Can density cumulant functional theory describe static correlation effects?

We evaluate the performance of density cumulant functional theory (DCT) for capturing static correlation effects. In particular, we examine systems with significant multideterminant character of the electronic wave function, such as the beryllium dimer, diatomic carbon, m-benzyne, 2,6-pyridyne, twisted ethylene, as well as the barrier for double-bond migration in cyclobutadiene. We compute molecular properties of these systems using the ODC-12 and DC-12 variants of DCT and compare these results to multireference configuration interaction and multireference coupled-cluster theories, as well as single-reference coupled-cluster theory with single, double (CCSD), and perturbative triple excitations [CCSD(T)]. For all systems the DCT methods show intermediate performance between that of CCSD and CCSD(T), with significant improvement over the former method. In particular, for the beryllium dimer, m-benzyne, and 2,6-pyridyne, the ODC-12 method along with CCSD(T) correctly predict the global minimum structures, while CCSD predictions fail qualitatively, underestimating the multireference effects. Our results suggest that the DC-12 and ODC-12 methods are capable of describing emerging static correlation effects but should be used cautiously when highly accurate results are required. Conveniently, the appearance of multireference effects in DCT can be diagnosed by analyzing the DCT natural orbital occupations, which are readily available at the end of the energy computation.

[1]  Andrew C Simmonett,et al.  A companion perturbation theory for state-specific multireference coupled cluster methods. , 2009, Physical chemistry chemical physics : PCCP.

[2]  Jürgen Gauss,et al.  Parallel Calculation of CCSD and CCSD(T) Analytic First and Second Derivatives. , 2008, Journal of chemical theory and computation.

[3]  A. DePrince,et al.  Parametric approach to variational two-electron reduced-density-matrix theory , 2007 .

[4]  R. Urdahl,et al.  An experimental determination of the heat of formation of C2 and the CH bond dissociation energy in C2H , 1991 .

[5]  Dmitry I. Lyakh,et al.  Multireference nature of chemistry: the coupled-cluster view. , 2012, Chemical reviews.

[6]  Ernest R. Davidson,et al.  Configuration interaction calculations on the nitrogen molecule , 1974 .

[7]  Trygve Helgaker,et al.  Electron correlation: The many‐body problem at the heart of chemistry , 2007, J. Comput. Chem..

[8]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[9]  C. Kollmar.  A size extensive energy functional derived from a double configuration interaction approach: the role of N representability conditions. , 2006, The Journal of chemical physics.

[10]  Hans-Joachim Werner,et al.  Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD) , 2001 .

[11]  D. Mazziotti.  Approximate solution for electron correlation through the use of Schwinger probes , 1998 .

[12]  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 .

[13]  Anna I. Krylov,et al.  Size-consistent wave functions for bond-breaking: the equation-of-motion spin-flip model , 2001 .

[14]  Francesco A Evangelista,et al.  Perturbative triples corrections in state-specific multireference coupled cluster theory. , 2010, The Journal of chemical physics.

[15]  Andrew C Simmonett,et al.  Density cumulant functional theory: the DC-12 method, an improved description of the one-particle density matrix. , 2013, The Journal of chemical physics.

[16]  Jeremiah J. Wilke,et al.  The Beryllium tetramer: profiling an elusive molecule. , 2011, The Journal of chemical physics.

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

[18]  Edward F. Valeev,et al.  Explicitly correlated R12/F12 methods for electronic structure. , 2012, Chemical reviews.

[19]  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.

[20]  Rodney J. Bartlett,et al.  A multireference coupled‐cluster study of the ground state and lowest excited states of cyclobutadiene , 1994 .

[21]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. VII. Valence, core-valence, and scalar relativistic basis sets for Li, Be, Na, and Mg , 2011 .

[22]  J. Gauss,et al.  Ground and excited state geometries via Mukherjee’s multireference coupled-cluster method , 2012 .

[23]  D. Cremer,et al.  m-Benzyne and bicyclo[3.1.0]hexatriene – which isomer is more stable? – a quantum chemical investigation , 2001 .

[24]  R. Bartlett,et al.  The full CCSDT model for molecular electronic structure , 1987 .

[25]  D. Mazziotti.  Variational method for solving the contracted Schrödinger equation through a projection of the N-particle power method onto the two-particle space , 2002 .

[26]  P. Knowles,et al.  An efficient method for the evaluation of coupling coefficients in configuration interaction calculations , 1988 .

[27]  V. Bondybey.  Electronic structure and bonding of Be2 , 1984 .

[28]  Branko Ruscic,et al.  Active Thermochemical Tables: dissociation energies of several homonuclear first-row diatomics and related thermochemical values , 2013, Theoretical Chemistry Accounts.

