Gary W. Trucks

A fifth-order perturbation comparison of electron correlation theories

Abstract Electron correlation theories such as configuration interaction (CI), coupled-cluster theory (CC), and quadratic configuration interaction (QCI) are assessed by means of a Moller-Plesset perturbation expansion of the correlation energy up to fifth order. The computational efficiencies and relative merits of the different techniques are outlined. A new augmented version of coupled-cluster theory, denoted as CCSD(T), is proposed to remedy some of the deficiencies of previous augmented coupled-cluster models.

Gaussian‐2 theory for molecular energies of first‐ and second‐row compounds

The Gaussian‐2 theoretical procedure (G2 theory), based on ab initio molecular orbital theory, for calculation of molecular energies (atomization energies, ionization potentials, electron affinities, and proton affinities) of compounds containing first‐ (Li–F) and second‐row atoms (Na–Cl) is presented. This new theoretical procedure adds three features to G1 theory [J. Chem. Phys. 90, 5622 (1989)] including a correction for nonadditivity of diffuse‐sp and 2df basis set extensions, a basis set extension containing a third d function on nonhydrogen and a second p function on hydrogen atoms, and a modification of the higher level correction. G2 theory is a significant improvement over G1 theory because it eliminates a number of deficiencies present in G1 theory. Of particular importance is the improvement in atomization energies of ionic molecules such as LiF and hydrides such as C2H6, NH3, N2H4, H2O2, and CH3SH. The average absolute deviation from experiment of atomization energies of 39 first‐row compounds...

A comparison of models for calculating nuclear magnetic resonance shielding tensors

The direct (recomputation of two‐electron integrals) implementation of the gauge‐including atomic orbital (GIAO) and the CSGT (continuous set of gauge transformations) methods for calculating nuclear magnetic shielding tensors at both the Hartree‐Fock and density functional levels of theory are presented. Isotropic 13C, 15N, and 17O magnetic shielding constants for several molecules, including taxol (C47H51NO14 using 1032 basis functions) are reported. Shielding tensor components determined using the GIAO and CSGT methods are found to converge to the same value at sufficiently large basis sets; however, GIAO shielding tensor components for atoms other than carbon are found to converge faster with respect to basis set size than those determined using the CSGT method for both Hartree‐Fock and DFT. For molecules where electron correlation effects are significant, shielding constants determined using (gradient‐corrected) pure DFT or hybrid methods (including a mixture of Hartree‐Fock exchange and DFT exchange...

Gaussian-1 theory of molecular energies for second-row compounds

The Gaussian‐1 theoretical procedure is extended and tested on compounds containing second‐row atoms (Na–Cl). This is a composite procedure based on ab initio molecular orbital theory, utilizing large basis sets (including diffuse‐sp, double‐d, and f‐polarization functions) and treating electron correlation by Mo/ller–Plesset perturbation theory and by quadratic configuration interaction. Total atomization energies for a set of 24 species agree with accurate experimental data to an accuracy of better than 3 kcal/mol in most cases, SO2 being the notable exception. Similar agreement is achieved for ionization energies, electron affinities, and proton affinities. The method is used to assess experimental data for a number of other compounds having less accurate atomization energies.

Analytic energy derivatives in many‐body methods. I. First derivatives

Second derivatives of the energy correspond to second‐order response properties and molecular force constants. Currently, both the theory and application of analytic second derivatives in many‐body methods are limited to second‐order perturbation theory. The general theory of analytic second derivatives for the coupled‐cluster (CC) model is presented. The analytic expressions for the second derivative of the energy are given in terms of the response (or ‘‘relaxed’’) density, discussed in part I, and the first‐derivative t amplitudes for efficient evaluation. Explicit expressions for the second derivatives of the coupled‐cluster singles, doubles, and linearized triples model (CCSDT‐1) are presented. Analytic derivatives for the finite‐order MBPT(3) and MBPT(4) models are derived as special cases of the theory.

Size-consistent Brueckner theory limited to double substitutions

Abstract A size-consistent set of equations for electron correlation which are limited to double substitutions, based on Brueckner orbitals, is discussed. Called BD theory, it is shown that at fifth order of perturbation theory, BD incorporates more terms than CCSD and QCISD. The simplicity of the equations leads to an elegant gradient theory. Preliminary applications are reported.

Highly correlated systems. Ionization energies of first row transition metals Sc–Zn

The low‐lying dns2→dn+1s1 excitation energies of the first row transition metal atoms Sc–Cu are calculated using fourth‐order M≂ller–Plesset perturbation theory (MP4) as well as quadratic configuration interaction (QCI) techniques with large spd and spdf  basis sets. The MP4 method performs well for Sc–Mn but fails dramatically for Fe–Cu. In contrast, the QCI technique performs uniformly for all excitation energies with a mean deviation from experiment of only 0.14 eV after including relativistic corrections. f functions contribute 0.1–0.4 eV to the excitation energies for these systems. The highly correlated d10 state of the Ni atom is also considered in detail. The QCI technique obtains the d9s1→d10 splitting of the Ni atom with an error of only 0.13 eV. The results show that single‐configuration Hartree–Fock based methods can be successful in calculating excitation energies of transition metal atoms.

Electronic Transition Energies: A Study of the Performance of a Large Range of Single Reference Density Functional and Wave Function Methods on Valence and Rydberg States Compared to Experiment

This work reports a comparison among wave function and DFT single reference methods for vertical electronic transition energy calculations toward singlet states, valence and Rydberg in nature. A series of 11 small organic molecules are used as test cases, where accurate experimental data in gas phase are available. We compared CIS, RPA, CIS(D), EOM-CCSD, and 28 multipurpose density functionals of the type LSDA, GGA, M-GGA, H-GGA, HM-GGA and with separated short and long-range exchange. The list of functionals is obviously not complete, but it spans more than 20 years of DFT development and includes functionals which are commonly used in the computation of a variety of molecular properties. Large differences in the results were found between the various functionals. The aim of this work is therefore to shed some light on the performance of the plethora of functionals available and compare them with some traditional wave function based methods on a molecular property of large interest as the transition energy.

Highly correlated systems: Structure, binding energy and harmonic vibrational frequencies of ozone

Abstract The structure, binding energy and harmonic vibrational frequencies of O 3 are calculated using the quadratic configuration interaction (QCI) method with a variety of basis sets. This method reproduces the geometry and vibrational frequencies of ozone fairly accurately using both restricted (RHF) and unrestricted Hartree-Fock (UHF) starting points. The asymmetric stretching frequency of ozone, which is extremely sensitive to the level of electron correlation, is calculated with a deviation of about 10% from experiment. The symmetric frequencies are calculated with errors of 1–5%. The vibrational frequencies do not depend greatly on the level of correlation if a UHF starting point is used. The atomization energy is also accurately calculated, using a composite method where the effects of larger basis sets are evaluated using fourth-order perturbation theory.

Theory and implementation of the MBPT density matrix. An application to one-electron properties

Abstract A perturbation-independent response density matrix has been derived and implemented for many-body perturbation theory. This density contains all orbital relaxation terms, which allows for fast, efficient computation of correlated one-electron response properties. As such, it eliminates the need for finite-field calculations of first-order properties. The method is applied to H 2 O using an extended basis set for the MBPT (2), MBPT (3), and SDQ-MBPT (4) levels of theory. The relationship of the response density to an average density matrix is discussed.