Electron Correlation Calculations Research Articles

Electron correlation effects on uranium isotope fractionation in U(VI)-U(VI) and U(IV)-U(VI) equilibrium isotopic exchange systems.

Uranium isotope fractionation has been extensively investigated in the fields of nuclear engineering and geochemical studies, yet the underlying mechanisms remain unclear. This study assessed isotope fractionations in U(VI)-U(VI) and U(IV)-U(VI) systems by employing various relativistic electron correlation methods to explore the effect of electron correlation and to realize accurate calculations of isotope fractionation coefficients (ε). The nuclear volume term, ln Knv, the major term in ε, was estimated using the exact two-component relativistic Hamiltonian in conjunction with either HF, DFT(B3LYP), MP2, CCSD, CCSD(T), FSCCSD, CASPT2, or RASPT2 approaches for small molecular models with high symmetry. In contrast, chemical species studied in prior experimental work had moderate sizes and were asymmetrical. In such cases, electron correlation calculations other than DFT calculations were not possible and so only the HF and B3LYP approaches were employed. For closed-shell U(VI)-U(VI) systems, the MP2, CCSD and CCSD(T) methods yielded similar ln Knv values that were intermediate between those for the HF and B3LYP methods. Comparisons with experimental results for U(VI)-U(VI) systems showed that the B3LYP calculations gave results closer to the experimental data than the HF calculations. Because of the open-shell structure of U(IV), multireference methods involving the FSCCSD, CASPT2 and RASPT2 techniques were used for U(IV)-U(VI) systems, but these calculations exhibited instability. The average-of-configuration HF method showed better agreement with the experimental ε values for U(IV)-U(VI) systems than the B3LYP method. Overall, electron correlation improved the description of ε for the U(VI)-U(VI) systems but challenges remain with regard to open-shell U(IV) calculations because an energy accuracy of 10-6-10-7Eh is required for ln Knv calculations.

Substituent Effects on Torsional Strain in Cyclopentene Derivatives: A Computational Study.

Density functional theory calculations were used to create a library of ring strain energies (RSEs) for 73 cyclopentene derivatives with potential use as monomers for ring-opening metathesis polymerization (ROMP). An overarching goal was to probe how substituent choice may influence torsional strain, which is the driving force for ROMP and one of the most understudied types of RSEs. Potential trends investigated include substituent location, size, electronegativity, hybridization, and steric bulk. Using traditional and recently developed homodesmotic equations, our results show that the size and substitution (bulk) of the atom directly bonded to the ring have the greatest influence on torsional RSE. A complex interplay between bond length, bond angle, and dihedral angle dictates the relative eclipsed conformations between the substituent and its neighboring hydrogens and was found to be responsible for the notable differences in RSEs. Furthermore, substituents placed on the homoallylic position resulted in higher RSEs than the same substituent placed on the allylic position due to increased eclipsing interactions. Different levels of theory were also assessed, and it was determined that consideration of electron correlation in calculations increased RSEs by ∼2-5 kcal mol-1. Further increasing the level of theory did not significantly change RSEs, indicating that the increased computational cost and time may not be necessary for improved accuracy.

Kylin 1.0: An ab-initio density matrix renormalization group quantum chemistry program.

The accurate evaluation of electron correlations is highly necessary for the proper descriptions of the electronic structures in strongly correlated molecules, ranging from bond-dissociating molecules, polyradicals, to large conjugated molecules and transition metal complexes. For this purpose, in this paper, a new ab-initio quantum chemistry program Kylin 1.0 for electron correlation calculations at various quantum many-body levels, including configuration interaction (CI), perturbation theory (PT), and density matrix renormalization group (DMRG), is presented. Furthermore, fundamental quantum chemistry methods such as Hartree-Fock self-consistent field (HF-SCF) and the complete active space SCF (CASSCF) are also implemented. The Kylin 1.0 program possesses the following features: (1) a matrix product operator (MPO) formulation-based efficient DMRG implementation for describing static electron correlation within a large active space composed of more than 100 orbitals, supporting both and symmetries; (2) an efficient second-order DMRG-self-consistent field (SCF) implementation; (3) an externally contracted multi-reference CI (MRCI) and Epstein-Nesbet PT with DMRG reference wave functions for including the remaining dynamic electron correlation outside the large active spaces. In this paper, we introduce the capabilities and numerical benchmark examples of the Kylin 1.0 program.