[29]  Garnet Kin-Lic Chan,et al.  Multireference quantum chemistry through a joint density matrix renormalization group and canonical transformation theory. , 2010, The Journal of chemical physics.

[30]  R. Bartlett,et al.  A study of the Be2 potential curve using the full (CCSDT) coupled‐cluster method: The importance of T4 clusters , 1988 .

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

[32]  Andrew C Simmonett,et al.  Analytic gradients for density cumulant functional theory: the DCFT-06 model. , 2012, The Journal of chemical physics.

[33]  Juana Vázquez,et al.  HEAT: High accuracy extrapolated ab initio thermochemistry. , 2004, The Journal of chemical physics.

[34]  Rodney J. Bartlett,et al.  The ‘tailored’ CCSD(T) description of the automerization of cyclobutadiene , 2011 .

[35]  Thom H. Dunning,et al.  Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon , 1995 .

[36]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[37]  Francesco A. Evangelista,et al.  Analytic gradients for Mukherjee's multireference coupled-cluster method using two-configurational self-consistent-field orbitals. , 2010, The Journal of chemical physics.

[38]  P. Knowles,et al.  Approximate variational coupled cluster theory. , 2011, The Journal of chemical physics.

[39]  Jürgen Gauss,et al.  State‐specific multireference coupled‐cluster theory , 2013 .

[40]  John D. Watts,et al.  Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods , 1990 .

[41]  Jeremy M Merritt,et al.  Beryllium Dimer—Caught in the Act of Bonding , 2009, Science.

[42]  B. A. Hess.  Do Bicyclic Forms of m‐ and p‐Benzyne Exist? , 2001 .

[43]  W. C. Lineberger,et al.  Ultraviolet Photoelectron Spectroscopy of the o-, m-, and p- Benzyne Negative Ions. Electron Affinities and Singlet−Triplet Splittings for o -, m -, and p -Benzyne , 1998 .

[44]  Francesco A Evangelista,et al.  Coupling term derivation and general implementation of state-specific multireference coupled cluster theories. , 2007, The Journal of chemical physics.

[45]  Sandeep Sharma.  A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer. , 2015, The Journal of chemical physics.

[46]  John D. Watts,et al.  Coupled‐cluster calculations on the C2 molecule and the C+2 and C−2 molecular ions , 1992 .

[47]  Alexander Yu Sokolov,et al.  Density cumulant functional theory from a unitary transformation: N-representability, three-particle correlation effects, and application to O4(+). , 2014, The Journal of chemical physics.

[48]  Seiichiro Ten-no,et al.  Initiation of explicitly correlated Slater-type geminal theory , 2004 .

[49]  George H. Booth,et al.  Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer. , 2014, The Journal of chemical physics.

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

[51]  H. P. Kelly.  CORRELATION EFFECTS IN MANY FERMION SYSTEMS: MULTIPLE PARTICLE EXCITATION EXPANSION - eScholarship , 1963 .

[52]  David A Mazziotti,et al.  Anti-hermitian contracted schrödinger equation: direct determination of the two-electron reduced density matrices of many-electron molecules. , 2006, Physical review letters.

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

[54]  D. Mazziotti.  Anti-hermitian part of the contracted Schrödinger equation for the direct calculation of two-electron reduced density matrices , 2007 .

[55]  Gustavo E. Scuseria,et al.  Particle-particle and quasiparticle random phase approximations: connections to coupled cluster theory. , 2013, The Journal of chemical physics.

[56]  Garnet Kin-Lic Chan,et al.  Canonical transformation theory from extended normal ordering. , 2007, The Journal of chemical physics.

[57]  H. Lischka,et al.  Multiconfiguration self-consistent field and multireference configuration interaction methods and applications. , 2012, Chemical reviews.

[58]  Garnet Kin-Lic Chan,et al.  Quadratic canonical transformation theory and higher order density matrices. , 2009, The Journal of chemical physics.

[59]  R. Bartlett,et al.  A study of Be2 with many‐body perturbation theory and a coupled‐cluster method including triple excitations , 1984 .

[60]  Francesco A Evangelista,et al.  Analytic gradients for the state-specific multireference coupled cluster singles and doubles model. , 2009, The Journal of chemical physics.

[61]  Daniel Kats,et al.  Communication: The distinguishable cluster approximation. II. The role of orbital relaxation. , 2014, The Journal of chemical physics.

[62]  Gustavo E. Scuseria,et al.  Seniority zero pair coupled cluster doubles theory. , 2014, The Journal of chemical physics.

[63]  Yasuda,et al.  Direct determination of the quantum-mechanical density matrix using the density equation. , 1996, Physical review letters.

