Miroslav Urban

Software news and update MOLCAS 7 : The Next Generation

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two‐electron integrals and in the generation of so‐called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self‐consistent field, density functional theory, 2nd order perturbation theory, complete‐active space self‐consistent field multiconfigurational reference 2nd order perturbation theory, and coupled‐cluster methods. The report further elaborates on the implementation of a restricted‐active space self‐consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas‐Kroll‐Hess transformation for one‐component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so‐called picture‐change‐free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies.

Towards a full CCSDT model for electron correlation

Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT‐1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth‐order MBPT. In this approximation, an MBPT(4)‐like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT‐1 results.

Towards a full CCSDT model for electron correlation. CCSDT-n models

Abstract The first numerical results using two extended coupled cluster models that include triple excitations, CCSDT-2 and CCSDT-3, are reported and compared to full CI for several systems. These methods are shown to be superior to CCSDT-1 when the reference function is poor, such as in bond breaking cases. The errors compared to full CI vary from 0.1 to 1.2 kcal mol .

Benzene Dimer: High-Level Wave Function and Density Functional Theory Calculations.

High-level OVOS (optimized virtual orbital space) CCSD(T) interaction energy calculations (up to the aug-cc-pVQZ basis set) and various extrapolations toward the complete basis set (CBS) limit are presented for the most important structures on the benzene dimer potential energy surface. The geometries of these structures were obtained via an all-coordinate gradient geometry optimization using the DFT-D/BLYP method, covering the empirical dispersion correction fitted exclusively for this system. The fit was carried out against two estimated CCSD(T)/CBS potential energy curves corresponding to the distance variation between two benzene rings for the parallel-displaced (PD) and T-shaped (T) structures. The effect of the connected quadruple excitations on the interaction energy was estimated using the CCSD(TQf) method in a 6-31G*(0.25) basis set, destabilizing the T and T-shaped tilted (TT) structures by ≈0.02 kcal/mol and the PD structure by ≈0.04 kcal/mol. Our best CCSD(T)/CBS results show, within the error bars of the applied methodology, that the energetically lowest-lying structure is the TT structure, which is nearly 0.1 kcal/mol more stable than the almost isoenergetic PD and T structures. The specifically parametrized DFT-D/BLYP method leads to a correct energy ordering of the structures, with the errors being smaller by 0.2 kcal/mol with respect to the most accurate CCSD(T) values.

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties: III. Alkali (Li, Na, K, Rb) and alkaline-earth (Be, Mg, Ca, Sr) atoms

Abstract The basis set polarization method is applied for the generation of medium size polarized basis sets for Li, Na, K, Rb, Be, Mg, Ca, and Sr. The derived basis sets are shown to give satisfactory results in calculations of atomic dipole polarizabilities and in calculations of dipole moments and dipole polarizabilities of diatomic hydrides and hydride ions at both the SCF and highly correlated levels of approximation. The MBPT and CC results for hydrides and hydride ions of the group Ia and IIa metals calculated with polarized basis sets derived in this study indicate the importance of the electron correlation contribution to the electric properties of those systems. The dominant part of this contribution involves excitations from core orbitais of the metal atom and is recognized as the core polarization effect. The valence approximation is found to be completely unsatisfactory for hydrides involving heavier metals of the present series. Details of the basis set data supplement this paper. Some possible applications of those basis sets are surveyed.

The fourth order diagrammatic MB‐RSPT calculations of the correlation energy of ten electron systems

The aim of this work is to analyze the correlation energy of the 10‐electron systems Ne, HF, H2O, and NH3, using the diagrammatic many‐body perturbation theory up to the fourth order. The second and third order contributions are included fully. In the fourth order, attention was directed to the detailed analysis of the inter‐relation of contributions which arise from all double excitations, from the renormalization term as well as from quadruple excitations which are due to non‐EPV contributions from quadruple excitations diagrams. The connections with other methods are also discussed.

Spin adapted restricted Hartree–Fock reference coupled cluster theory for open shell systems

The coupled clusters (CC) method for effective calculations of open shell systems with the single restricted Hartree–Fock (ROHF) reference determinants is formulated. We apply the spin adaptation described in our previous work, aimed at removing the spin contamination in both coupled cluster (CC) amplitudes and CC energy, both for the linear and nonlinear versions of the single and double excitation coupled cluster (CCSD) method. We give a comparison of results with adapted and nonadapted methods. Together with the elimination of the spin contamination, our spin adaptation yields CC equations, which reduce the number of CC amplitudes and the number of arithmetical operations, which results in computational time comparable with analogous closed shell calculations. The complication in the full spin adapted CC method is that individual spin states require specific spin adapted excitations, so that for every spin state, a different implementation is needed. It is possible to define a very effective approximat...