Cluster-in-Molecule Method Combined with the Domain-Based Local Pair Natural Orbital Approach for Electron Correlation Calculations of Periodic Systems.

The cluster-in-molecule (CIM) method was extended to systems with periodic boundary conditions (PBCs) in a previous work (PBC-CIM) [J. Chem. Theory Comput.2019, 15, 2933], which is able to compute the electronic structures of periodic systems at second-order Møller-Plesset perturbation theory (MP2) and coupled cluster singles and doubles (CCSD) levels. However, the high computational costs of CCSD with respect to the size of clusters limit the usage of PBC-CIM to crystals with small or medium unit cells. In this work, we further develop the PBC-CIM method by employing the domain-based local pair natural orbital (DLPNO) methods for the electron correlation calculations of clusters to reduce the computational costs. The combined approach allows CCSD with perturbative triples, denoted as CCSD(T), to be computationally available for accurate descriptions of periodic systems. The distant-pair correction is also implemented to improve the accuracy of PBC-CIM. As in the molecular cases, the distant pair correction significantly improves the accuracy of various PBC-CIM methods with few additional costs. The PBC-CIM-DLPNO-CCSD(T) approach has been applied to investigate the optimized lattice parameter of the cubic LiCl crystal and two adsorption problems (CO on the NaCl(100) surface and H2O on the h-BN surface). The results show that the CIM-DLPNO-CCSD(T) method offers accurate and efficient descriptions for the studied systems. Another application to the cohesive energy of the acetic acid crystal reveals that large basis sets are necessary for reliable calculations on the cohesive energies of molecular crystals.

Dynamic Cooperativity of Ligand-Residue Interactions Evaluated with the Fragment Molecular Orbital Method.

By the splendid advance in computation power realized with the Fugaku supercomputer, it has become possible to perform ab initio fragment molecular orbital (FMO) calculations for thousands of dynamic structures of protein-ligand complexes in a parallel way. We thus carried out electron-correlated FMO calculations for a complex of the 3C-like (3CL) main protease (Mpro) of the new coronavirus (SARS-CoV-2) and its inhibitor N3 incorporating the structural fluctuations sampled by classical molecular dynamics (MD) simulation in hydrated conditions. Along with a statistical evaluation of the interfragment interaction energies (IFIEs) between the N3 ligand and the surrounding amino-acid residues for 1000 dynamic structure samples, in this study we applied a novel approach based on principal component analysis (PCA) and singular value decomposition (SVD) to the analysis of IFIE data in order to extract the dynamically cooperative interactions between the ligand and the residues. We found that the relative importance of each residue is modified via the structural fluctuations and that the ligand is bound in the pharmacophore in a dynamic manner through collective interactions formed by multiple residues, thus providing new insight into structure-based drug discovery.

Structures and Spectroscopic Properties of Large Molecules and Condensed-Phase Systems Predicted by Generalized Energy-Based Fragmentation Approach.

ConspectusThe structures and spectroscopic properties of molecules and condensed-phase systems are usually experimentally characterized by X-ray, infrared (IR), Raman, nuclear magnetic resonance (NMR), and electronic absorption/emission spectra. Quantum mechanics (QM) calculations are critical in quantitatively understanding the relationship between the structure and physicochemical properties of various chemical systems. However, it is very challenging to apply traditional QM methods to large molecules and condensed-phase systems with large unit cells due to their steep computational scaling with the system size. To overcome this difficulty, theoretical chemists have developed various linear (or low) scaling QM methods, among which energy-based fragmentation methods have achieved great success for large molecules or clusters. One of the most popular energy-based fragmentation methods is the generalized energy-based fragmentation (GEBF) approach developed by us.In this approach, the ground-state energy of a large molecule can be evaluated from the ground-state energies of a series of embedded subsystems. In this Account, we focus on the recent developments and applicability of the GEBF approach for the structures and spectroscopic properties of complicated large molecules and condensed-phase systems. With new fragmentation schemes, the GEBF approach can now describe ionic liquid clusters and metal-containing supramolecular systems accurately and can provide accurate binding energies for host-guest complexes. In addition, the GEBF approach is now available for describing the localized excited states of large systems including a chromophore. More importantly, the GEBF approach under periodic boundary conditions (PBC-GEBF) has been developed to deal with periodic molecular crystals and liquids. Then, the ground-state energy (or property) per unit cell of a periodic condensed phase system can be predicted with QM calculations on nonperiodic embedded subsystems. This feature enables accurate electron correlation calculations on molecular crystals and liquids to be feasible on ordinary workstations. The PBC-GEBF approach has been applied to predict the crystal structures, lattice energies, and spectroscopic properties of some typical molecular crystals and solutions. By combining the GEBF method and machine learning (ML) method, a GEBF-ML force field has been developed for long normal alkanes, and the IR spectra of long alkanes can be obtained from the GEBF-ML molecular dynamics (MD) simulations. The GEBF and its periodic variant are expected to play increasingly important roles in investigating real-life chemical systems of broad interests at the ab initio levels.

