Fock Space Multi-reference Coupled-cluster Research Articles

An Intruder-Free Fock Space Coupled-Cluster Study of the Potential Energy Curves of LiMg+ within the (2,0) Sector.

The potential energy curves (PECs) and spectroscopic constants of the ground and excited states of a LiMg+ molecular cation were investigated. We obtained accurate results for the fifteen lowest-lying states of the LiMg+ cation using the Intermediate Hamiltonian Fock Space Multireference Coupled Cluster (IH-FS-CC) method applied to the (2,0) sector. Relativistic corrections were accounted for using the third-order Douglas-Kroll method. In each instance, smooth PECs were successfully computed across the entire range of interatomic distances from equilibrium to the dissociation limit. The results are in good accordance with previous studies of this molecular cation. Notably, this study marks the first application of IH-FS-CC in investigating a mixed alkali and alkaline earth molecular cation, proving its usability in determining accurate PECs of such diatomics and their spectroscopic constants.

Theoretical investigations of electronic spectra of silver atom using all-electron scalar relativistic basis

Exploration of the tractable size basis set that can provide reliable estimates of computed properties for systems containing heavy elements has been the subject of interest in quantum chemistry over many decades. In this connection, the recently developed segmented all-electron relativistically contracted (SARC) basis set proposed by Rolfes et al. [J. Comput. Chem. 41, 1842 (2020)] appears to be worth studying. In the present attempt, ground and excited state properties of the Ag atom is computed on this basis at the Fock-space multi-reference coupled cluster (FSMRCC) level of theory with four-component relativistic spinors. The computed quantities resulting from the SARC basis are subsequently compared with those obtained using an even-tempered basis to assess the efficacy of the SARC basis. Computations have also been performed with the extended SARC basis to improve the quality of the property of interest. The accuracy of the computed quantities such ionization energy, electron affinity, excitation energies, etc., obtained using the SARC basis at the FSMRCC level of theory demonstrates that the SARC basis (particularly the extended one), which is primarily designed for quantum chemical calculations at the two-component scalar relativistic level for systems containing heavy atoms, can be used for fully relativistic calculations. The magnetic dipole hyperfine structure constant A, oscillator strengths f and transition rates Afi calculated using the SARC basis also agree well with the experiment and with the available theoretical estimates.

Three-Body Excitations in Fock-Space Coupled-Cluster: Fourth Order Perturbation Correction to Electron Affinity and Its Relation to Bondonic Formalism.

In this paper, we present a formulation of highly correlated Fock-space multi-reference coupled-cluster (FSMRCC) methods, including approximate triples on top of the FSMRCC with singles and doubles, which correct the electron affinities by at least at third and up to the fourth order in perturbation. We discuss various partial fourth-order schemes, which are reliable and yet computationally more efficient than the full fourth-order triples scheme. The third-order scheme is called MRCCSD+T*(3). We present two approximate fourth-order schemes, MRCCSD+T*−a(4) and MRCCSD+T*(4). The results that are presented allow one to choose an appropriate fourth-order scheme, which is less expensive and right for the problem. All these schemes are based on the effective Hamiltonian scheme, and provide a direct calculation of the vertical electron affinities. We apply these schemes to a prototype Li2 molecule, using four different basis sets, as well as BeO and CH+. We have calculated the vertical electron affinities of Li2 at the geometry of the neutral Li2 molecule. We also present the vertical ionization potentials of the Li2 anion at the geometry of the anion ground state. We have also shown how to calculate adiabatic electron affinity, though in that case we lose the advantages of direct calculation. BeO has been examined in two basis sets. For CH+, four different basis sets have been used. We have presented the partial fourth-order schemes to the EA in all the basis sets. The results are analyzed to illustrate the importance of triples, as well as highlight computationally efficient partial fourth-order schemes. The choice of the basis set on the electron affinity calculation is also emphasized. Comparisons with available experimental and theoretical results are presented. The general fourth-order schemes, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles, doubles, and triplets (MRCCSD+T) methods, based on bondonic formalism, are also presented here in a composed way, for quantum electronic affinity.

Fock-space multireference coupled cluster calculations of Auger energies of noble gas elements using relativistic spinors.

