Pivot invariance of multiconfiguration perturbation theory via frame vectors.

Multiconfiguration perturbation theory (MCPT) is a general framework for correcting the reference function of arbitrary structures. The variants of MCPT introduced so far differ in the specification of their zero-order Hamiltonian, i.e.

Many-Body Perturbation Theory with Localized Orbitals: Accounting for Localization Diagrams as Integral Dressing.

We argue that the so-called localization diagrams, originating from off-diagonal Fockian elements, do not have to be dealt with explicitly in the Davidson-Kapuy many-body perturbation theory with localized orbitals but can be accounted for by dressed two-electron integrals.

A note on perturbation-adapted perturbation theory.

The partitioning introduced recently by Knowles [J. Chem. Phys.

The function in quantum theory II. Mathematical challenges and paradoxa.

While the square root of Dirac's is not defined in any standard mathematical formalism, postulating its existence with some further assumptions defines a generalized function called which permits a quasi-classical treatment of simple systems like the H atom or the 1D harmonic oscillator for which accurate quantum mechanical energies were previously reported. The so-defined is neither a traditional function nor a distribution, and it remains to be seen that any consistent mathematical approaches can be set up to deal with it rigorously. A straightforward use of generates several paradoxical situations which are collected here.

Improving half-projected spin-contaminated wave functions by multi-configuration perturbation theory.

Allowing triplet components of individual geminals, spin-contaminated strongly orthogonal geminal wave functions may emerge, which can be ameliorated by spin-projection techniques. Of the latter, half-projection was previously shown to be useful, offering a compromise between the amount of remaining spin-contamination and the violation of size consistency generated by projection. This paper investigates how a half-projected spin-contaminated geminal wave function can be improved by multi-configuration perturbation theory to incorporate dynamical correlation effects.

Symmetry-Adapted Perturbation with Half-Projection for Spin Unrestricted Geminals.

Perturbative correction to a wave function built from singlet-triplet mixed two-electron functions (geminals) is derived in the context of symmetry-adapted schemes, applying partial spin-projection. Imposing the constraint of strong orthogonality of geminals results in a reference function that captures static correlation in a computationally feasible way. In case of a lack of spin purification, the product of spin-unrestricted geminals is generally spin-contaminated, potentially undermining performance of a subsequent dynamic correlation treatment.

Half-Projection of the Strongly Orthogonal Unrestricted Geminals' Product Wave Function.

Half-projection of a wave function built as a product of singlet-triplet mixed two-electron fragments (geminals) is explored. The condition of strong orthogonality is imposed between geminals, the initial Ansatz accommodating the unrestricted Hartree-Fock (UHF) wave function as a special case. The here explored geminal product is more general than UHF, it allowing for single covalent bond breaking in a spin pure manner.

Geminal perturbation theory based on the unrestricted Hartree-Fock wavefunction.

A perturbative correction exploiting natural orbitals and the pair function structure of the unrestricted Hartree-Fock (UHF) wavefunction is devised. The method offers a simple framework for describing multireference systems where static correlation is captured by UHF. The UHF wavefunction is built of two-electron fragments (geminals), involving both singlet and triplet (m = 0) parts.

Application of the Cauchy integral formula as a tool of analytic continuation for the resummation of divergent perturbation series.

Previous attempts to the resummation of divergent power series by means of analytic continuation are improved applying the Cauchy integral formula for complex functions. The idea is tested on divergent Møller-Plesset perturbation expansions of the electron correlation energy. In particular, the potential curve of the LiH molecule is computed from single reference MPn results which are divergent for bond distances larger than 3.

Effect of partitioning on the convergence properties of the Rayleigh-Schrödinger perturbation series.

Convergence features of the Rayleigh-Schrödinger perturbation theory (PT) strongly depend on the partitioning applied. We investigate the large order behavior of the Møller-Plesset and Epstein Nesbet partitionings in comparison with a less known partitioning obtained by level shift parameters minimizing the norm of operator Q^W^, with W^ being the perturbation operator while Q standing for the reduced resolvent of the zero order Hamiltonian H^. Numerical results, presented for molecular systems for the first time, indicate that it is possible to find level shift parameters in this way which convert divergent perturbation expansions to convergent ones in some cases.

Spin Symmetry and Size Consistency of Strongly Orthogonal Geminals.

An overview of geminal-based wavefunctions is given, allowing for singlet-triplet mixing within the two-electron units. Spin contamination of the total wavefunction (obtained as an antisymmetrized product) is restored by spin projection. Full variation after projection is examined for two models.

Linearized Coupled Cluster Corrections to Antisymmetrized Product of Strongly Orthogonal Geminals: Role of Dispersive Interactions.

A linearized Multireference Coupled Cluster (MR-LCC) theory is formulated based on the Antisymmetrized Product of Strongly Orthogonal Geminals (APSG) reference state. The role of dispersive interbond interactions is discussed. The presented theory has led to qualitatively correct potential curves for the case when both OH bonds dissociate in H2O, a result that cannot be achieved by adding only perturbative corrections to APSG.

Spin-adaptation and redundancy in state-specific multireference perturbation theory.

Spin-adaptation of virtual functions in state-specific multireference perturbation theory is examined. Redundancy occurring among virtual functions generated by unitary group based excitation operators on a model-space function is handled by canonical orthogonalization. The treatment is found to remove non-physical kinks observed earlier on potential energy surfaces.

Jahn-Teller distortion of ionized and excited carbon nanotubes.

Due to their rotational (C(n)) symmetry, neutral zigzag and armchair type nanotubes possess doubly degenerate orbitals. As the energies of highest occupied molecular orbital and lowest unoccupied molecular orbital are usually different, neutral nanotubes exhibit a nondegenerate ground state. Ionized or excited forms of these tubes, however, may undergo Jahn-Teller distortion if degenerate orbitals show up in the vicinity of the Fermi level.

Comparative study of multireference perturbative theories for ground and excited states.

Three recently developed multireference perturbation theories (PTs)-generalized Van Vleck PT (GVVPT), state-specific multireference PT (SS-MRPT), and multiconfiguration PT (MCPT)-are briefly reviewed and compared numerically on representative examples, at the second order of approximations. We compute the dissociation potential curve of the LiH molecule and the BeH(2) system at various geometries, both in the ground and in the first excited singlet state. Furthermore, the ethylene twisting process is studied.

A sparse matrix based full-configuration interaction algorithm.

We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure.

Idempotency-conserving iteration scheme for the one-electron density matrix.

For the first order density matrix P of a noninteracting N-electron problem, an iterative formula is presented that preserves the trace and idempotency of P so that no purification is needed. Hermiticity--which may be slightly violated in the course of the iteration--gets restored when the iteration converges and the converged P corresponds to the exact solution. For sparse P, the energy is obtained by an O(N) procedure that needs no prior knowledge of the chemical potential.

Stability and properties of polyhelicenes and annelated fused-ring carbon helices: models toward helical graphites.

The geometrical structures and properties of conjugated polyhelicenes and annelated fused-ring carbon helices with analogous frameworks were theoretically studied at the HF/6-31G and B3LYP/6-31G levels. These studies focused on the stability of the fused-ring structures with special emphasis on the helical geometrical arrangements. To elucidate bonding patterns, the orbitals, electron density contours, and the electrostatic potential of these helical compounds were analyzed.

Comparison of low-order multireference many-body perturbation theories.

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations.

Multiconfiguration perturbation theory: size consistency at second order.

A modified version of a previously elaborated multiconfiguration perturbation theory (MCPT) [Rolik et al. J. Chem.