First-principle calculation of electronic and optical properties of VO2 by GGA-1/2 quasiparticle approximation

Correctly elucidating the strong electron correlations of vanadium dioxide (VO2) is of great significance to understand the physics of the metal–insulator transition (MIT) and develop potential applications of VO2. Standard density functional theory is believed to be inappropriate to describe the MIT of VO2. Herein, the recently developed GGA-1/2 quasiparticle approximation is employed to perform first-calculations on VO2. The electronic structures of the metallic and insulating phases of VO2 are well described. The GGA-1/2 calculations indicate that the preferential occupancy of the d// orbitals leads to strong Mott–Hubbard correlation, which induces the splitting of the d// orbitals and the MIT of VO2. The calculations on electron energy-loss function reveal that the satellite electronic energy-loss spectroscopy peak of metallic phase VO2 is resulting from the plasma resonance. This work demonstrates that the GGA-1/2 approach facilitates the electron correlation calculations of VO2 and suggests that the strong Coulomb correlation is necessary to trigger the MIT.

Efficient Treatment of Correlation Energies at the Basis-Set Limit by Monte Carlo Summation of Continuum States.

The calculation of electron correlation is vital for the description of atomistic phenomena in physics, chemistry, and biology. However, accurate wavefunction-based methods exhibit steep scaling and often sluggish convergence with respect to the basis set at hand. Because of their delocalization and ease of extrapolation to the basis-set limit, plane waves would be ideally suited for the calculation of basis-set limit correlation energies. However, the routine use of correlated wavefunction approaches in a plane-wave basis set is hampered by prohibitive scaling due to a large number of virtual continuum states and has not been feasible for all but the smallest systems, even if substantial computational resources are available and methods with comparably beneficial scaling, such as the Møller–Plesset perturbation theory to second order (MP2), are used. Here, we introduce a stochastic sampling of the MP2 integrand based on Monte Carlo summation over continuum orbitals, which allows for speedups of up to a factor of 1000. Given a fixed number of sampling points, the resulting algorithm is dominated by a flat scaling of . Absolute correlation energies are accurate to <0.1 kcal/mol with respect to conventional calculations for several hundreds of electrons. This allows for the calculation of unbiased basis-set limit correlation energies for systems containing hundreds of electrons with unprecedented efficiency gains based on a straightforward treatment of continuum contributions.

Stabilization of Plutonium(V) Within a Crown Ether Inclusion Complex

Crystalline coordination complexes of actinides, especially in atypical oxidation states, are not only fundamentally important for expanding the notably limited knowledge on the bonding nature of a...

Pariser–Parr–Pople Model Based Configuration-Interaction Study of Linear Optical Absorption in Lower-Symmetry Polycyclic Aromatic Hydrocarbon Molecules

The electronic and optical properties of various polycyclic aromatic hydrocarbons (PAHs) with lower symmetry, namely, benzo[ghi]perylene (C22H12), benzo[a]coronene (C28H14), naphtho[2,3a]coronene (C32H16), anthra[2,3a]coronene (C36H18), and naphtho[8,1,2-abc]coronene (C30H14), were investigated. We performed electron-correlated calculations using screened and standard parameters in the π-electron Pariser–Parr–Pople (PPP) Hamiltonian, and the correlation effects were included, both for ground and excited states, using multireference singles–doubles configuration-interaction (MRSDCI) methodology. The PPP model Hamiltonian includes long-range Coulomb interactions, which increase the accuracy of our calculations. The results of our calculations predict that, with the increasing sizes of the coronene derivatives, optical spectra are red-shifted, and the optical gaps decrease. In each spectrum, the first peak representing the optical gap is of moderate intensity, while the more intense peaks appear at higher energies. Our computed spectra are in good agreement with the available experimental data. For the purpose of comparison, we also performed first-principles time-dependent density-functional theory (TDDFT) calculations of the optical gaps of these molecules using Gaussian basis functions and found that they yielded values lower than our configuration-interaction (CI) results.

