Timothy J. Lee

A doubles correction to electronic excited states from configuration interaction in the space of single substitutions

Abstract A perturbative correction to the method of configuration interaction with single substitutions (CIS) is presented. This CIS (D) correction approximately introduces the effect of double substitutions which are absent in CIS excited states. CIS (D) is a second-order perturbation expansion of the coupled-cluster excited state method, restricted to single and double substitutions, in a series in which CIS is zeroth order, and the first-order correction vanishes. CIS (D) excitation energies are size consistent and the calculational complexity scales with the fifth power of molecular size, akin to second-order Moller-Plesset theory for the ground state. Calculations on singlet excited states of ethylene, formaldehyde, acetaldehyde, butadiene and benzene show that CIS (D) is a uniform improvement over CIS. CIS (D) appears to be a promising method for examining excited states of large molecules, where more accurate methods are not feasible.

Analytic evaluation of energy gradients for the single and double excitation coupled cluster (CCSD) wave function: Theory and application

The theory for the analytic evaluation of energy gradients for coupled cluster (CC) wave functions is presented. In particular, explicit expressions for the analytic energy gradient of the CC singles and doubles (CCSD) wave function for a closed‐shell restricted Hartree–Fock reference determinant are presented and shown to scale as N6 where N is the one‐electron number of atomic basis functions for the molecular system. Thus analytic CCSD gradients are found to be of the same magnitude in computational cost as is the evaluation of analytic gradients for the configuration interaction singles and doubles (CISD) wave function. Applications of this method are presented for the water molecule and the formaldehyde molecule using a double‐ζ plus polarization (DZ+P) basis set. The CCSD equilibrium geometries, dipole moments, and, via finite differences of gradients, CCSD harmonic vibrational frequencies and infrared intensities are reported. For H2O these results are compared to analogous CISD, CISDT, CISDTQ, and...

THE ANHARMONIC FORCE FIELD OF ETHYLENE, C2H4, BY MEANS OF ACCURATE AB INITIO CALCULATIONS

UNIV INSTELLING ANTWERP,INST MAT SCI,DEPT CHEM,B-2610 WILRIJK,BELGIUM. NASA,AMES RES CTR,MOFFETT FIELD,CA 94035. SAN DIEGO SUPERCOMP CTR,SAN DIEGO,CA 92186.MARTIN, JML, LIMBURGS UNIV CENTRUM,DEPT SBG,UNIV CAMPUS,B-3590 DIEPENBEEK,BELGIUM.

Comparison of coupled‐cluster methods which include the effects of connected triple excitations

Electron correlation energies have been determined for 14 different molecules which represent a range of chemical bonding situations. These have been determined with the coupled‐cluster single, double, and triple (CCSDT) excitation model as well as with several coupled‐cluster methods that include only an approximate treatment of connected triple excitations, viz. CCSDT‐1a, CCSDT‐1b, CCSDT‐2, CCSDT‐3, CCSDT‐4, and the recently proposed CCSD(T) method. All of the CCSDT‐x methods include the effects of connected triple excitations in an iterative manner, whereas in CCSDT(T) these are included perturbationally. For chemical systems which are well represented by a single‐determinant reference function, some of the CCSDT‐x methods (CCSDT‐1a, CCSDT‐1b, and CCSDT‐4) perform marginally better than the CCSD(T) approach in reproducing the CCSDT results. However, as nondynamical correlation becomes more important the good agreement from the CCSDT‐x methods deteriorates rapidly, while the error in CCSD(T) remains m...

Systematic study of molecular anions within the self‐consistent‐field approximation: OH−, CN−, C2H−, NH−2, and CH−3

The title molecular anions have been studied at the self‐consistent‐field (SCF) level of theory with several different basis sets. The smallest of these bases is triple zeta (TZ) in quality while the largest can be labeled near Hartree–Fock limit. The dependence of proton affinities, dipole moments, harmonic frequencies, and infrared intensities on the inclusion of diffuse functions in the basis set is investigated. It is concluded that at the SCF level of theory the addition of diffuse s and p functions (for first row elements) is necessary in order to obtain reliable results. This is true especially for NH−2 and CH−3. A method to extend any standard Gaussian basis set is suggested. Finally, predictions are made for some of the as yet unobserved fundamentals of the anions.

The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results

A single and double excitation coupled cluster (CCSD) method restricted to closed‐shell single configuration reference functions is described in explicit detail. Some significant simplifications resulting from the restriction to closed‐shell systems are exploited to achieve maximum computational efficiency. Comparisons for energetic results and computational requirements are made with the single and double excitation configuration interaction (CISD) method. The specific molecules considered include N2, H2O, H3O+, H5O+2, HSOH, and s‐tetrazine (C2N4H2).

