Peter J. Knowles

An efficient internally contracted multiconfiguration–reference configuration interaction method

A new internally contracted direct multiconfiguration–reference configuration interaction (MRCI) method is described which allows the use of much larger reference spaces than any previous MRCI method. The configurations with two electrons in the external orbital space are generated by applying pair excitation operators to the reference wave function as a whole, while the singly external and internal configurations are standard uncontracted spin eigenfunctions. A new efficient and simple method for the calculation of the coupling coefficients is used, which is well suited for vector machines, and allows the recalculation of all coupling coefficients each time they are needed. The vector H⋅c is computed partly in a nonorthogonal configuration basis. In order to test the accuracy of the internally contracted wave functions, benchmark calculations have been performed for F−, H2O, NH2, CH2, CH3, OH, NO, N2, and O2 at various geometries. The deviations of the energies obtained with internally contracted and unc...

A second order multiconfiguration SCF procedure with optimum convergence

An MCSCF procedure is described which is based on the direct minimization of an approximate energy expression which is periodic and correct to second order in the changes in the orthonormal orbitals. Within this approximation, the CI coefficients are fully optimized, thereby accounting for the coupling between orbital rotations and CI coefficients to higher order than in previous treatments. Additional transformations among the internal orbitals and their associated one‐ and two‐electron integrals are performed which amounts to treating the rotations among internal orbitals to higher than second order. These extra steps are cheap compared to the four index transformation performed in each iteration, but lead to a remarkable enhancement of convergence and overall efficiency. In all calculations attempted to date, convergence has been achieved in at most three iterations. The energy has been observed to converge better than quadratically from the first iteration even when the initial Hessian matrix has many...

An efficient method for the evaluation of coupling coefficients in configuration interaction calculations

Abstract A new method for evaluating one-particle coupling coefficients in a general configuration interaction calculation is presented. Through repeated application and use of resolutions of the identity, two-, three- and four-body coupling coefficients and density matrices may be built in a simple and efficient way. The method is therefore of use in both multiconfiguration SCF (MC SCF) and multireference configuration interaction (MRCI) calculations. Examples show that the approach is efficient for both these applications.

An efficient second-order MC SCF method for long configuration expansions

A new second-order optimisation procedure for general MC SCF wavefunctions is described. The method shows greatly improved convergence as compared to previous methods. Using a determinant-based direct CI procedure which avoids the construction of a formula tape, very long complete active space (CAS SCF) wavefunctions can be handled. Energy averages of several states can also be optimised. Sample calculations for CH2, FeO, and the vinoxy radical CH2CHO with up to 178916 configurations are presented.

Molpro: a general-purpose quantum chemistry program package

Molpro (available at http://www.molpro.net) is a general‐purpose quantum chemical program. The original focus was on high‐accuracy wave function calculations for small molecules, but using local approximations combined with explicit correlation treatments, highly accurate coupled‐cluster calculations are now possible for molecules with up to approximately 100 atoms. Recently, multireference correlation treatments were also made applicable to larger molecules. Furthermore, an efficient implementation of density functional theory is available.

Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations

We apply density fitting approximations to generate the 2-electron integrals in local MP2 (LMP2) to produce a method denoted DF-LMP2. The method can equally be seen as a local version of the well-known RI-MP2 method, which in this work is referred to as DF-MP2. Local approximations reduce the asymptotic scaling of computational resources to O(N), and the most expensive step of DF-MP2 [the O(N5] assembly) is rendered negligible in DF-LMP2. It is demonstrated that for large molecules DF-LMP2 is much faster (1–2 orders of magnitude) than either LMP2 or DF-MP2. The availablility of LMP2, DF-MP2 and DF-LMP2 has for the first time made it possible to assess the accuracy of local and density fitting approximations for extended molecules using cc-pVDZ and cc-pVTZ basis sets. The density fitting errors are found to be consistently small, but the errors arising from local approximations are somewhat larger than expected from calculations on smaller systems. It is proposed to apply local density fitting approximatio...

Spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions

An efficient method for the calculation of Breit-Pauli spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions is presented. Instead of taking all two-electron contributions of the wavefunction explicitly into account, the most important two-electron contributions of the spin-orbit operator are incorporated by means of an effective one-electron Fock operator. As a further refinement, explicit two-electron contributions can be reinstated for the dominant all-internal parts of the wavefunctions.

Fast Hartree-Fock theory using local density fitting approximations

Density fitting approximations are applied to generate the Fock matrix in Hartree–Fock calculations. By localizing the orbitals in each iteration and performing separate fits for each orbital the scaling of the computational effort for the exchange can be reduced to . We also use the Poisson method to replace almost all Coulomb integrals with simple overlaps, an efficient alternative to diagonalization, and dual basis sets such that the Hartree–Fock calculation is performed in a smaller basis than the subsequent treatment of electron correlation. The accuracy and efficiency of the method is demonstrated in calculations with almost 4000 basis functions. The errors introduced by the local approximations on HF and MP2 energies are small compared to those that arise from the density fitting, and the fitting errors themselves (typically 1–10 microhartree per atom) are very small compared, for example, to the effect of basis set variations.

A determinant based full configuration interaction program

Abstract The program FCI solves the Full Configuration Interaction (Full CI) problem of quantum chemistry, in which the electronic Schrodinger equation is solved exactly within a given one particle basis set. The Slater determinant based algorithm leads to highly efficient implementation on a vector computer, and has enabled Full CI calculations of dimension more than 10 7 to be performed.

The A 2Π–X 2Σ+ red and B 2Σ+–X 2Σ+ violet systems of the CN radical: Accurate multireference configuration interaction calculations of the radiative transition probabilities

Potential energy, dipole moment, and electronic transition moment functions have been calculated for the X 2Σ+, A2Π, and B 2Σ+ states of the CN radical using internally contracted CASSCF‐CI electronic wave functions (configuration interaction with complete active space self‐consistent‐field reference functions) and large basis sets. All molecular orbitals which can be formed from the atomic 2s and 2p orbitals were included in the active space. The effect of adding δ orbitals to the active space was found to be small. The largest calculations included up to 987 reference configurations and were equivalent to uncontracted MR‐CI calculations with 11.8 million configurations. These calculations are the most accurate that have been carried out to date in terms of the size of the basis set and the treatment of electron correlation effects. Using the theoretical transition moment functions and RKR potential energy functions, radiative lifetimes of the A 2Π and B 2Σ+ states have been derived. The lifetimes of the...