Correction to "Systematic First-Principles Configuration-Interaction Calculations of Linear Optical Absorption Spectra in Silicon Hydrides: Si2H2n (n = 1-3)".

We have performed first-principles electron-correlated calculations employing large basis sets to optimize the geometries and to compute linear optical absorption spectra of various low-lying conformers of silicon hydrides: Si2H2n, n = 1, 2, 3. The geometry optimization for various isomers was carried out at the coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] level of theory, while their excited states and absorption spectra were computed using a large-scale multireference singles-doubles configuration-interaction approach, which includes electron-correlation effects at a sophisticated level. Our calculated spectra are the first ones for Si2H2 and Si2H4 conformers, while for Si2H6, we obtain excellent agreement with the experimental measurements, suggesting that our computational approach is reliable. Our calculated absorption spectra exhibit a strong structure-property relationship, suggesting the possibility of identifying various conformers based on their optical absorption fingerprints. Furthermore, we have also performed geometry optimization for the selected optically excited states, providing insights into their character.

Systematic First-Principles Configuration-Interaction Calculations of Linear Optical Absorption Spectra in Silicon Hydrides: Si2H2n (n = 1-3).

We have performed first-principles electron-correlated calculations employing large basis sets to optimize the geometries and to compute linear optical absorption spectra of various low-lying conformers of silicon hydrides: Si2H2n, n = 1, 2, 3. The geometry optimization for various isomers was carried out at the coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] level of theory, while their excited states and absorption spectra were computed using a large-scale multireference singles-doubles configuration-interaction approach, which includes electron-correlation effects at a sophisticated level. Our calculated spectra are the first ones for Si2H2 and Si2H4 conformers, while for Si2H6, we obtain excellent agreement with the experimental measurements, suggesting that our computational approach is reliable. Our calculated absorption spectra exhibit a strong structure-property relationship, suggesting the possibility of identifying various conformers based on their optical absorption fingerprints. Furthermore, we have also performed geometry optimization for the selected optically excited states, providing insights into their character.

Analytic evaluation of first-order properties within the mean-field variant of spin-free exact two-component theory.

We present a scheme for the calculation of energies and analytic energy gradients within spin-free exact two-component (SFX2C) theory in its mean-field variant, which we refer to as SFX2C-mf. In the presented scheme, the Foldy-Wouthuysen transformation is carried out after the spin-free four-component Hartree-Fock treatment such that in electron-correlated calculations only the non-mean-field part of the two-electron interactions is handled in an untransformed manner. The formulation of analytic gradients requires some adjustments in comparison with the nonrelativistic case, i.e., the additional solution of the spin-free Dirac Coulomb coupled-perturbed Hartee-Fock equations together with a simplified treatment of orbital relaxation at the SFX2C-mf level. The improved accuracy of SFX2C-mf in comparison with SFX2C-1e is demonstrated in the calculation of energies, dipole moments, and electric-field gradients for the hydrogen halides HX, X = F-At. It is shown that the main contribution to the improvement stems from the elimination of the error at the Hartree-Fock (HF) level; however, the corresponding correlation contribution is also improved such that SFX2C-mf can be considered a suitable scheme for the treatment of heavy-element compounds for which the error of SFX2C-1e is rather substantial.

Excited States and Optical Properties of Hydrogen-Passivated Rectangular Graphenes: A Computational Study

In this paper, we perform large-scale electron-correlated calculations of optoelectronic properties of rectangular graphene-like polycyclic aromatic hydrocarbon molecules. Theoretical methodology employed in this work is based upon Pariser-Parr-Pople (PPP) π-electron model Hamiltonian, which includes long-range electron-electron interactions. Electron-correlation effects were incorporated using multi-reference singles-doubles configurationinteraction (MRSDCI) method, and the ground and excited state wave functions thus obtained were employed to calculate the linear optical absorption spectra of these molecules, within the electric-dipole approximation. As far as the ground state wave functions of these molecules are concerned, we find that with the increasing size, they develop a strong diradical open-shell character. Our results on optical absorption spectra are in very good agreement with the available experimental results, outlining the importance of electron-correlation effects in accurate description of the excited states. In addition to the optical gap, spin gap of each molecule was also computed using the same methodology. Calculated spin gaps exhibit a decreasing trend with the increasing sizes of the molecules, suggesting that the infinite graphene has a vanishing spin gap.

