Study of correlation holes. II. CI calculations on model polyatomic systems

The shape of correlation holes in many-electron systems is at present scarcely known, even where correlated wave functions are available. We investigate here the kind of electron correlation brought about by configuration interaction (CI ), within a given basis set, in the wavefunction of a polyatomic system. The model ring system H₆ (in two different bonding circumstances) and H₁₄ have been chosen for a detailed study, because of their paradigmatic importance. We set out the equal-spin and different-spin correlation holes as obtained from complete CI calculations in H6 and partial ct in H₁₄, both within a minimal basis set. We basically find the spinless correlation as being short range, while the spin-dependent correlation holes show long-range oscillations of antiferromagnetic character. We also present a natural spin-geminal analysis of the two-body reduced density matrices in these systems; we find a peculiarity possibly related to the long-range correlation discussed above. Finally, we compare the electron correlation as given from our CI wavefunction to other pictures of electron correlation, as obtained essentially from alternant molecular orbital wave functions and from the electron–gas literature.     

Quantum Monte Carlo Calculation of Correlation Effects on Bond Orders

We present a computational approach, using quantum Monte Carlo, that provides some insight into the effect of electron correlation on chemical bonding between individual pairs of atoms. Our approach rests upon a recently suggested relation between the bond order and charge fluctuations with respect to atomic domains. Within the present implementation we have taken a compromise between conceptual rigour and computational simplicity. In a first step atomic domains were obtained from Hartree-Fock (HF) densities, using Bader’s definition of atoms in molecules. These domains were used in a second step in quantum Monte Carlo calculations to determine bond orders for pairs of atoms. Correlation effects have been studied by comparison of HF bond orders with those obtained from pure diffusion quantum Monte Carlo calculations. We illustrate this concept for C–O and C–S bonds in different molecular environments. Our results suggest an approximate linear relation between bond order and bond length for these kinds of bonds.     

Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb-Ba)+

We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.     

SPOCK.CI: a multireference spin-orbit configuration interaction method for large molecules

We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.     

大体系多电子相关研究中应用群对称定域轨道的构想

大体系多电子相关研究中应用群对称定域轨道的构想周泰锦，刘爱民（厦门大学化学系，厦门３６１００５）关键词：组态相关，多构型自治叠代，多中心积分，群对称定域轨道，对称约化有关原子簇化合物及化学吸附、过渡态、激发态、催化反应等大体系的量子化学研究，对于探讨...     

Spin–orbit and correlation effects in platinum hydride (PtH)

The low-lying electronic states of PtH were studied by all-electron one- and two-component variational calculations on the multireference CI levels. The orbital optimization is performed within a one-component formalism, whereas the further refinement of the wave functions follows two different schemes: The most demanding approach introduces spin–orbit coupling in the CI optimization step, giving a simultaneous treatment of electron correlation and spin–orbit coupling. The second, considerably less demanding approach, corresponds almost to a perturbational treatment, introducing spin–orbit coupling as a final step after the CI optimization by diagonalizing the resulting Hamiltonian matrix over CI states. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 53–64, 1998     

General implementation of the relativistic coupled-cluster method

We report the development of a general order relativistic coupled-cluster (CC) code. Our implementation is based on Kramers-paired molecular spinors, utilizes double group symmetry, and is applicable with the full Dirac-Coulomb and several approximate relativistic Hamiltonians. The available methods include iterative and perturbative single-reference CC approaches with arbitrary excitations as well as a state-selective multi-reference CC ansatz. To illustrate the performance of the new code, benchmark calculations have been performed for the total energies, bond lengths, and vibrational frequencies of the monoxides of Group IVa elements. The trends due to the simultaneous inclusion of relativity as well as higher-order electron correlation effects are analyzed. The newly developed code significantly widens the scope of the ab initio relativistic calculations, for both molecules and atoms alike, surpassing the accuracy and reliability of the currently available implementations in the literature.     

The generalized separated electron pair model. 1. An application to NH3

The utility of the separated electron pair (SEP ) model (strongly orthogonal geminals) is examined quantitatively, for pyramidal and planar nuclear configurations of the NH₃ molecule. The best SEP wave function computed for each species is capable of recovering about half of the correlation energy obtained by a fairly accurate configuration interaction (CI ) calculation, (corresponding to roughly 25% of the total molecular correlation energy). It is illustrated that the model can be systematically extended with only a modest effort to yield more accurate results (about 40% of the total correlation energy). The fact that the corrections to the SEP model have a simple physical interpretation suggests that this model may be a useful starting point for “brute force” CI calculations on larger chemical systems.     

Application of EPMA data for the development of the code systems TRANSURANUS and ALEPH.

In the present article, electron probe microanalysis data for Pu and Nd is being used for validating the predictions of the radial power profile in a nuclear fuel rod at an ultrahigh burn-up of 95 and 102 MWd/kgHM. As such the validation of both the new Monte Carlo burn-up code ALEPH and the simpler TUBRNP model of the fuel rod performance code TRANSURANUS has been extended. The analysis of the absolute concentrations and individual isotopes also indicates potential improvements in the predictive capabilities of the simple TUBRNP model, based on the one-group cross sections inferred from the neutron transport calculations in the ALEPH code. This is a first important step toward extending the application range of the fuel rod performance code to burn-up values projected in nuclear power rods based on current trends.     

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.     

The calculation of electron localization and delocalization indices at the Hartree–Fock, density functional and post-Hartree–Fock levels of theory

 Localization, λ(A), and delocalization indices, δ(A,B), as defined in the atoms in molecules theory, are a convenient tool for the analysis of molecular electronic structure from an electron-pair perspective. These indices can be calculated at any level of theory, provided that first- and second-order electron densities are available. In particular, calculations at the Hartree–Fock (HF) and configuration interaction (CI) levels have been previously reported for many molecules. However, λ(A) and δ(A,B) cannot be calculated exactly in the framework of Kohn–Sham (KS) density functional theory (DFT), where the electron-pair density is not defined. As a practical workaround, one can derive a HF-like electron-pair density from the KS orbitals and calculate approximate localization and delocalization indices at the DFT level. Recently, several calculations using this approach have been reported. Here we present HF, CI and approximate DFT calculations of λ(A) and δ(A,B) values for a number of molecules. Furthermore, we also perform approximate CI calculations using the HF formalism to obtain the electron-pair density. In general, the approximate DFT and CI results are closer to the HF results than to the CI ones. Indeed, the approximate calculations take into account Coulomb electron correlation effects on the first-order electron density but not on the electron-pair density. In summary, approximate DFT and CI localization and delocalization indices are easy to calculate and can be useful in the analysis of molecular electronic structure; however, one should take into account that this approximation increases systematically the delocalization between covalently bonded atoms, with respect to the exact CI results. Received: 13 February 2002 / Accepted: 24 April 2002 / Published online: 18 June 2002     

Radial limit of lithium revisited

Configuration interaction (CI) calculations are carried out for the ground state of lithium using a thoroughly optimized basis set of s-type Slater functions. They establish that the radial limit of the nonrelativistic energy of the ground ²S state of lithium is no higher than −7.448666443E_h. Thus, radial correlation accounts for 35.2% of the total correlation energy. The radial CI wave function predicts a significantly more accurate Fermi contact parameter than the Hartree-Fock wave function. However, the imbalanced treatment of electron correlation in the radial CI wave function leads to an excessively diffuse electron density that is worse than that of the Hartree-Fock wave function. © 1997 John Wiley & Sons, Inc.     

Direct selected multireference configuration interaction calculations for large systems using localized orbitals

A selected multireference configuration interaction (CI) method and the corresponding code are presented. It is based on a procedure of localization that permits to obtain well localized occupied and virtual orbitals. Due to the local character of the electron correlation, using local orbitals allows one to neglect long range interactions. In a first step, three topological matrices are constructed, which determine whether two orbitals must be considered as interacting or not. Two of them concern the truncation of the determinant basis, one for occupied/virtual, the second one for dispersive interactions. The third one concerns the truncation of the list of two electron integrals. This approach permits a fine analysis of each kind of approximation and induces a huge reduction of the CI size and of the computational time. The procedure is tested on linear polyene aldehyde chains, dissociation potential energy curve, and reaction energy of a pesticide-Ca(2+) complex and finally on transition energies of a large iron system presenting a light-induced excited spin-state trapping effect.     

