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The Complete Active Space Second-Order Perturbation Theory (CASPT2) is well-established as a high-accuracy electronic structure method. It was originally implemented in the early 1990s to an efficient computer code in the molcas program suite, and this implementation has been extensively used as a standard tool. Here, we report a comparison of it against two independent computer-aided implementations of the CASPT2 method, revealing that the CASPT2 energies provided by the original code of molcas (version 8 or earlier) are inconsistent with the predictions of the lately developed computer-aided implementations. It is shown that this error is associated with the projections of the first-order equation onto the fully internally contracted multireference bases which are partially inconsistent between the left- and right-hand sides. The degree of the errors is assessed by performing illustrative CASPT2 calculations. The errors in total CASPT2 energies are demonstrated to be negligible relative to chemical accuracy in many cases, while there is a difficult case where they may substantially alter chemical description. The incorporation of the consistent projections into molcas has been carried out, which is available in the version 8 sp1. (Less)

The well-known natural orbitals are defined as eigenfunctions of a one-particle reduced density operator, and can be obtained from a computed density matrix by diagonalization. Similarly, in this article we define the binatural orbitals, which are obtained for a pair of wave functions by a singular value decomposition of a reduced transition density matrix. The pair of states would usually be eigenstates of the electronic Hamiltonian, and the binatural orbitals then serve as a useful tool for the analysis of the transition between these states. More generally, application to any two state functions gives important information as to how the two states differ. Some examples are shown.

The value of the two-particle density function at coalescence is frequently used as an additional variable for formulating approximate exchange-correlation or correlation functionals. Here, its applications as one of the key variables for the construction of new DFT (preferably multi-determinant) functionals is investigated. The basic formalism is presented and it is shown that this replacement avoids some difficulty to construct a Fock matrix in a ROKS (restricted open-shell Kohn–Sham) method and also to reduce the ‘double counting’ of correlation energy in CASDFT (complete active space density functional theory) calculations. Calculations of excitation energies for transition metals and dissociation curves for diatomic molecules are presented as an example.

The two-photon spectrum of the 2 1 A g ı1 1 A g transition in trans -stilbene has been calculated at the complete active space self-consistent field (CASSCF) level of theory. Energies were obtained at the complete active space second-order perturbation (CASPT2) level of theory, while the geometries of both the initial and final states were optimized at the CASSCF level. The energy and the geometry optimizations were performed using an active space of 14 electrons in 14 active πorbitals. The vibrational frequencies of both states and the two-photon transition (TPT) cross-section were calculated with a smaller active space where the two lowest πorbitals were kept inactive. A newly implemented algorithm, in the quantum chemical package Molcas was used to determine the two-photon transition intensity. This method requires only the linear response of the CASSCF wavefunction. Furthermore, the vibronic structure of this TPT was studied. The Franck-Condon factors were obtained by calculating the overlap between the vibrational states involved, which were determined from the force fields of both the initial and final states, at the CASSCF level of theory. The results are in agreement with experiment.