: 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 distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 11A′ – 21A′ conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 11A1 to 21A1 electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.

Extended multi-configuration quasi-degenerate perturbation theory: the new approach to multi-state multi-reference perturbation theory.

Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications

Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations Trygve Helgaker,* Sonia Coriani, Poul Jørgensen, Kasper Kristensen, Jeppe Olsen, and Kenneth Ruud Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway Dipartimento di Scienze Chimiche e Farmaceutiche, Universit a degli Studi di Trieste, Via Giorgieri 1, I-34127 Trieste, Italy Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway

Recent advances in wave function-based methods of molecular-property calculations.

Multireference nature of chemistry: the coupled-cluster view.

A revision of second-order Generalized Van Vleck Perturbation Theory (GVVPT2) for the description of dynamic electron correlation in molecules is presented. It is shown that the basic formulas of the suggested method are well-defined approximations to the theoretically carefully constructed self-consistent quasidegenerate perturbation theory. Furthermore, it is shown that nonlinear responses to the perturbations can be obtained by explicit formulas. The revised GVVPT2 makes active use of the recently introduced concept of macroconfigurations, whereby vast numbers of null Hamiltonian matrix elements are prescreened with minimal computational cost and the remainders are organized for facile computation by Table-CI-like methodology. Moreover, use of macroconfigurations allows the efficient use of incomplete model spaces, which extends drastically the applicability of the method. Representative calculations on model systems studied previously with the original formulation show close agreement and on additional model systems show the wide applicability of the revised formulation.

Explication and revision of generalized Van Vleck perturbation theory for molecular electronic structure

Using the technique of Perdew and Levy [Phys. Rev. B 31, 6264 (1985)], it is shown that both the density function theory (DFT)-in-DFT and wave function theory (WFT)-in-DFT embedding approaches are formally correct in studying not only the ground state but also a subset of the excited states of the total system. Without further approximations, the DFT-in-DFT embedding approach results in a pair of coupled Euler–Lagrange equations. In contrast to DFT-in-DFT, the WFT-in-DFT approach is shown to ensure a systematic description of excited states if such states are mainly related to excitations within the embedded subsystem. Possible ways for the practical realization of the WFT-in-DFT approach for studying excited states are briefly discussed.

Embedding theory for excited states

A new, efficient, configuration-driven algorithm utilizing the unitary group approach (UGA) was developed and implemented for the generalized van Vleck perturbation theory (GVVPT) variant of multireference perturbation theory. The computational speed has been improved by 1 or 2 orders of magnitude compared to the previous implementation based on the Table-CI technique. It is shown that the reformulation is applicable to both the second-order (GVVPT2) and third-order (GVVPT3) approximations. Calculations on model problems and on a chemically realistic description of cyclobutadiene are used to illustrate the performance of the method. The calculations on cyclobutadiene, using over 2.3 billion CSFs, provide results on geometric parameters and the barrier height of the automerization reaction in good agreement with established high accuracy results.

Configuration-driven unitary group approach for generalized Van Vleck variant multireference perturbation theory.

A new quasidegenerate perturbation theory is developed that describes the interactions of electronic states of interest with energetically low-lying excited states variationally and with more high-lying excited states perturbatively. The states of interest, the low-lying excited states and the more high-lying excited states, define primary, secondary, and external subspaces, respectively. The task of determination of the lowest solutions of the full configuration interaction (CI) problem is shown to be equivalent to the task of searching iteratively for an optimal primary subspace within the model space spanned by the initial unperturbed primary and secondary states. It is also shown that the present approach, which we refer to as the self-consistent quasidegenerate perturbation theory (SC-QDPT), theoretically satisfies the following criteria: (1) it avoids instabilities due to intruder states; (2) it ensures the additivity of the energy for noninteracting subsystems; (3) the projection of the correlated ...

A self-consistent version of quasidegenerate perturbation theory

First results on electron densities and energies for a number of molecular complexes with different interaction strengths (ranging from ca. 0.3 to 40 kcal/mol), obtained using our recently introduced DFT-in-DFT embedding equations (i.e., Kohn–Sham equations with constrained electron density (KSCED) and external orbital orthogonality (ext orth), KSCED(x, ext orth), where x denotes the single particle support: monomer (m); supermolecular (s); or extended monomer (e)) are compared with densities from supermolecular Kohn–Sham (KS)-DFT calculations and traditional DFT-in-DFT results. Because our methodology does not rely on error-prone potentials that are not present in supermolecular KS-DFT calculations, it allows DFT-in-DFT calculations to achieve much higher accuracy than previous protocols of DFT-in-DFT that employed such potentials. It is shown that whereas conventional DFT-in-DFT embedding theory leads to errors in the electron density at the boundary between subsystems, the situation is remedied when or...

Yuriy G. Khait

Papers

Explication and revision of generalized Van Vleck perturbation theory for molecular electronic structure

Embedding theory for excited states

Configuration-driven unitary group approach for generalized Van Vleck variant multireference perturbation theory.

A self-consistent version of quasidegenerate perturbation theory

Density differences in embedding theory with external orbital orthogonality.