Cluster-in-Molecule Local Correlation Approach for Periodic Systems.

In this article, the cluster-in-molecule (CIM) local correlation approach for periodic systems with periodic boundary condition has been developed, which allows electron-correlation calculations of various crystals computationally tractable. In this approach, the correlation energy per unit cell of a periodic system can be evaluated as the summation of the correlation contributions from electron-correlation calculations on a series of finite-sized clusters. Each cluster is defined to contain a subset of localized Wannier functions (WFs) (for the occupied space) and projected atomic orbitals (for the virtual space), which can be derived from a periodic Hartree-Fock calculation. Electron-correlation calculations on clusters at second-order Møller-Plesset perturbation theory (MP2) or coupled cluster singles and doubles (CCSD) can be performed with well-established molecular quantum chemistry packages. We perform illustrative calculations at the MP2 and CCSD levels on several types of crystals (neon lattice, carbon monoxide and ammonia crystals, two ionic liquid crystals, and diamond). The results show that CIM is a powerful framework for accurate electron-correlation calculations of crystals.

Fully optimized implementation of the cluster-in-molecule local correlation approach for electron correlation calculations of large systems.

A fully optimized implementation of the cluster-in-molecule (CIM) local correlation method for faster and more accurate electron correlation calculations of large systems is reported. The speedup comes from the new procedure of constructing virtual localized molecular orbitals of clusters. In the new procedure, Boughton-Pulay projection method is employed instead of a much more expensive Boys localization procedure. In addition, basis set superposition error correction for binding energy calculations and parallelized electron correlation calculations of clusters are now implemented. Benchmark calculations and illustrative applications at the Møller-Plesset perturbation theory, coupled cluster singles and doubles (CCSD), and CCSD with perturbative triples correction levels show that this newly optimized CIM approach is a reliable theoretical tool for electron correlation calculations of various large chemical systems. © 2018 Wiley Periodicals, Inc.

Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction.

We present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix-vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 1016 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2-5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.

First principles electron-correlated calculations of optical absorption in magnesium clusters

In this paper, we report large-scale configuration interaction (CI) calculations of linear optical absorption spectra of various isomers of magnesium clusters Mg$_{n}$ (n=2--5), corresponding to valence transitions. Geometry optimization of several low-lying isomers of each cluster was carried out using coupled-cluster singles doubles (CCSD) approach, and these geometries were subsequently employed to perform ground and excited state calculations using either the full-CI (FCI) or the multi-reference singles-doubles configuration interaction (MRSDCI) approach, within the frozen-core approximation. Our calculated photoabsorption spectrum of magnesium dimer (Mg$_{2}$) isomer is in excellent agreement with the experiments both for peak positions, and intensities. Owing to the sufficiently inclusive electron-correlation effects, these results can serve as benchmarks against which future experiments, as well as calculations performed using other theoretical approaches, can be tested.

Zeroth order regular approximation approach to electric dipole moment interactions of the electron.

A quasi-relativistic two-component approach for an efficient calculation of P,T-odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock and a complex generalized Kohn-Sham scheme within the zeroth order regular approximation. In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electric field acting on the unpaired electron for RaF, BaF, YbF, and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.

Theory of linear optical absorption in diamond-shaped graphene quantum dots

In this paper, optical and electronic properties of diamond-shaped graphene quantum dots (DQDs) have been studied by employing large-scale electron-correlated calculations. The computations have been performed using the $\ensuremath{\pi}$-electron Pariser-Parr-Pople model Hamiltonian, which incorporates long-range Coulomb interactions. The influence of electron-correlation effects on the ground and excited states has been included by means of the configuration-interaction approach used at various levels. Our calculations have revealed that the absorption spectra are redshifted with the increasing sizes of quantum dots. It has been observed that the first peak of the linear optical absorption, which represents the optical gap, is not the most intense peak. This result is in excellent agreement with the experimental data, but in stark contrast to the predictions of the tight-binding model, according to which the first peak is the most intense peak, pointing to the importance of electron-correlation effects.