Hybrid correlation models based on active-space partitioning: seeking accurate O(N5) ab initio methods for bond breaking.

Moller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N5) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N5) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H2O, CH+, CH4, and Li2 molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N5) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.

[1]  R. Bartlett,et al.  Critical comparison of various connected quadruple excitation approximations in the coupled-cluster treatment of bond breaking. , 2005, The Journal of chemical physics.

[2]  C. David Sherrill,et al.  The Configuration Interaction Method: Advances in Highly Correlated Approaches , 1999 .

[3]  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 .

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

[5]  Antara Dutta,et al.  Full configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods , 2003 .

[6]  Poul Jørgensen,et al.  The second-order approximate coupled cluster singles and doubles model CC2 , 1995 .

[7]  Anna I. Krylov,et al.  A spin-complete version of the spin-flip approach to bond breaking: What is the impact of obtaining spin eigenfunctions? , 2003 .

[8]  Martin Head-Gordon,et al.  A nonorthogonal approach to perfect pairing , 2000 .

[9]  Anna I. Krylov,et al.  Spin-flip configuration interaction: an electronic structure model that is both variational and size-consistent , 2001 .

[10]  C. David Sherrill,et al.  Chapter 4 Bond Breaking in Quantum Chemistry , 2005 .

[11]  Anna I. Krylov,et al.  The spin–flip approach within time-dependent density functional theory: Theory and applications to diradicals , 2003 .

[12]  Anna I. Krylov,et al.  Spin-contamination of coupled-cluster wave functions , 2000 .

[13]  W. Kutzelnigg.  Pair Correlation Theories , 1977 .

[14]  Karol Kowalski,et al.  Extension of the method of moments of coupled-cluster equations to excited states: The triples and quadruples corrections to the equation-of-motion coupled-cluster singles and doubles energies , 2002 .

[15]  Michael J. McGuire,et al.  Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches , 2002 .

[16]  Anna I. Krylov,et al.  Perturbative corrections to the equation-of-motion spin–flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals , 2002 .

[17]  Marcel Nooijen,et al.  Combining coupled cluster and perturbation theory , 1999 .

[18]  The state-universal multi-reference coupled-cluster theory with perturbative description of core-virtual excitations , 2001 .

[19]  Berhane Temelso,et al.  A Comparison of One-Particle Basis Set Completeness, Higher-Order Electron Correlation, Relativistic Effects, and Adiabatic Corrections for Spectroscopic Constants of BH, CH+, and NH† , 2004 .

[20]  C David Sherrill,et al.  Hybrid correlation models based on active-space partitioning: correcting second-order Moller-Plesset perturbation theory for bond-breaking reactions. , 2005, The Journal of chemical physics.

[21]  J. Olsen,et al.  Comparison of full-configuration interaction and coupled-cluster harmonic and fundamental frequencies for BH and HF , 2001 .

[22]  Karol Kowalski,et al.  Extension of renormalized coupled-cluster methods including triple excitations to excited electronic states of open-shell molecules. , 2005, The Journal of chemical physics.

[23]  R. Bartlett,et al.  A direct product decomposition approach for symmetry exploitation in many-body methods. I. Energy calculations , 1991 .

[24]  Ernest R. Davidson,et al.  Different forms of perturbation theory for the calculation of the correlation energy , 1992 .

[25]  P. Piecuch,et al.  Improved computational strategy for the state‐selective coupled‐cluster theory with semi‐internal triexcited clusters: Potential energy surface of the HF molecule , 1995 .

[26]  Gregory J O Beran,et al.  Second-order correction to perfect pairing: an inexpensive electronic structure method for the treatment of strong electron-electron correlations. , 2006, The Journal of chemical physics.

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

[28]  On the application of the Kohn–Sham theory to the calculation of potential energy curves , 1998 .

[29]  S. Kucharski,et al.  Coupled-cluster methods with internal and semi-internal triply excited clusters: Vibrational spectrum of the HF molecule , 1999 .

[30]  P. Piecuch,et al.  Molecular quadrupole moment functions of HF and N2. I. Ab initio linear‐response coupled‐cluster results , 1996 .

[31]  Christof Hättig,et al.  Geometry optimizations with the coupled-cluster model CC2 using the resolution-of-the-identity approximation , 2003 .

[32]  R. Bartlett,et al.  The description of N2 and F2 potential energy surfaces using multireference coupled cluster theory , 1987 .

[33]  Wei Chen,et al.  Evaluation of S2 for correlated wave functions and spin projection of unrestricted Mo/ller–Plesset perturbation theory , 1994 .

[34]  S. Kucharski,et al.  Method of Moments of Coupled-Cluster Equations: A New Theoretical Framework for Designing "Black-Box" Approaches for Molecular Potential Energy Surfaces , 2002 .

[35]  P. Piecuch,et al.  The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances , 2002 .

[36]  H. Schaefer.  Methods of Electronic Structure Theory , 1977 .

[37]  Martin Head-Gordon,et al.  The imperfect pairing approximation , 2000 .

[38]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .