Per-Åke Malmqvist

Second-order perturbation theory with a complete active space self-consistent field reference function

The recently implemented second‐order perturbation theory based on a complete active space self‐consistent field reference function has been extended by allowing the Fock‐type one‐electron operator, which defines the zeroth‐order Hamiltonian to have nonzero elements also in nondiagonal matrix blocks. The computer implementation is now less straightforward and more computer time will be needed in obtaining the second‐order energy. The method is illustrated in a series of calculations on N2, NO, O2, CH3, CH2, and F−.

Molcas: a program package for computational chemistry.

The program system MOLCAS is a package for calculations of electronic and structural properties of molecular systems in gas, liquid, or solid phase. It contains a number of modern quantum chemical methods for studies of the electronic structure in ground and excited electronic states. A macromolecular environment can be modeled by a combination of quantum chemistry and molecular mechanics. It is further possible to describe a crystalline material using model potentials. Solvent effects can be treated using continuum models or by combining quantum chemical calculations with molecular dynamics or Monte-Carlo simulations. MOLCAS is especially adapted to treat systems with a complex electronic structure, where the simplest quantum chemical models do not work. These features together with the inclusion of relativistic effects makes it possible to treat with good accuracy systems including atoms from the entire periodic system. MOLCAS has effective methods for geometry optimization of equilibria, transition states, conical intersections, etc. This facilitates studies of excited state energy surfaces, spectroscopy, and photochemical processes.

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.

The multi-state CASPT2 method

Abstract An extension of the multiconfigurational second-order perturbation approach CASPT2 is suggested, where several electronic states are coupled at second order via an effective-Hamiltonian approach. The method has been implemented into the MOLCAS-4 program system, where it will replace the single-state CASPT2 program. The accuracy of the method is illustrated through calculations of the ionic-neutral avoided crossing in the potential curves for LiF and of the valence-Rydberg mixing in the V-state of the ethylene molecule.

The CASSCF state interaction method

Abstract A method is described to calculate the matrix elements of one- and two-electron operators for CASSCF wavefunctions employing individually optimized orbitals. The computation procedure is very efficient, and matrix elements between CAS wavefunctions with up to a few hundred thousand configurations are easily evaluated. An implementation of this method is presented, which sets up and solves the Hamiltonian secular problem in a basis of independently optimized CASSCF wavefunctions. In the program, the only restriction imposed is that the AO basis set and the number of active orbitals is the same for all states. The method is illustrated by calculations on π-excited states of some aromatic molecules.

Multiconfiguration perturbation theory with imaginary level shift

Abstract In multiconfigurational perturbation theory, so-called intruders may cause singularities in the potential energy functions, at geometries where an energy denominator becomes zero. When the singularities are weak, they may be successfully removed by level shift techniques. When applied to excited states, a small shift merely moves the singularity. A large shift may cause new divergencies, and too large shifts are unacceptable since the potential function is affected in regions further away from the singularities. This Letter presents an alternative which may be regarded as an imaginary shift. The singularities are not moved, but disappear completely. They are replaced by a small distortion of the potential function. Applications to the N 2 ground state, its A 3 / gE u + state, and the Cr 2 ground state show that the distortion caused by this procedure is small.

Cholesky decomposition-based multiconfiguration second-order perturbation theory (CD-CASPT2): Application to the spin-state energetics of Co-III(diiminato)(NPh)

The electronic structure and low-lying electronic states of a Co(III)(diiminato)(NPh) complex have been studied using multiconfigurational wave function theory (CASSCF/CASPT2). The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

New Relativistic Atomic Natural Orbital Basis Sets for Lanthanide Atoms with Applications to the Ce Diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are included as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.

The Cr2 potential energy curve studied with multiconfigurational second-order perturbation theory

The Cr2 potential energy curve studied with multiconfigurational second-order perturbation theory

A CASSCF‐CCI study of the valence and lower excited states of the benzene molecule

Ab initio complete active space (CAS) SCF and contracted CI calculations have been carried out for all valence and the lower Rydberg states of the benzene molecule. The CASSCF active space comprised 12 π‐type molecular orbitals and the basis set included both polarization functions and diffuse functions in order to describe properly both valence and Rydberg type orbitals. Resulting excitation energies for the Rydberg states are in close agreement with experiment. CASSCF results for the valence states give errors ranging from 0.0 for the covalent states up to more than 1.0 eV for the most ionic states. Inclusion of σ–π correlation effects reduces the errors in the ionic states to less than 0.6 eV. The 1E1u state is computed to lie 7.4 eV above the ground state with a transition moment of 1.70 a.u., experimental values are 7.0 eV and 1.61 a.u., respectively.