https://zenodo.org/record/1258869/files/article.pdf

NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations

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 uncontracted MRCI wave functions are mostly smaller than 1 mH and typically 3–5 times smaller than the deviations between the uncontracted MRCI and the full CI. Dipole moments, electric dipole polarizabilities, and electronic dipole transition moments calculated with uncontracted and contracted MRCI wave functions also are found to be in close agreement. The efficiency of the method is demonstrated in large scale calculations for the CN, NH3, CO2, and Cr2 molecules. In these calculations up to 3088 reference configurations and up to 154 orbitals were employed. The biggest calculation is equivalent to an uncontracted MRCI with more than 78 million configurations.

An efficient internally contracted multiconfiguration–reference configuration interaction method

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 negative eigenvalues

A second order multiconfiguration SCF procedure with optimum convergence

MP2 energy evaluation by direct methods

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

Weakly Bonded Systems

A thorough analysis of the direct CI method as applied to the case of a general set of reference configurations coupled to all single and double substitutions is presented. It is pointed out that there is no single strategy which proves optimal under all circumstances. A variety of procedures are therefore presented together with rules to enable the selection of the most favourable under a given circumstance. Much emphasis has been placed on organizing the calculations via a series of matrix multiplications, which enables a vector or array processing computer to be used to best effect. Some consideration is given to using an atomic integral (rather than molecular integral) driven scheme for some interactions, thus removing the necessity for a complete transformation of the molecular integrals to a molecular orbital basis, and the advantages and disadvantages of so doing are discussed. Improved procedures for carrying out both full and partial transformations of the molecular integrals are described. A num...

The direct CI method

The basis set superposition error in correlated electronic structure calculations

A new and very general form of valence‐bond theory is described. In this theory the molecular wave function is written as any desired linear combination of valence‐bond structures, and the nonorthogonal orbitals used in the construction of the valence‐bond structures are allowed to distort to their optimal shapes. The orbital optimization is achieved through successive transformations of an orbital basis. The theory of the method is based on an extension of the ‘‘generalized Brillouin theorem’’ which is presented in the text. The new VB–SCF method is a generalization of the molecular orbital MC–SCF method to permit the use of nonorthogonal orbitals. It, therefore, encompasses the MC–SCF method as a restricted subclass. Several different forms of restriction may be imposed on the orbitals and on the optimization procedures. One of these only allows orbitals centered on the same atom to mix during optimization and in this way generates optimal hybrid orbitals, which it is expected will prove to be of particular interest in providing simple qualitative descriptions of the chemical bond. Test calculations are presented for LiH, He+2, and for the ground‐state potential energy curve of OH. The VB–SCF wave function and optimized orbitals may be used as a starting point for the construction of a larger multistructure valence‐bond wave function which we term a VB‐CI function. The VB–SCF and VB–CI results presented in the paper show that the method is capable of yielding very accurate molecular potential energy curves.

J.H. van Lenthe

Papers

Weakly Bonded Systems

The direct CI method

The basis set superposition error in correlated electronic structure calculations

The valence‐bond self‐consistent field method (VB–SCF): Theory and test calculations

The ZORA formalism applied to the Dirac-Fock equation