Ionization potentials and electron affinities of Cu, Ag, and Au: Electron correlation and relativistic effects

The electron correlation and relativistic effects on ionization potentials and electron affinities of Cu, Ag, and Au are investigated in the framework of the coupled cluster method and different 1-component approximations to the relativistic Dirac-Coulomb Hamiltonian. The first-order perturbation approach based on the massvelocity and Darwin terms is found to be sufficiently accurate for Cu and Ag while it fails for Au. The spin-averaged Douglas-Kroll no-pair method gives excellent results for the studied atomic properties. The ionization potentials obtained within this method and the coupled cluster scheme for the electron correlation effects are 7.733(7.735) eV for Cu, 7.461(7.575) eV for Ag, and 9.123(9.225) eV for Au (experimental values given in parentheses). The calculated (experimental) electron affinity results for Cu, Ag, and Au are 1.236(1.226), 1.254(1.303), and 2.229(2.309) eV, respectively. There is a marked relativistic effect on both the ionization potential and electron affinity of Ag which sharply increases for Au while Cu exhibits only a little relativistic character. A similar pattern of relativistic effects is also observed for electric dipole polarizabilities of the coinage metal atoms and their ions. The coupled cluster dipole polarizabilities of the coinage metal atoms calculated in this article in the Douglas-Kroll no-pair formalism (Cu: 46.50 au; Ag: 52.46 au; Au: 36.06 au) are compared with our earlier data for their singly positive and singly negative ions.

Optimized virtual orbitals for correlated calculations: an alternative approach

We propose an alternative formulation for creating the optimized virtual orbital space (OVOS). Our technique exploits and extends the method developed by Adamowicz and co-workers [L. Adamowicz, R.J. Bartlett. J. chem. Phys., 86, 6314 (1987); L. Adamowicz, R.J. Bartlett, A.J. Sadlej. J. chem. Phys., 88, 5749 (1988).]. The aim of the OVOS technique is to reduce the original SCF basis of the virtual molecular orbitals and to reduce the computer time in the coupled cluster (CC) and related highly sophisticated correlated methods. OVOS is created by using an invariant unitary rotation of the virtual orbitals subspace. New optimization functionals are proposed and implemented. The first type are ‘energy’ functionals. Their optimization leads to the minimal difference between the CCSD, CCD, or the second-order perturbation energy, MP2, in the original orbital basis and the OVOS basis, respectively. Alternatively, linearized ‘overlap’ functionals optimize the overlap between the correlated wave function in the full and the OVOS space, respectively. The original exponential parametrization was replaced by the efficient algorithm for the virtual orbital subspace rotation based on the Lagrangian multipliers technique which ensures orthogonality within rotated virtual orbitals.  The method is illustrated by calculations of correlation energies and/or reaction energies, spectroscopic constants or dipole moments of HF, HCN, HNC, CO and F2 molecules and dissociation energies of pentane to propene and ethane. The ‘overlap’ functional is shown to be more efficient than the ‘energy’ one, particularly in representing triple excitations using OVOS. The basis set dependence of the efficiency of the OVOS technique was also studied.

Mutual dependence of relativistic and electron correlation contributions to molecular properties: the dipole moment of AgH

Abstract A method for the evaluation of relativistic contributions to atomic and molecular properties is presented. The proposed method is based on the Cowan—Griffin quasi-relativistic approximation for a many-electron Hamiltonian. The respective relativistic corrections to properties of many-electron systems are evaluated in the framework of the finite-field perturbation approach. The method is used at both the SCF HF and different correlated levels of approximation. The relativistic corrections to the dipole moment of AgH are evaluated through the first-order with respect to the Cowan—Griffin perturbation operator and through the complete fourth-order with respect to the electron correlation perturbation by using many-body perturbation theory. The final predicted value of the AgH dipole moment at the experimental equilibrium bond distance (1.618 A) is 2.86 D. A considerable correction to the SCF HF result is given by the first-order pure relativistic term. The mixed relativistic—correlation contributions are non-negligible.