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

[65]  R. Bartlett,et al.  The coupled‐cluster single, double, triple, and quadruple excitation method , 1992 .

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

[67]  T. Crawford,et al.  The structures of m-benzyne and tetrafluoro-m-benzyne. , 2005, The Journal of chemical physics.

[68]  R. Ahlrichs,et al.  Many body perturbation calculations and coupled electron pair models , 1979 .

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

[70]  Frederick R. Manby,et al.  Fast linear scaling second-order Møller-Plesset perturbation theory (MP2) using local and density fitting approximations , 2003 .

[71]  J. Paier,et al.  Photochemistry of ethylene: a multireference configuration interaction investigation of the excited-state energy surfaces. , 2004, The Journal of chemical physics.

[72]  Frederick R. Manby,et al.  R12 methods in explicitly correlated molecular electronic structure theory , 2006 .

[73]  Sandeep Sharma,et al.  The density matrix renormalization group in quantum chemistry. , 2011, Annual review of physical chemistry.

[74]  R. Bartlett,et al.  Ab initio calculations on the energy of activation and tunneling in the automerization of cyclobutadiene , 1988 .

[75]  S. Langhoff,et al.  An initio calculations on C2, Si2, and SiC , 1987 .

[76]  Josef Paldus,et al.  Accounting for the exact degeneracy and quasidegeneracy in the automerization of cyclobutadiene via multireference coupled-cluster methods. , 2009, The Journal of chemical physics.

[77]  Leszek Meissner,et al.  Size-consistency corrections for configuration interaction calculations , 1988 .

[78]  Todd J. Martínez,et al.  Photodynamics of ethylene: ab initio studies of conical intersections , 2000 .

[79]  Matthew L. Leininger,et al.  Psi4: an open‐source ab initio electronic structure program , 2012 .

[80]  L. Gagliardi,et al.  Full configuration interaction calculations on Be2 , 1994 .

[81]  Frank Neese,et al.  Natural triple excitations in local coupled cluster calculations with pair natural orbitals. , 2013, The Journal of chemical physics.

[82]  B. Roos.  The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations , 2007 .

[83]  G. A. Petersson,et al.  The convergence of coupled-cluster methods for Be2 , 1991 .

[84]  Alexander Yu Sokolov,et al.  Orbital-optimized density cumulant functional theory. , 2013, The Journal of chemical physics.

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

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

[87]  P. Knowles,et al.  A second order multiconfiguration SCF procedure with optimum convergence , 1985 .

[88]  Frank Neese,et al.  An efficient and near linear scaling pair natural orbital based local coupled cluster method. , 2013, The Journal of chemical physics.

[89]  C. David Sherrill,et al.  Full configuration interaction potential energy curves for the X 1Σg+, B 1Δg, and B′ 1Σg+ states of C2: A challenge for approximate methods , 2004 .

[90]  W. Sander.  m-Benzyne and p-Benzyne , 1999 .

[91]  David A Mazziotti,et al.  Parametrization of the two-electron reduced density matrix for its direct calculation without the many-electron wave function. , 2008, Physical review letters.

[92]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[93]  P. Knowles,et al.  An efficient internally contracted multiconfiguration–reference configuration interaction method , 1988 .

[94]  Frank Neese,et al.  The coupled electron pair approximation: variational formulation and spin adaptation , 2010 .

[95]  Krishnan Raghavachari,et al.  Electron Correlation Effects in Molecules , 1996 .

[96]  Alexander Yu Sokolov,et al.  Benchmark Study of Density Cumulant Functional Theory: Thermochemistry and Kinetics. , 2014, Journal of chemical theory and computation.

[97]  Jeremiah J. Wilke,et al.  Density cumulant functional theory: first implementation and benchmark results for the DCFT-06 model. , 2010, The Journal of chemical physics.

[98]  Garnet Kin-Lic Chan,et al.  Canonical transformation theory for multireference problems. , 2006, The Journal of chemical physics.

[99]  C. Valdemoro,et al.  Approximating q-order reduced density matrices in terms of the lower-order ones. II. Applications. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[100]  A. J. Merer,et al.  Ultraviolet spectra and excited states of ethylene and its alkyl derivatives , 1969 .

[101]  David Feller,et al.  The use of systematic sequences of wave functions for estimating the complete basis set, full configuration interaction limit in water , 1993 .

[102]  Konrad Patkowski,et al.  On the Elusive Twelfth Vibrational State of Beryllium Dimer , 2009, Science.

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

[104]  P. Knowles,et al.  An efficient second-order MC SCF method for long configuration expansions , 1985 .