI previously located with CASSCF for uracil+, which will therefore have a different geometry and higher energy. Simulating the electronic and vibrational absorptions allows us to characterise spectral fingerprints that could be used to monitor these cation photo-processes experimentally.