Density cumulant functional theory: first implementation and benchmark results for the DCFT-06 model.

Density cumulant functional theory [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] is implemented for the first time. Benchmark results are provided for atoms and diatomic molecules, demonstrating the performance of DCFT-06 for both nonbonded and bonded interactions. The results show that DCFT-06 appears to perform similarly to coupled cluster theory with single and double excitations (CCSD) in describing dispersion. For covalently bound systems, the physical properties predicted by DCFT-06 appear to be at least of CCSD quality around equilibrium geometries. The computational scaling of both DCFT-06 and CCSD is O(N(6)), but the former has reduced nonlinearities among the variables and a Hermitian energy functional, making it an attractive alternative.

[1]  Werner Kutzelnigg,et al.  Quantum chemistry in Fock space. I. The universal wave and energy operators , 1982 .

[2]  Matthew L. Leininger,et al.  PSI3: An open‐source Ab Initio electronic structure package , 2007, J. Comput. Chem..

[3]  P. Ayers,et al.  Subsystem constraints in variational second order density matrix optimization: curing the dissociative behavior. , 2009, The Journal of chemical physics.

[4]  Frank Neese,et al.  Accurate theoretical chemistry with coupled pair models. , 2009, Accounts of chemical research.

[5]  Werner Kutzelnigg,et al.  Density-cumulant functional theory. , 2006, The Journal of chemical physics.

[6]  Maho Nakata,et al.  Size extensivity of the variational reduced-density-matrix method , 2009 .

[7]  David A Mazziotti,et al.  Quantum chemistry without wave functions: two-electron reduced density matrices. , 2006, Accounts of chemical research.

[8]  E. Davidson.  Linear Inequalities for Density Matrices , 1969 .

[9]  Jun Li,et al.  Basis Set Exchange: A Community Database for Computational Sciences , 2007, J. Chem. Inf. Model..

[10]  A. J. Coleman.  THE STRUCTURE OF FERMION DENSITY MATRICES , 1963 .

[11]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton , 1993 .

[12]  P. Ayers,et al.  Incorrect diatomic dissociation in variational reduced density matrix theory arises from the flawed description of fractionally charged atoms. , 2009, Physical chemistry chemical physics : PCCP.

[13]  V. H. Smith,et al.  On Different Criteria for the Best Independent‐Particle Model Approximation , 1964 .

[14]  Debashis Mukherjee,et al.  Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory , 2005 .

[15]  F. Neese,et al.  Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method. , 2009, The Journal of chemical physics.

[16]  T. Crawford,et al.  An Introduction to Coupled Cluster Theory for Computational Chemists , 2007 .

[17]  W. Kutzelnigg,et al.  Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems. IV. Perturbative analysis. , 2004, The Journal of chemical physics.

[18]  D. Mazziotti.  Variational minimization of atomic and molecular ground-state energies via the two-particle reduced density matrix , 2002 .

[19]  H. H. Nielsen.  The Vibration-Rotation Energies of Molecules , 1951 .

[20]  F. Neese,et al.  A comparative study of single reference correlation methods of the coupled-pair type , 2008 .

[21]  P. Löwdin.  Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction , 1955 .

[22]  Debashis Mukherjee,et al.  Normal order and extended Wick theorem for a multiconfiguration reference wave function , 1997 .

[23]  David Feller.  The role of databases in support of computational chemistry calculations , 1996 .

[24]  R. Bartlett.  Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules , 1981 .

[25]  E. Davidson,et al.  Necessary conditions for the N-representability of pair distribution functions , 2006 .

[26]  J. Percus,et al.  Reduction of the N‐Particle Variational Problem , 1964 .

[27]  J. Stanton.  Why CCSD(T) works: a different perspective , 1997 .

[28]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[29]  K. Fujisawa,et al.  Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm , 2001 .

[30]  Wilfried Meyer,et al.  PNO–CI Studies of electron correlation effects. I. Configuration expansion by means of nonorthogonal orbitals, and application to the ground state and ionized states of methane , 1973 .

[31]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[32]  Mituhiro Fukuda,et al.  Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known N-representability conditions. , 2006, The Journal of chemical physics.

[33]  Mituhiro Fukuda,et al.  Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver. , 2008, The Journal of chemical physics.

[34]  Andrew G. Taube,et al.  Rethinking linearized coupled-cluster theory. , 2009, The Journal of chemical physics.

[35]  Debashis Mukherjee,et al.  Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems. I. The equations satisfied by the density cumulants , 2001 .

[36]  F. Weinhold,et al.  Reduced Density Matrices of Atoms and Molecules. II. On the N‐Representability Problem , 1967 .

[37]  Debashis Mukherjee,et al.  Cumulant expansion of the reduced density matrices , 1999 .

[38]  D. Mazziotti.  Contracted Schrödinger equation: Determining quantum energies and two-particle density matrices without wave functions , 1998 .

[39]  C. David Sherrill,et al.  High-Accuracy Quantum Mechanical Studies of π−π Interactions in Benzene Dimers , 2006 .