The analytic configuration interaction gradient method: Application to the cyclic and open isomers of the S3 molecule

The theory for the ab initio evaluation of potential energy gradients at the configuration interaction level of accuracy is presented, with special attention to the treatment of the various types of orbitals (frozen core, active, frozen virtual) which may arise. The new method has been used for a study of the D3h and C2v geometries of S3. SCF and CISD calculations predict the D3h structure to be lower than the C2v by 9.3 and 2.3 kcal/mol, respectively, whereas CASSCF and MRCISD predict the C2v structure to be the lowest by 8.9 and 8.2 kcal/mol, respectively, using good basis sets. These calculations support the prediction of Carlsen and Schaefer that both forms should be observable experimentally.

Achieving Chemical Accuracy with Coupled-Cluster Theory

Due to formal and computational advances in coupled-cluster theory over the past few years, it is now possible to obtain very accurate molecular geometries, vibrational frequencies, heats of formation, binding energies, and vertical electronic excitation energies. For example, based on statistical analyses of a large number of calculations, it is shown that the CCSD(T)/spdfg level of theory gives rXH,rXY (double bonds), and rXY (triple bonds) with an average error of 0.0010, 0.0020, and 0.0026 A, respectively, with the theoretical bond distances usually too long relative to experiment. This level of theory yields bond angle predictions that are too small by 0.21 degrees on average. Fundamental vibrational frequencies predicted at the CCSD(T)/spdfg level of theory are accurate to better than 8.0 cm-1 on average, but the remaining errors are less systematic than those found for the geometrical parameters, except for X–Y stretches which are usually underestimated relative to experiment. For molecules described reasonably well by a single determinant reference function, single- and multiple-bond energies are given to within 1.0 and 2.0 kcal/mol, respectively, at the CCSD(T)/spdfg level of theory. The present monograph reviews the advances that have lead to the current state-of-the art, and also summarizes selected examples from the published literature.

Theoretical investigations of molecules composed only of fluorine, oxygen and nitrogen: determination of the equilibrium structures of FOOF, (NO)2 and FNNF and the transition state structure for FNNF cis-trans isomerization

The deficiencies of common ab initio methods for the reliable prediction of the equilibrium structures of compounds composed of only the fluorine, oxygen and nitrogen atoms are investigated. Specifically, the importance of using large one-particle basis sets with multiple sets of polarization functions has been studied. Additionally, the need for a set of f basis functions was investigated. Several different single reference electron correlation methods have been tested in order to determine whether it is possible for a single reference based method to be routinely used on such chemical systems. These electron correlation methods include second order Møller-Plesset perturbation theory (MP2), singles and doubles configuration interaction (CISD), the coupled pair functional (CPF) approach and singles and doubles coupled cluster (CCSD) theory. The molecular systems studied include difluoroperoxide (FOOF), the cis form of the NO dimer, cis and trans difluorodiazene (FNNF) and the transition state to interconversion of the cis and trans isomers of FNNF. To the best of our knowledge, this is the first time that the cis-trans isomerization transition state has been reported. At the highest level of theory employed, the equilibrium structures of cis and trans FNNF agree very well with the experimental structures. However, the barrier to interconversion is predicted to be 65 kcal/mole, which is substantially higher than the experimental activation energy of 32 kcal/mole. Potential sources of error are discussed. A new diagnostic method for determining a priori the reliability of single reference based electron correlation methods is suggested and discussed.

An Accurate ab initio Quartic Force Field and Vibrational Frequencies for CH4 and Isotopomers

A very accurate ab initio quartic force field for CH4 and its isotopomers is presented. The quartic force field was determined with the singles and doubles coupled‐cluster procedure that includes a quasiperturbative estimate of the effects of connected triple excitations, CCSD(T), using the correlation consistent polarized valence triple zeta, cc‐pVTZ, basis set. Improved quadratic force constants were evaluated with the correlation consistent polarized valence quadruple zeta, cc‐pVQZ, basis set. Fundamental vibrational frequencies are determined using second‐order perturbation theory anharmonic analyses. All fundamentals of CH4 and isotopomers for which accurate experimental values exist and for which there is not a large Fermi resonance, are predicted to within ±6 cm−1. It is thus concluded that our predictions for the harmonic frequencies and the anharmonic constants are the most accurate estimates available. It is also shown that using cubic and quartic force constants determined with the correlation ...