Matthew M. Steiner

Brillouin–Wigner based multi-reference perturbation theory for electronic correlation effects

We investigate basis set reduction (BSR), a configuration-based multi-reference perturbation theory using an implicit effective Hamiltonian motivated by Brillouin-Wigner perturbation theory. This approach avoids the intruder-state and level-crossing problems by construction and yields a rapidly converging perturbation expansion. Formulated to systematically approximate multi-reference configuration interaction, BSR yields accurate results in second order, because it includes relaxation effects of the primary space wavefunction in the presence of the perturbation. We benchmark the method for molecules (CH2,O3) in which both dynamical and non-dynamical correlation effects are known to be important, obtaining accuracies of the order of 1 kcal/mol across the potential energy surface in second-order perturbation theory. We address the critical issues of perturbative orbital optimization for the primary orbital space, the choice of the secondary orbital space and the effects of single excitations.

The efficient treatment of higher excitations in CI calculations: A comparison of exact and approximate results

Abstract The importance hierarchy exhibited by natural orbitals suggests a partitioning scheme which in turn determines a restricted many-electron space. Within this space the energy is computed exactly. Alternatively, the space is divided into internal and external subspaces. Subsequent to the exact solution in the internal subspace, the contributions from the external subspace are computed perturbatively. Agreement with the exact result is good if the norm of the external wavefunction is less than ≈ 0.003, which can be achieved by increasing the size of the internal space. Results are further improved if the internal wavefunction is reminimized to account for interactions with the external space.

Multireference basis-set reduction

We review “Hilbert space basis-set reduction” (BSR) as an approach to reduce the computational effort of accurate correlation calculations for large basis sets. We partition the single-particle basis into a small “internal” and a large “external” set. We use the MRCI method for the calculation for that part of configuration space in which only internal orbitals are occupied and perturbatively correct for the remaining configurations using a method similar to Shavitts Bk method. The present implementation approximates the MRCI result for the unpartitioned basis set, with a significantly reduced computational effort. To demonstrate the viability of the method, we present results for selected states of small molecules (Be2, CH2, O3). For the examples investigated, we find that relative energy differences can be reproduced to an accuracy of approximately 1 kcal/mol with a significant computational saving.

Coherent electron–hole correlations in quantum dots

Using numerical time propagation of the electron–hole wave function, we demonstrate how various coherent correlation effects can be observed by laser excitation of a nanoscale semiconductor quantum dot. The lowest-lying states of an electron–hole pair, when appropriately excited by a laser pulse, give rise to charge oscillations that are manifested by beatings in the optical or intraband polarizations. A GaAs 5×25×25 nm3 dot in the effective-mass approximation, including the screened Coulomb interaction between the electron and a heavy or light hole, is simulated.

SCALING BEHAVIOR OF DYNAMIC CORRELATION EFFECTS

The authors present an analytical estimate of the intrinsic errors of second-order perturbation theory in the complete basis set limit in the framework a scaling theory, which employs the maximal sharpness of the orbitals in a given basis set, quantified by the average momentum, as its fundamental variable. The authors find that the intrinsic errors of second-order perturbation theory fall with the third inverse power of the maximal momentum representable in the basis set, while the basis set truncation errors fall with the second inverse power of the momentum. These analytical arguments are verified in a numerical investigation employing distributed basis sets of up to 600 orbitals for the helium atom, water, and ethene. Extending the analysis to generic multireference perturbation theory (MRPT) the authors find that the leading contribution for the relaxation of the orthogonal complement of the zero-order wave function in the primary space scales with the same power as the leading overall perturbative correction, which yields an analytical argument for the perturbation inclusion of such feedback effects in the formulation of efficient versions of MRPT.