Simulating the optical properties of CdSe clusters using the RT-TDDFT approach

The structural and electronic properties of the CdSe nanoclusters, which have been intended to model quantum dots, have been examined by means of time-dependent density functional (TDDFT) calculations. The optical spectra were first simulated using the standard linear response implementation of the TDDFT (LR-TDDFT) in a series of calculations performed using different basis sets and exchange–correlation functionals. In a second step, the real-time TDDFT implementation (RT-TDDFT) was used to simulate the optical absorption spectra of the CdSe nanoclusters, both naked and capped with ligands. In general, we found that the RT-TDDFT approach successfully reproduced the optical spectrum of CdSe clusters offering a good compromise to render both the optical and the geometrical properties of the CdSe clusters at lower computational costs. While for small systems, the standard TDDFT is better suited, for medium- to large-sized systems, the real-time TDDFT becomes competitive and more efficient.     

Excited states of linear polyenes in the SCF–RPA method

In the framework of the PPP Hamiltonian, we have studied the low-lying spectra of all trans linear polyenes with the dielectirc function method. It is shown that higher order processes, not included in the RPA scheme as local field correction (LFC) and self-energy (SE) effects can be introduced in a effective way by a suitable parametrization of the residual coulomb interaction. This parametrization is fixed along the polyene series both for singlet and triplet states, at variance with previous RPA calculations. Comparison with the most refined CI calculations, as well as with the experimental findings shows very good agreement. Furthermore, chain length and geometry dependence of the electron–electron correlation is briefly discussed.     

Correlation effects in the low–lying excited states of the PPP models of alternant hydrocarbons. I. Qualitative rules for the effect of limited configuration interaction

Simple rules for an estimate of the correlation effects in the low-lying states of alternant hydrocarbons, as described by the Pariser–Parr–Pople Hamiltonian, are formulated. These rules are based on the alternancy and spin symmetry classification of states in both strongly and weakly correlated limits and on the valence bond characteristics of those states in the fully correlated limit. It is shown that the largest effect of the electron correlation will be found for the singlet “minus” states (using Pariser's classification of the alternancy symmetry species), a smaller effect for the triplet “plus” states, and a much smaller effect for the remaining states. These rules are exemplified by limited CI calculations including all monoexcited and all mono- and bi-excited configurations, respectively, for a number of π-electronic systems. In view of these rules the success of the PPP model in the monoexcited CI approximation may be understood.     

The effect of electron correlation on the topological and atomic properties of the electron density distributions of molecules

The topological properties of the electron density and the properties of an atom in a molecule are calculated by means of second-order Møller-Plesset perturbation theory (MP2) and compared with the results of configuration interaction calculations (C12) which include all single and double substitutions from the Hartree-Fock reference configuration. A software package for analyzing the effects of electron correlation on the topological properties of the electron density of molecules is described. H₂CO is used to provide a numerical example and to indicate that the number of bond critical points is unaffected by the inclusion of electron correlation. Correlation leads to only a small shift in the positions of bond critical points and a small change in the electron density at bond critical points. It is further shown that the energy of an atom in a molecule can be calculated to an accuracy of 1 kcal/mol and the electron population of an atom to about 0.001e. A statistical method is used to show that the deviation of the MP2 correlation correction relative to the CI2 correlation correction for a variety of atomic properties is about 25%.     

A method to fast determine the coupling coefficients in CI calculation

A new algorithm for evaluating the coupling coefficients and the addresses of molecular integrals in configuration interaction (CI) calculations is presented, which leads to an improved CI calculation program CGUGA. The validity and efficiency of the new code are compared with other programs, such as MELD and GAUSSIAN-94.     

Hole-particle characterization of coupled-cluster singles and doubles and related models

The hole-particle analysis introduced in the paper [J. Chem. Phys. 124, 224109 (2006)] is fully described and extended for coupled-cluster models of practical importance. Based on operator renormalization of the conventional amplitudes t(ai) and t(ab,ij), we present a simplified method for estimating the hole-particle density matrices for coupled-cluster singles and doubles (CCSD). With this procedure we convert the first-order density matrix of the configuration interaction (CI) singles and doubles (CISD) model, which lacks size consistency, into an approximately size-consistent expression. This permits us to correctly estimate specific indices for CCSD, including the hole and particle occupation numbers for each atom, the total occupation of holes/particles, and the entropylike measure for effective unpaired geminals. Our calculations for simple diatomic and triatomic systems indicate reasonable agreement with the full CI values. For CCSD and CISD we derive special types of two-center indices, which are similar to the charge transfer analysis of excited states previously given within the CIS model. These new quantities, termed charge transfer correlation indices, reveal the concealed effects of atomic influence on electronic redistribution due to electron correlation.