Björn O. Roos

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−.

A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach

Abstract A density matrix formulation of the super-CI MCSCF method is presented. The MC expansion is assumed to be complete in an active subset of the orbital space, and the corresponding CI secular problem is solved by a direct scheme using the unitary group approach. With a density matrix formulation the orbital optimization step becomes independent of the size of the CI expansion. It is possible to formulate the super-CI in terms of density matrices defined only in the small active subspace; the doubly occupied orbitals (the inactive subspace) do not enter. Further, in the unitary group formalism it is straightforward and simple to obtain the necessary density matrices from the symbolic formula list. It then becomes possible to treat very long MC expansions, the largest so far comprising 726 configurations. The method is demonstrated in a calculation of the potential curves for the three lowest states (1Σ+g, 3Σ+u and 3Πg) of the N2 molecule, using a medium-sized gaussian basis set. Seven active orbitals were used yielding the following results: De: 8.76 (9.90), 2.43 (3.68) and 3.39 (4.90) eV; re: 1.108 (1.098), 1.309 (1.287) and 1.230 (1.213) A; ωe: 2333 (2359), 1385 (1461) and 1680 (1733) cm−1, for the three states (experimental values within parentheses). The results of these calculations indicate that it is important to consider not only the dissociation limit but also the united atom limit in partitioning the occupied orbital space into an active and an inactive part.

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 complete active space SCF (CASSCF) method in a Newton–Raphson formulation with application to the HNO molecule

The complete active space (CAS) SCF method is presented in detail with special emphasis on computational aspects. The CASSCF wave function is formed from a complete distribution of a number of active electrons in a set of active orbitals, which in general constitute a subset of the total occupied space. In contrast to other MCSCF schemes, a CASSCF calculation involves no selection of individual configurations, and the wave function therefore typically consists of a large number of terms. The largest case treated here includes 10 416 spin and space adapted configurations. To be able to treat such large CI expansions, a density‐matrix oriented formalism is used. The Newton–Raphson scheme is applied to calculate the orbital rotations, and the secular problem is solved with recent developments of CI techniques. The applicability of the method is demonstrated in calculations on the HNO molecule in ground and excited states, using a triple‐zeta basis and different sizes of the active space. With a reasonable ch...

Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces

A restricted active space (RAS) wave function is introduced, which encompasses many commonly used restricted CI expansions. A highly vectorized algorithm is developed for full CI and other RAS calculations. The algorithm is based on Slater determinants expressed as products of alphastrings and betastrings and lends itself to a matrix indexing C(Iα, Iβ ) of the CI vector. The major features are: (1) The intermediate summation over determinants is replaced by two intermediate summations over strings, the number of which is only the square root of the number of determinants. (2) Intermediate summations over strings outside the RAS CI space is avoided and RAS calculations are therefore almost as efficient as full CI calculations with the same number of determinants. (3) An additional simplification is devised for MS =0 states, halving the number of operations. For a case with all single and double replacements out from 415 206 Slater determinants yielding 1 136 838 Slater determinants each CI iteration takes ...

The restricted active space (RAS) state interaction approach with spin–orbit coupling

A method to compute spin-orbit coupling between electronic states is presented. An effective one-electron spin-orbit Hamiltonian is used, based on atomic mean field integrals, The basic electronic states are obtained using the restricted active space (RAS) SCF method. The Hamiltonian matrix is obtained by an extension of the restricted active space state interaction (RASSI) method. Several hundred states can be included. Tests for atoms and molecules from the entire periodic system show accurate results. Computed spin-orbit effects on relative energies are normally accurate within a few percent. The method has been included in the MOLCAS-5.0 quantum chemistry software

A Comparison of the Super-CI and the Newton-Raphson Scheme in the Complete Active Space SCF Method

A density matrix formulation is presented of the super-C I and Newton-Raphson methods in complete active space SCF (CASSCF) calculations. The CASSCF method is a special form of the MC-SCF method, where the C I wave function is assumed to be complete in a subset of the orbital space (the active space), leaving the remaining orbitals doubly occupied in all configurations. Explicit formulas are given for all matrix elements in the super-C I method and the first and second derivatives in the Newton-Raphson formulation. The similarities between the two methods are pointed out and the differences in the detailed formulations are discussed. Especially interesting is the fact, that while the second derivatives can be expressed in terms of first and second order density matrices, the matrix elements between the super-C I states involve also the third order density matrix in some cases.

Multiconfigurational perturbation theory with level shift — the Cr2 potential revisited

Abstract A level shift technique is suggested for removal of intruder states in multiconfigurational second-order perturbation theory (CASPT2). The first-order wavefunction is first calculated with a level shift parameter large enough to remove the intruder states. The effect of the level shift on the second-order energy is removed by a back correction technique (the LS correction). It is shown that intruder states are removed with little effect on the remaining part of the correlation energy. New potential curves have been computed for the X 1 Σ g + and the a 3 Σ u + states of Cr 2 using large basis sets (ANO: 8s7p6d4f2g) and accounting for relativistic effects, 3s and 3p correlation, and basis set superposition effects. The computed spectroscopic constants (experimental values in parentheses) for the X 1 Σ g + state are r e = 1.69(1.68) A , ΔG 1 2 = 535(452) cm −1 , D 0 = 1.54(1.44) eV. The corresponding values for a 3 Σ u + are r e = 1.64(1.65) A , ΔG 1 2 = 667(574) cm −1 , T e = 1.79(1.76) eV.