Jozef Noga

BASIS-SET CONVERGENCE OF CORRELATED CALCULATIONS ON WATER

The basis-set convergence of the electronic correlation energy in the water molecule is investigated at the second-order Mo/ller–Plesset level and at the coupled-cluster singles-and-doubles level with and without perturbative triples corrections applied. The basis-set limits of the correlation energy are established to within 2 mEh by means of (1) extrapolations from sequences of calculations using correlation-consistent basis sets and (2) from explicitly correlated calculations employing terms linear in the interelectronic distances rij. For the extrapolations to the basis-set limit of the correlation energies, fits of the form a+bX−3 (where X is two for double-zeta sets, three for triple-zeta sets, etc.) are found to be useful. CCSD(T) calculations involving as many as 492 atomic orbitals are reported.

The full CCSDT model for molecular electronic structure

The full coupled‐cluster model (CCSDT) single, double, and triple excitation method defined by the wave function exp(T1+T2+T3)‖Φ0〉 is formulated and computationally implemented for the first time. Explicit computational equations are presented. The method is applied to numerous examples including BH, FH, C2H2, CO, Ne, F−, and H2O to assess its applicability to the correlation problem. Results from CCSDT agree with full CI, to an average error of less than 1 kcal/mol even for difficult bond breaking examples. A series of results for various approximate, but computationally more efficient versions of the full CCSDT model are also studied and shown to give results in excellent agreement with CCSDT. Additional comparisons with fifth‐order MBPT are reported.

Towards a full CCSDT model for electron correlation

Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT‐1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth‐order MBPT. In this approximation, an MBPT(4)‐like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT‐1 results.

Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods

Abstract In critical cases, single-reference correlated methods like coupled-cluster theory or its quadratic CI approximations fail because of the importance of additional highly excited excitations that cannot usually be included, like connected triple and quadruple excitations. Here we present the first, non-iterative method to evaluate the full set of fifth-order corrections to CCSD and QCISD and assess their accuracy compared to full CI for the very sensitive Be 2 curve and other cases.

COUPLED CLUSTER THEORY THAT TAKES CARE OF THE CORRELATION CUSP BY INCLUSION OF LINEAR TERMS IN THE INTERELECTRONIC COORDINATES

CC‐R12—a combination of coupled cluster theory and the R12 method, is presented in which the correlation cusp is treated via inclusion of terms explicitly dependent on the interelectronic distance rij into the exponential expansion of the wave function. A diagrammatic derivation of the CC‐R12 equations within the so‐called ‘‘standard approximation B’’ is given at the level of singles, doubles and triples (CCSDT‐R12). MBPT(4)‐R12 is derived as a byproduct of CCSDT‐R12. Fifth order noniterative corrections are also discussed.

Towards a full CCSDT model for electron correlation. CCSDT-n models

Abstract The first numerical results using two extended coupled cluster models that include triple excitations, CCSDT-2 and CCSDT-3, are reported and compared to full CI for several systems. These methods are shown to be superior to CCSDT-1 when the reference function is poor, such as in bond breaking cases. The errors compared to full CI vary from 0.1 to 1.2 kcal mol .

An explicitly correlated coupled cluster calculation of the helium–helium interatomic potential

Explicitly correlated coupled cluster (CCSDT‐1a‐R12) results were obtained for the He2 interatomic potential from a new, integral‐direct implementation. With the new code, Gaussian basis sets as large as 11s8p6d5f4g3h could be employed, and the potential energy curve was calculated over a wide range using a basis of the type 11s8p6d5f4g.This curve is very close to represent the basis set limit of the CCSDT‐1a approach. At the internuclear separation R=5.6 a0, the CCSDT‐1a limiting value for the interaction energy is −10.68 K. As the effect of quadruple substitutions can be estimated as −0.32 K, this limiting value is perfectly consistent with the accurate quantum Monte Carlo calculation of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], who reported a well depth of −11.01±0.10 K. On the other hand, however, CCSDT‐1a‐R12 calculations of the He2 potential energy curve strongly indicate that the most recent semiempirical potentials available in the literature are slightly too repulsive for short (R≤4.0 a0) ...

The expectation value coupled-cluster method and analytical energy derivatives☆

Abstract A new method for correlation energies and properties based upon the coupled-cluster expectation value (XCC) expression is developed. The size-extensive XCC method is shown to satisfy the generalized Hellmann-Feynman theorem, aiding the evaluation of first and higher derivatives to define molecular properties or to search energy surfaces and predict vibrational spectra. Though truncated at order n , XCC( n ) methods include effects of infinite-order correlation, containing MBPT( n ) as a special case. In XCC(5), the contributions from connected quadruple excitations arise, but these may be evaluated with only an ∼ n 7 algorithm instead of the ∼ n 10 that might have been expected.

The fourth order diagrammatic MB‐RSPT calculations of the correlation energy of ten electron systems

The aim of this work is to analyze the correlation energy of the 10‐electron systems Ne, HF, H2O, and NH3, using the diagrammatic many‐body perturbation theory up to the fourth order. The second and third order contributions are included fully. In the fourth order, attention was directed to the detailed analysis of the inter‐relation of contributions which arise from all double excitations, from the renormalization term as well as from quadruple excitations which are due to non‐EPV contributions from quadruple excitations diagrams. The connections with other methods are also discussed.

Explicitly correlated electronic structure theory from R12/F12 ansätze

Fundamental aspects of the explicitly correlated R12 and F12 theories are summarized in the perspective of recent advances related to our contribution in this field. Starting from the basics of pair functions and second quantized formulations, the R12/F12 ansätze have been applied to MP2, coupled‐cluster, and equation of motion coupled‐cluster theories. Emphasis is given to approaches that use the rational generator to create the exact cusp conditions (SP ansatz). Computational aspects of the evaluation of many‐electron integrals are also discussed in conjunction with the use of the Slater‐type geminal, which is the predominant choice for the correlation factor in modern R12/F12 theories.