A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

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−.

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

Molcas: a program package for computational chemistry.

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

The second-order approximate coupled cluster singles and doubles model CC2

Second-order perturbation theory based on a CASSCF reference state is derived and implemented. The first-order wave function includes the full space of interacting states. Expressions for the contributions to the second-order energy are obtained in terms of up to four-particle density matrices for the CASSCF reference state. The zeroth-order Hamiltonian reduces to the MOller-Plesset Hamiltonian for a closed-shell reference state. The limit of the implementation is given by the number of active orbitals, which determines the size of the density matrices. It is presently around 13 orbitals. The method is illustrated in a series of calculations on H 2 , H 2 O, CH 2 , and F - , and the results are compared with corresponding full CI results

Second-order perturbation theory with a CASSCF reference function

An MCSCF method based on a restricted active space (RAS) type wave function has been implemented. The RAS concept is an extension of the complete active space (CAS) formalism, where the active orbitals are partitioned into three subspaces: RAS1, which contains up to a given maximum number of hole; RAS2, where all possible distributions of electrons are allowed; and RAS3, which contains up to a given maximum number of electrons. A typical example of a RAS wave function is all single, double, etc. excitations with a CAS reference space. Spin-adapted configurations are used as the basis for the MC expansion

The restricted active space self-consistent-field method, implemented with a split graph unitary group approach

A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described. This model is particularly effective for cases where a chemical system requires a balanced orbital active space that is too large to be addressed by the complete active space self-consistent field model with or without second-order perturbation theory (CASPT2 or CASSCF, respectively). Rather than permitting all possible electronic configurations of the electrons in the active space to appear in the reference wave function, certain orbitals are sequestered into two subspaces that permit a maximum number of occupations or holes, respectively, in any given configuration, thereby reducing the total number of possible configurations. Subsequent second-order perturbation theory captures additional dynamical correlation effects. Applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented. In the mononuclear case, RASPT2 and CASPT2 provide very similar results. In the binuclear cases, however, only RASPT2 proves quantitatively useful, owing to the very large size of the necessary active space.

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The restricted active space followed by second-order perturbation theory method : Theory and application to the study of CUO2 and CU2O2 systems

The cr2 potential energy curve studied with multiconfigurational second-order perturbation theory

The electronic ground state of ozone and, in particular, its equilibrium geometry and harmonic vibration frequencies was studied by a variety of multiconfiguration and single‐configuration methods. It is well known that the antisymmetric stretch frequency cannot be correctly obtained by single‐reference methods unless at least triple excitations are included. Extensive comparison with other work in the literature shows that basis‐set effects must be taken into account since the ω3 frequency is very sensitive to computational details. The multiconfiguration methods are shown to give good results provided that an adequate configuration space is used. In particular, the second‐order complete active space perturbation method performs very satisfactorily. Traditional multireference configuration interaction (MRCI) methods, using a few reference functions, do not perform so well. A two‐reference CI is able to give reasonable results, but only when the orbitals have been prepared by some properly correlated method. Adding several reference functions gives small improvements, and the result is capriciously dependent on the type of reference functions included. The success of the perturbation method, as well as an extreme type of MRCI, indicates that it is far more important to include a large number of diverse configurations in the reference than to treat the remaining dynamical correlation accurately.

P.-Å. Malmqvist

Papers

Second-order perturbation theory with a CASSCF reference function

The restricted active space self-consistent-field method, implemented with a split graph unitary group approach

The restricted active space followed by second-order perturbation theory method : Theory and application to the study of CUO2 and CU2O2 systems

The cr2 potential energy curve studied with multiconfigurational second-order perturbation theory

Vibrational frequencies of ozone : a multiconfigurational approach