Nevin Oliphant

A state‐selective multireference coupled‐cluster theory employing the single‐reference formalism

A new state‐selective multireference (MR) coupled‐cluster (CC) method exploiting the single‐reference (SR) particle‐hole formalism is described. It is an extension of a simple two‐reference formalism, which we presented in our earlier paper [N. Oliphant and L. Adamowicz, J. Chem. Phys. 94, 1229 (1991)], and a rigorous formulation of another method of ours, which we obtained as an approximation of the SRCC approach truncated at triple excitations (SRCCSDT) [N. Oliphant and L. Adamowicz, J. Chem. Phys. 96, 3739 (1992)]. The size extensivity of the resulting correlation energies is achieved by employing a SRCC‐like ansatz for the multideterminantal wave function. General considerations are supplemented by suggesting a hierarchy of approximate schemes, with the MRCCSD approach (MRCC approach truncated at double excitations from the reference determinants) representing the most important one. Our state‐selective MRCCSD theory emerges through a suitable selection of the most essential cluster components appearing in the full SRCCSDTQ method (SRCC method truncated at quadruple excitations), when the latter is applied to quasidegenerate states. The complete set of equations describing our MRCCSD formalism is presented and the possibility of the recursive intermediate factorization [S. A. Kucharski and R. J. Bartlett, Theor. Chim. Acta 80, 387 (1991)] of our approach, leading to an efficient computer algorithm, is discussed.

Multireference coupled‐cluster method using a single‐reference formalism

A multireference coupled‐cluster singles and doubles method utilizing two reference determinants which differ by a two electron excitation is proposed. One of these determinants is selected as the formal reference determinant. The proposed method includes single‐reference coupled‐cluster equations truncated after quadruples. These equations are graphically derived using Feynman diagrams. The appropriate restrictions are then placed on the triple and quadruple amplitudes to allow only those amplitudes which correspond to single and double excitations from the second reference determinant.

The implementation of the multireference coupled-cluster method based on the single-reference formalism

A generalized version of the multireference coupled‐cluster method using a single‐reference formalism, which we presented in an earlier paper, has been implemented. Any number of determinants, that differ from the formal reference determinant by single or double excitations, can now be included in the reference space. In the present implementation, the single and double excitations from the secondary reference determinants have been truncated to include only those that correspond to triple excitations from the formal reference determinant. Calculations are done on a few model systems, LiH, BH, and H2O, at equilibrium and stretched geometries. Comparisons are made with full configuration interaction (CI) treatment for the single bond stretch in LiH and BH, and the results are quite promising. For the water molecule, comparisons are made with the results obtained with the coupled cluster method truncated at triple excitations (CCSDT), as well as with the full CI results. While the multireference method did not do as well for the simultaneous two‐bond stretch in H2O as it did for the single bond cases, it did at least as well as the CCSDT at representing the points on the full CI potential curve.

Coupled‐cluster method truncated at quadruples

The coupled‐cluster (CC) equations including single, double, triple, and quadruple excitation amplitudes (CCSDTQ) are derived diagramatically, and the complete set of CCSDTQ equations are presented. These equations have been programmed and an iterative reduced linear equation method is used to solve these equations. The potential curves for the dissociation of a model system with a single bond (Li2 and LiH) is calculated using CC doubles (CCD), singles and doubles (CCSD), singles, doubles, and triples (CCSDT), and CCSDTQ. These calculations demonstrate the magnitude of the CC contributions arising from single, double, triple, and quadruple excitation amplitudes to the stretching of a chemical bond.

