On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods
01 Dec 1966-Journal of Chemical Physics (American Institute of Physics)-Vol. 45, Iss: 11, pp 4256-4266
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.
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TL;DR: In this paper, a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness).
Abstract: The calculation of accurate electron affinities (EAs) of atomic or molecular species is one of the most challenging tasks in quantum chemistry. We describe a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness). This procedure involves the use of the recently proposed correlation‐consistent basis sets augmented with functions to describe the more diffuse character of the atomic anion coupled with a straightforward, uniform expansion of the reference space for multireference singles and doubles configuration‐interaction (MRSD‐CI) calculations. Comparison with previous results and with corresponding full CI calculations are given. The most accurate EAs obtained from the MRSD‐CI calculations are (with experimental values in parentheses) hydrogen 0.740 eV (0.754), boron 0.258 (0.277), carbon 1.245 (1.263), oxygen 1.384 (1.461), and fluorine 3.337 (3.401). The EAs obtained from the MR‐SD...
12,969 citations
TL;DR: In this paper, a new augmented version of coupled-cluster theory, denoted as CCSD(T), is proposed to remedy some of the deficiencies of previous augmented coupledcluster models.
7,249 citations
TL;DR: The coupled cluster singles and doubles model (CCSD) as discussed by the authors is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin-orbital form, and the computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are compared with full CI calculations for H2O and BeH2.
Abstract: The coupled‐cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher‐order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth‐order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low‐order models provide estimates of the effect of the higher‐order terms T1T2, T21T2, T31, and T41 on the correlation energy.
5,603 citations
TL;DR: An overview of NWChem is provided focusing primarily on the core theoretical modules provided by the code and their parallel performance, as well as Scalable parallel implementations and modular software design enable efficient utilization of current computational architectures.
4,666 citations
TL;DR: In this article, a general procedure for calculation of the electron correlation energy, starting from a single Hartree-Fock determinant, is introduced, and the relation of this method to coupled-cluster (CCSD) theory is discussed.
Abstract: A general procedure is introduced for calculation of the electron correlation energy, starting from a single Hartree–Fock determinant. The normal equations of (linear) configuration interaction theory are modified by introducing new terms which are quadratic in the configuration coefficients and which ensure size consistency in the resulting total energy. When used in the truncated configuration space of single and double substitutions, the method, termed QCISD, leads to a tractable set of quadratic equations. The relation of this method to coupled‐cluster (CCSD) theory is discussed. A simplified method of adding corrections for triple substitutions is outlined, leading to a method termed QCISD(T). Both of these new procedures are tested (and compared with other procedures) by application to some small systems for which full configuration interaction results are available.
4,194 citations
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1,002 citations
TL;DR: In this article, the ground state wave functions of a closed shell nucleus are approximated by a Slater determinant in the restricted region of configuration space where all internucleon distances are larger than a certain "healing distance".
991 citations
TL;DR: In this paper, the correlation energy per particle of an electron gas expressed in rydbergs is computed for small values of rs (high density) and found to be given by ec=Alnrs+C+O(rs).
Abstract: The quantity ec is defined as the correlation energy per particle of an electron gas expressed in rydbergs. It is a function of the conventional dimensionless parameter rs, where rs-3 is proportional to the electron density. Here ec is computed for small values of rs (high density) and found to be given by ec=Alnrs+C+O(rs). The value of A is found to be 0.0622, a result that could be deduced from previous work of Wigner, Macke, and Pines. An exact formula for the constant C is given here for the first time; earlier workers had made only approximate calculations of C. Further, it is shown how the next correction in rs can be computed. The method is based on summing the most highly divergent terms of the perturbation series under the integral sign to give a convergent result. The summation is performed by a technique similar to Feynman's methods in field theory.
985 citations
TL;DR: In this paper, an exact formal solution to the problem of a system of fermions in interaction is obtained in a form which avoids the problems of unlinked clusters in manybody theory.
Abstract: An exact formal solution is obtained to the problem of a system of fermions in interaction. This solution is expressed in a form which avoids the problem of unlinked clusters in manybody theory. The technique of Feynman graphs is used to derive the series and to define linked terms. The graphs are those appropriate to a system of many fermions and are used to give a new derivation of the Hartree-Fock and Brueckner methods for this problem.
844 citations
TL;DR: In this paper, a theory is developed to see what the physically important features of correlation in atoms and molecules are, based on this to obtain a quantitative scheme for N −electron systems as in He and H2.
Abstract: A theory is developed (a) to see what the physically important features of correlation in atoms and molecules are; (b) based on this to obtain a quantitative scheme for N‐electron systems as in He and H2; (c) to see what happens to the ``chemical'' picture, to semiempirical theories, and to shell structure, when correlation is brought in. It is shown why, unlike in an electron gas, in many atoms and in molecules mainly pair correlations are significant. In configuration‐interaction, multiple excitations arise not as three or more electron ``collisions,'' but as several binary ``collisions'' taking place separately but at the same time. The validity of theory is shown on Be, LiH, and boron. The theory does not depend on any perturbation or series expansion and the r12‐coordinate method can now be used for an N‐electron system as in He and H2.
439 citations