We report the Auger and Coster-Kronig transition energies (related to double ionization potentials) of noble gas elements obtained using the Fock-space multireference coupled cluster (FSMRCC) method with relativistic spinors. The resulting Auger and Coster-Kronig lines are found to be in agreement with the experimental data and with other reference theoretical estimates. To the best of our knowledge, no prior report of relativistic calculations is available for Auger transition energies at the FSMRCC level of theory. The ionization potentials resulted from this method with no extra cost are also found to be in agreement with experiment, particularly the outer-valence ones. Interestingly, the FSMRCC and the multiconfiguration Dirac-Fock calculations exhibit an inversion in the 3P energy levels of the xenon atom for N4,5-O23O23 Auger transitions, where the 3Pj state energies appear in the order J = 1, 0, 2, a feature which can be verified experimentally.

Analytical dipole moments and dipole polarizabilities of doublet radicals using Cholesky representation of constrained variational linear response to Fock-space multi-reference coupled-cluster method with single and double substitutions

We present dipole moments and dipole polarizabilities of doublet radicals computed analytically using constrained variational approach (CVA) based Fock-space (FS) multi-reference (MR) coupled-cluster (CC) method with single and double substitutions (SD) after Cholesky decomposition (CD) of electron repulsion integrals (ERI’s) in molecular orbital (MO) basis. We present our results computed with CD tolerance of 10-1,10-2 and 10-3 and test their accuracy by comparing them with the ones obtained by the conventional CVA-FSMRCCSD.

Intermediate Hamiltonian Fock Space Multireference Coupled Cluster Approach to Core Excitation Spectra.

The Fock space multireference coupled cluster (FSMRCC) method provides an efficient approach for the direct calculation of excitation energies. In intermediate Hamiltonian (IH-FSMRCC) formulation, the method is free from intruder state problems and associated convergence difficulties, even with a large model space. In this paper, we demonstrate that the IH-FSMRCC method with suitably chosen model space can be used for the accurate description of core excitation spectra of molecules, and our results are in excellent agreement with the experimental values. We have investigated the effect of choice of model space on the computed results. Unlike the equation-of-motion (EOM)-based method, the IH-FSMRCC does not require any special technique for convergence and in singles and doubles approximation gives a performance comparable to that of the standard EOMEE-CCSD method, even better in some of the cases.

Structure, Stability, and Properties of the Trans Peroxo Nitrate Radical: The Importance of Nondynamic Correlation

We report a comparative single-reference and multireference coupled-cluster investigation on the structure, potential energy surface, and IR spectroscopic properties of the trans peroxo nitrate radical, one of the key intermediates in stratospheric NOX chemistry. The previous single-reference ab initio studies predicted an unbound structure for the trans peroxo nitrate radical. However, our Fock space multireference coupled-cluster calculation confirms a bound structure for the trans peroxo nitrate radical, in accordance with the experimental results reported earlier. Further, the analysis of the potential energy surface in FSMRCC method indicates a well-behaved minima, contrary to the shallow minima predicted by the single-reference coupled-cluster method. The harmonic force field analysis, of various possible isomers of peroxo nitrate also reveals that only the trans structure leads to the experimentally observed IR peak at 1840 cm(-1). The present study highlights the critical importance of nondynamic correlation in predicting the structure and properties of high-energy stratospheric NOx radicals.

Fock-space multi-reference coupled-cluster response with the effect of triples on dipole moment of ClO and SF radicals#

Dipole moment calculations of SF and ClO radicals have been carried out using the recently developed partial triples correction to Fock-space multi-reference coupled cluster method. Theoretical calculation of the doublet SF and ClO radicals is useful due to their importance in atmospheric chemistry. The dipole moments of these radicals are extremely sensitive to correlation effects. A brief insight to the way the triples correction has been implemented is presented. We compare the results obtained from our analytic response treatment with that of restricted open Hartree-Fock (ROHF) calculations. Results are presented for both relaxed and non-relaxed approach in the ROHF method. Results suggest the importance of triples corrections. The effects of orbital relaxation are also analysed from the results.