A systematic comparison of molecular properties obtained using Hartree–Fock, a hybrid Hartree–Fock density‐functional‐theory, and coupled‐cluster methods

We present results of a systematic study of the theoretical determination of equilibrium geometries, harmonic frequencies, total atomization energies, and dipole moments using Hartree–Fock, a hybrid Hartree–Fock density‐functional‐theory, and coupled‐cluster methods in conjunction with a triple zeta basis set for a large set of molecules. This allows a direct comparison of the three theoretical methods applied to a range of chemical systems. The average errors (‖experimental value‐theoretical value‖) for the Hartree–Fock, hybrid Hartree–Fock density‐functional‐theory, and coupled‐cluster methods, respectively, are bond length (A) 0.022, 0.005, 0.005; bond angle (degrees) 2.7, 1.7, 1.9; harmonic frequencies (cm−1) 144, 40, 30; atomization energies (kcal/mol) 81.9, 3.6, 11.5; and dipole moments (debye) 0.29, 0.14, 0.10. This clearly demonstrates that the relatively inexpensive hybrid Hartree–Fock density‐functional‐theory method yields results which represent a reliable, significant improvement over those o...

Multireference coupled cluster method for electronic structure of molecules

Abstract In this review we present a systematic derivation of the multireference coupled cluster theory based on the single reference formalism. The coupled cluster theories have recently emerged as one of the major method development activities in the electronic structure theory of atoms and molecules. Due to its size-extensive nature, using the coupled cluster method the total electronic energy of the system can be determined with the same relative accuracy as the total electronic energies of the fragments which the system separates into in the process of chemical decomposition. This feature is essential for the correct theoretical determination of dissociation energies as well as other molecular properties. One of the most difficult challenges in advancing the coupled cluster theory has been the development of the multireference coupled cluster methodology, i.e. generating a scheme which allows the reference function to incorporate more than one Slater determinant. Such development would enable a very ...

Fourier transform emission spectroscopy of the jet-cooled CCN free radical

The A 2Δ–X 2Π electronic transition of the CCN free radical was observed in emission with a high‐resolution Fourier transform spectrometer. The CCN was jet‐cooled in a corona‐excited supersonic jet expansion of diazoacetonitrile (HC(N2)CN) in helium. From the 000–000, 000–001, 000–002, and 000–100 vibronic bands spectroscopic constants were derived including the ground‐state vibrational frequencies, ν3=1050.7636(6), 2ν3=2094.8157(18), and ν1=1923.2547(69) cm−1.

Converging the single-reference coupled-cluster equations

Abstract A scheme for stabilizing the reduced linear equation method of solving the single-reference coupled system of equations is developed and implemented. When one or more secondary determinants become as important as the primary determinant in describing the chemical system, numerical instabilities frequently arise in the procedure of solving the coupled-cluster equations. This is avoided by “quasi-linearizing” certain non-linear terms in the equations and including them with the linear terms. A study on the LiH molecule with an internuclear separation of 9.045 au is used to demonstrate the effectiveness of this procedure.

Coupled cluster calculations for the BC molecule using numerical correlation orbitals

Abstract Calculations were performed on the BC molecule using a method which combines the numerical MCSCF technique and the coupled cluster method involving single, double and triple excitations (CCSD+T(CCSD) level) in an attempt to determine, very accurately, re in the ground electronic state. The result of 2.817 au agrees quite well with one of the experimentally suggested values which is 2.820 au.

PROPERTY EVALUATION USING THE HARTREE-FOCK-DENSITY-FUNCTIONAL-THEORY METHOD : AN EFFICIENT FORMALISM FOR FIRST- AND SECOND-ORDER PROPERTIES

We present an efficient formalism for property evaluation using the Hartree–Fock‐density‐ functional‐theory method. The formalism uses the relaxed density concept for first‐order properties which allows us to compute many different components of a property as well as many different properties once we have solved a single set of linear equations spanning the particle–hole space of the system. The density matrix representation of the method indicates that the method accounts for the correlation correction to Hartree–Fock only through particle–hole space. We also show why conventional density functionals based upon a local density and its gradient fail to account for electromagnetic effects. For second‐order properties, we show that no extra linear equations need to be solved, once the regular coupled perturbed Hartree–Fock equations are solved.