Petr Čársky

Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory

We present a simple a posteriori correction for the state-specific multireference Brillouin–Wigner coupled-cluster (MR BWCCSD) theory, which eliminates its size-extensivity error. In the converged amplitudes we drop terms that were identified to be responsible for the lack of size extensivity. We performed MR BWCCSD calculations with this correction on CH2, SiH2, twisted ethylene, F2, and ozone that are all, from the computational point of view, typical representatives of two-reference problems. Comparison with rigorously size-extensive calculations and experiment shows that the size-extensivity error of the corrected MR BWCCSD is only a few tenths of kcal/mol.

Assessment of the single-root multireference Brillouin–Wigner coupled- cluster method: Test calculations on CH2, SiH2, and twisted ethylene

Recently developed single-root multireference Brillouin–Wigner coupled-cluster (MR BWCC) theory, which belongs to a broad family of state-selective multireference coupled-cluster methods, has been implemented in the ACES II program package at the CCSD level of approximation. The method represents a new approach to quasidegenerate problems, which is able to continuously switch between the single-reference CC in a nondegenerate situation and the Hilbert-space MRCC in a degenerate case. An assessment of the method has been carried out by means of a comparison with the full configuration interaction (CI) treatments of CH2, SiH2, and twisted ethylene diradicals. The problem of size-extensivity is discussed.

Multireference coupled-cluster calculations on the energy of activation in the automerization of cyclobutadiene: Assessment of the state-specific multireference Brillouin–Wigner theory

Hilbert-space state-universal multireference coupled-cluster (MR CC) data on cyclobutadiene [A. Balkova and R. J. Bartlett, J. Chem. Phys. 101, 8972 (1994)] were used as a benchmark for testing our recently developed state-specific (single-root) multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory. For the energy of activation in the automerization of cyclobutadiene (i.e., the energy difference between the square and rectangular structures) at the CCSD/[3s2p1d/2s] level of theory, our MR BWCCSD method gives the value of 6.2 kcal/mol, compared to 6.5 kcal/mol given by MR CCSD. With the cc-pVDZ and cc-pVTZ/cc-pVDZ basis sets, the MR BWCCSD activation barrier is 6.4 and 7.0 kcal/mol, respectively. The effect of the triple excitations [in MR CCSD(T)] and of the frozen core approximation were estimated previously to be below 0.1 kcal/mol and in the opposite direction. This shows the way of how to arrive at a more accurate automerization barrier in future calculations: extension of the basis set see...

State-specific Brillouin–Wigner multireference coupled cluster study of the F2 molecule: assessment of the a posteriori size-extensivity correction ☆

Abstract We tested a posteriori correction suggested previously for the state-specific multireference Brillouin–Wigner coupled-cluster singles and doubles (MR BW CCSD) theory, to eliminate its size-extensivity error. The correction was applied to a two-reference BW CCSD model by using the cc-pVXZ basis sets ( X =2,3,4) and it was tested by calculating the spectroscopic constants of the F 2 molecule.

The superposition error problem: The (HF)2 and (H2O)2 complexes at the SCF and MP2 levels

Abstract The title calculations were performed with the aim of providing data for the critical examination of the utility of the basis set superposition error (BSSE) correction. The main results obtained are as follows. The SCF interaction energies corrected for the BSSE and evaluated with the basis sets of split-valence and DZ origin are similar. With the stabilization energy, both the basis set superposition error and the intersystem correlation energy are important. MP2 stabilization energies are only slightly dependent on basis set for basis sets of DZ + P or better quality. The basis set superposition error at both the SCF and MP2 levels remains almost unchanged when passing from the 6–31G* to the 6–311G(2 d , 2 p ) basis set. At the SCF level sufficiently accurate geometries were obtained with the standard 6–31G* basis set. Optimization at the MP2 level with this and larger basis sets brings about only small changes with respect to optimum SCF geometries.

Multireference Coupled-Cluster Methods: Recent Developments

The objective of this paper is to provide an overview of various multi-reference (MR) coupled-cluster (CC) approaches, particularly those relating to our own research. Although MR CC methods have been around for almost three decades and much work has been expended on their development and implementation, no general purpose codes are presently available. In view of the complexity, inherent difficulties, and computational demands of both genuine valence and state universal (VU and SU) MR CC methods, attention has been directed towards the state selective or state specific (SS) approaches that focus on one state at a time. These methods are based on either the genuine MR CC formalism or on a single-reference (SR) CC Ansatz, in which higher-than-pair clusters are accounted for by relying on basic ideas of general MR approaches. This is achieved either internally by relying on CC or MBPT formalism or by exploiting some external source providing approximate values of these clusters and accomplished by either correcting equations yielding the cluster amplitudes or directly by evaluating the corrections to the CCSD energy. Nowadays there exists a whole plethora of such various approaches for handling of quasi-degenerate states with a various degree of MR character and our goal is to outline their basic features and comment on their pro’s and con’s, their usefulness and weaknesses, as well as point out their mutual relationship.

Ab initio calculations of substituent constants: a reinvestigation

Abstract A set of various substituent constants σF, σr, σα, and σx for 21 common substituents was recalculated according to the models of Marriott and Topsom which are based on ab initio calculations. Some inconsistencies in the original methods as to the use of molecular geometries and basis sets were eliminated and a few values of the original work were corrected. The set was extended by an additional 10 substituents derived from the amido and thioamido groups, with particular interest for QSAR. Comparison with standard experimental data confirmed the physical meaning and significance of the computational model for σF, σR, σα, but not for σx.

Conjugated radicals : Theoretical study of redox equilibria

Abstract Possibilities and limitations of the Coulomb repulsion integrals to estimate semiquinone formation constants of radicals are discussed. Elucidation of general dependency of semiquinone formation constants for violenes on the size of molecules and the aza-substitution is given.

Semiempirical all-valence-electron MO calculations on the electronic spectra of linear radicals with degenerate ground states

Abstract INDO-CI calculations are presented for CH, CF, NO, O 2 + , CCN, CNC, C 2 + , F 2 + , HF + , OH, CO 2 + , BO 2 , N 3 , N 2 O + , NCO, and diacetylene cation radicals. The results give a good account of transition energies for valence electronic states. The limits and merits of the method are briefly discussed.

Applicability of the supermolecule MP2 approach to intermolecular interactions: He2 and Ne2

Abstract Arguments are given for applying the full counterpoise correction to eliminate properly the basis set superposition error in the correlation energy. Comparison is made with the intermolecular perturbation theory and more complete treatments (MP4, CEPA). The results for the dimers studied suggest that MP2 is a poor approximation. Even if very extended basis sets are used, hardly more than 65% of the stabilization energy is recovered.