Fock-space multireference coupled-cluster calculations of the hyperfine structure of isoelectronic33S−and35,37Cl

Due to its flexibility and possible systematic improvement, the Fock-space (FS) multireference coupled-cluster (MRCC) method remains a very important tool for the computation of energy differences of spectroscopic interest. In the present work, the FS MRCC method for the electron detachment process has been applied to determine the magnetic hyperfine constant ${A}_{J}$ and nuclear quadrupole moments $Q$ (related to electric hyperfine constant ${B}_{J}$) for the lowest multiplets of ${}^{33}$S${}^{\ensuremath{-}}$, ${}^{35}$Cl, and ${}^{37}$Cl with Dirac-Fock orbitals. In addition, we also report ${}^{2}$${P}_{3/2}$([Ne]$3{s}^{2}3{p}^{5}$) $\ensuremath{\rightarrow}$ ${}^{2}$${P}_{1/2}$([Ne]$3{s}^{2}3{p}^{5}$) magnetic dipole transition matrix element and electron affinity of ${}^{35}\mathrm{Cl}$ (i.e., ionization energy of Cl${}^{\ensuremath{-}}$). Calculated properties are in very good agreement with the available new standard or reference values.

First- and second-order electrical properties computed at the FSMRCCSD level for excited states of closed-shell molecules using the constrained-variational approach

Fock space multireference coupled-cluster (FSMRCC) method emerged as an efficient tool to describe the electronic structure of nearly degenerate cases. Development of linear response has been one of the challenging problems in FSMRCC due to the multiple-root nature of the effective Hamiltonian. A response from any of the roots would span the space for getting the properties. Hence, all roots perturbed by the external field would proliferate the excited states. We recently developed the FSMRCC method for the efficient evaluation of analytic response properties using a constrained variation approach. In this paper, we present analytic dipole moments and polarizabilities of H(2)O, O(3), and CH(+) molecules in low-lying excited states along with brief discussion of singlet triplet decoupling of (1,1) sector of FSMRCC resulting from spin adaptation.

Magnetizability of doublet radicals using Fock space multi‐reference coupled cluster method

AbstractIn this article, we report the first implementation of the recently developed Fock space multireference coupled cluster (FSMRCC) response approach for magnetizabilities. The FSMRCC treats dynamic and static correlation in a very extensive manner. We report pilot application of the diamagnetizability of NO, NO2, OH, and BH2 radicals. We also report preliminary applications of the paramagnetic magnetizability of the NO radical. Standard atom‐centered Gaussian basis functions have been used, and this allowed us to study the gauge dependence of the magnetizabilities. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Analytical Dipole Moments and Dipole Polarizabilities of Oxygen Mono-Fluoride and Nitrogen Dioxide: A Constrained Variational Response to Fock-Space Multi-Reference Coupled-Cluster Method

In this article, we present analytical dipole moments and dipole polarizabilities of oxygen monofluoride and nitrogen dioxide using the recently developed constrained variational approach in Fock-space multi-reference coupled-cluster singles and doubles (CVA-FSMRCCSD) method. Both these molecules are important in atmospheric chemistry. The near-degeneracy in low-lying states of these molecules demands for MR description of the wavefunction. We also report our study of variation in the properties of oxygen monofluoride with respect to basis set. Benchmark results, wherever available, have been duly reported for comparison.

Analytically continued Fock space multi-reference coupled-cluster theory: Application to the shape resonance

The Fock space multi-reference coupled-cluster (FSMRCC) method is used for the study of the shape resonance energy and width in an electron–atom/molecule collision. The procedure is based upon combining a complex absorbing potential (CAP) with FSMRCC theory. Accurate resonance parameters are obtained by solving a small non-Hermitian eigen-value problem. We study the shape resonances in e −–C 2H 4 and e −–Mg.

Constrained variational response to Fock-space multi-reference coupled-cluster theory: Some pilot applications

Fock space (FS) multi-reference (MR) coupled-cluster (CC) has been established to be state-of-the-art method for energies of open-shell radicals, ionized, electron attached states and excited states. Due to the multi-root nature of the method, the linear response of MRCC, however, is non-trivial. Constrained variation approach (CVA) makes it plausible to calculate response of the MRCC method efficiently. However, the approach is used for only one root of the problem at a time. In the present article, we make first implementation of the approach and present test results of dipole moments of small radicals.

