Generalizations of the direct CI method based on the graphical unitary group approach. II. Single and double replacements from any set of reference configurations
01 Feb 1980-Journal of Chemical Physics (American Institute of Physics)-Vol. 72, Iss: 3, pp 1647-1656
TL;DR: In this paper, the coupling coefficients appearing in the direct CI formalism are factorized into a complicated internal part and a simple external part, which is then used for the unitary group formulation of the correlation problem.
Abstract: The direct CI method is generalized to the case of all single and double replacements from an arbitrary set of reference configurations. This is a continuation of the work and ideas presented in an earlier paper on first order wave functions. The analysis is done using the unitary group formulation of the correlation problem, and the resulting method is a combination of the direct CI method and the unitary group approach as formulated particularly by Paldus and Shavitt. The main idea in the present work is the factorization of the coupling coefficients appearing in the direct CI formalism, into a complicated internal part and a simple external part. The general philosophy is like in all direct CI methods to allow long CI expansions by avoiding the storage and retrieval of a large formula tape. The longest CI expansion treated in this paper is an application on the system CH2(3B1)+H2→CH3+H with five reference states, resulting in 16 096 configurations. The barrier height for the reaction is calculated to b...
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TL;DR: In this article, 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.
Abstract: 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.
3,375 citations
TL;DR: In this article, a density matrix formulation of the super-CI MCSCF method is presented, where the MC expansion is assumed to be complete in an active subset of the orbital space, and the corresponding CI problem is solved by a direct scheme using the unitary group approach.
3,120 citations
TL;DR: In this article, 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.
Abstract: 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
2,739 citations
TL;DR: In this article, a new method for evaluating one-particle coupling coefficients in 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.
2,455 citations
TL;DR: MOLCAS as discussed by the authors is a package for calculations of electronic and structural properties of molecular systems in gas, liquid, or solid phase, which contains a number of modern quantum chemical methods for studies of the electronic structure in ground and excited electronic states.
1,678 citations
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TL;DR: In this article, a method for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation is proposed.
Abstract: A method is suggested for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one‐electron approximation. The method is based on the use of the creation and annihilation operators, hole—particle formalism, Wick's theorem, and the technique of Feynman‐like diagrams. The connection of this method with the configuration‐interaction method as well as with the perturbation theory in the quantum‐field theoretical form is discussed. The method is applied to the simple models of nitrogen and benzene molecules. The results are compared with those obtained with the configuration‐interaction method considering all possible configurations within the chosen basis of one‐electron functions.
2,676 citations
TL;DR: In this paper, a new method for obtaining the coefficients in a large Cl expansion is proposed, where the expansion coefficients are obtained directly from the list of two-electron integrals by means of an iterative procedure.
468 citations
TL;DR: In this article, the configuration interaction (CI) method has been applied to determine an accurate potential energy surface for linear H3, and the calculated surface is believed to lie no more than 0.8 kcal/mole and no less than 2.2 kcal /mole above the exact surface, a significant improvement over all previous calculations.
Abstract: The configuration interaction (CI) method has been applied to determine an accurate potential energy surface for linear H3. The calculated surface is believed to lie no more than 0.8 kcal/mole and no less than 0.2 kcal/mole above the exact surface, a significant improvement over all previous calculations. The calculation yields a linear symmetric saddle point at an internuclear separation of 1.757 a.u. The saddle point energy is 9.8 kcal/mole above the calculated energy of an isolated hydrogen atom and a hydrogen molecule, and 10.28 kcal/mole above the exact energy of the isolated systems. An estimated lower bound for the barrier height is 9.5 kcal/mole. Comparison of the calculated H3 potential surface with the best semiempirical surface and the best previous ab initio surface shows good qualitative agreement. However, there are quantitative differences, whose effect can only be determined by accurate dynamical calculations. The method employed in the H3 calculation was designed to approach the complete ...
458 citations
TL;DR: In this paper, a formalism for the generation of spin-symmetry adapted configuration interaction (CI) matrices of the N −electron atomic or molecular systems, described by nonrelativistic spin-independent Hamiltonians, is presented.
Abstract: A formalism for an efficient generation of spin‐symmetry adapted configuration interaction (CI) matrices of the N‐electron atomic or molecular systems, described by nonrelativistic spin‐independent Hamiltonians, is presented. The Gelfand and Tsetlin canonical basis for the finite dimensional irreducible representations of the unitary groups is used as an N‐electron CI basis. A simplified Gelfand‐type pattern pertaining to the N‐electron problem is introduced, which considerably simplifies the canonical basis generation and, more importantly, the calculation of representation matrices of the (infinitesimal) generators of the pertinent unitary group in this basis. The calculation of the CI matrices for the above mentioned systems is then straightforward, since any particle number conserving operator may be written as a sum of n‐degree forms in the unitary group generators. The computation of CI matrices for various Hamiltonians as well as the problems of the space‐symmetry adaptation of the Gelfand‐Tsetlin basis and of limited CI calculations are briefly discussed.
424 citations