Analytically continued Fock space multireference coupled-cluster theory: Application to the Πg2 shape resonance in e-N2 scattering

The technique of Fock space multireference coupled-cluster (FSMRCC) is applied for the first time to the correlated calculation of the energy and width of a shape resonance in an electron-molecule collision. The procedure is based upon combining a complex absorbing potential with FSMRCC theory. Accurate resonance parameters are obtained by solving a small non-Hermitian eigenvalue problem. The potential-energy curve of the (2)Pi(g) state of N2- is calculated using the FSMRCC and multireference configuration-interaction (MRCI) level of theories. Comparison with the single-determinant Hartree-Fock theory indicates that correlation effects are important in determining the behavior of the resonance state.

Energies and Dipole Moments of Excited States of Ozone and Ozone Radical Cation Using Fock Space Multireference Coupled-Cluster Analytical Response Approach

Using the Fock space multireference coupled-cluster (FS-MRCC) analytical linear response approach, we report the dipole moments of low-lying singlet and triplet excited states of ozone. The low-lying singlet and triplet excited states are calculated at the ground-state geometry and at the adiabatic geometry for the 1A2 and 1B1. For comparison we also calculate at the ground-state geometry the dipole moments of the 1A2, 1B1 and 1B2 using multireference configuration interaction (MRCI) with a bigger VQZ basis and complete active space. We also report as by-product the excitation energy values in the singles and doubles approximation. At the ground-state geometry we also report the energy and the dipole moments of the 2A1, 2A2 and 2B1 states of the ozone radical cation. The energy of the ozone cation radical is compared with the other correlated approaches. It matches well with the experimental values.

Fock space multireference coupled-cluster theory for general single determinant reference functions

The technique of Fock space multireference coupled-cluster (FSMRCC) theory is applied for the first time to problems involving a high-spin open-shell ground state. Explicit spin–orbital equations applicable to any single determinant reference state are presented and some computational aspects of FSMRCC are discussed. The method is illustrated by two applications in which calculations are limited to single and double excitation operators (FSMRCCSD). First, several basis sets and choices of open-shell reference function are used to calculate selected ionization potentials of O2. The FSMRCCSD results obtained with a large generally contracted basis set are uniformly within 0.1 eV of experiment. In addition, FSMRCCSD is applied to a study of symmetry breaking in the 3A2 state of CO2, a classic multireference problem. The force constant for asymmetric distortion is shown to be predicted correctly as positive, unlike ordinary single-reference CCSD which predicts a double-minimum potential. The results of this paper suggest that the open-shell reference FSMRCC approach has wide applicability for the solution of chemical problems, particularly when significant nondynamic electron correlation effects are present.

Coupled-cluster method for open-shell singlet states

Open-shell singlet states of molecules must be described by two (spin-orbital) determinants, hence they cannot be calculated with standard single-reference correlated methods. We show that this problem can be solved using elements of the Hilbert space multi-reference coupled-cluster theory. Explicit algebraic equations are introduced and their application is illustrated by studying several excited states of ozone, ketene and diazomethane. Comparison with Fock space multi-reference coupled-cluster solutions is presented.

Transformation of the Hamiltonian in excitation energy calculations: Comparison between Fock-space multireference coupled-cluster and equation-of-motion coupled-cluster methods

A use of the transformed form of the Hamiltonian in excitation energy calculations is discussed and a comparison between methods using this form is performed. It is shown that use of a similarity-transformed Hamiltonian can lead to separation of the ground state and excited state eigenvalue problems. Then standard approaches for determination of excited state energies can be used. Since these energies are usually quasidegenerate, it is convenient to use the effective Hamiltonian scheme. For different approximate methods, various advantages and disadvantages referring to desirable features of a ‘‘theoretical model chemistry’’ are discussed.

The equation-of-motion coupled-cluster method: Excitation energies of Be and CO

The equation-of-motion coupled-cluster (EOM-CC) method for the calculation of excitation energies is presented. The procedure is based upon representing an excited state as an excitation from a coupled-cluster ground state and the excitation energies are obtained by solving a non-Hermitian eigenvalue problem. Numerical applications are reported for Be and CO, and compared to full CI, Fock space multi-reference coupled-cluster, multi-reference MBPT, and propagator results.