Jürgen Gauss

Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients

A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open‐shell Hartree‐Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD...

HEAT: High accuracy extrapolated ab initio thermochemistry

A theoretical model chemistry designed to achieve high accuracy for enthalpies of formation of atoms and small molecules is described. This approach is entirely independent of experimental data and contains no empirical scaling factors, and includes a treatment of electron correlation up to the full coupled-cluster singles, doubles, triples and quadruples approach. Energies are further augmented by anharmonic zero-point vibrational energies, a scalar relativistic correction, first-order spin-orbit coupling, and the diagonal Born-Oppenheimer correction. The accuracy of the approach is assessed by several means. Enthalpies of formation (at 0 K) calculated for a test suite of 31 atoms and molecules via direct calculation of the corresponding elemental formation reactions are within 1 kJ mol(-1) to experiment in all cases. Given the quite different bonding environments in the product and reactant sides of these reactions, the results strongly indicate that even greater accuracy may be expected in reactions that preserve (either exactly or approximately) the number and types of chemical bonds.

Effects of electron correlation in the calculation of nuclear magnetic resonance chemical shifts

Using second‐order many‐body perturbation theory [MBPT(2)] and the gauge‐including atomic orbital (GIAO) ansatz, electron correlation effects are investigated in the calculation of NMR chemical shieldings and shifts. A thorough discussion of the theory, aspects of the implementation as well as the computational requirements of the GIAO‐MBPT(2) method are presented. The performance of the GIAO‐MBPT(2) approach is tested in benchmark calculations of 13C, 15N, and 17O chemical shifts. Comparison with available experimental gas phase NMR data shows that GIAO‐MBPT(2) improves in all cases considered here over the GIAO results obtained at the Hartree–Fock self‐consistent‐field (HF‐SCF) level. Correlation effects turn out to be particularly important for molecules with multiple bonds, e.g., carbonyl or cyano compounds, and it seems that GIAO‐MBPT(2) slightly overestimates these effects for difficult cases having relatively large correlation contributions of 30 to 110 ppm. For CO, N2, N2O, additional calculations...

Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method

The theory for analytic energy derivatives of excited electronic states described by the equation‐of‐motion coupled cluster (EOM‐CC) method has been generalized to treat cases in which reference and final states differ in the number of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the reference, the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant reference functions, several electronic configurations are treated in a balanced way by EOM‐CC. Therefore, this quantum chemical approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell reference state is used—a desirable feature that is not easily achieved in standard coupled cluster approaches. The efficient implementation of analytic gradien...

Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants

A theory for the calculation of nuclear magnetic shielding constants at the coupled‐cluster singles and doubles level augmented by a perturbative correction for connected triple excitations (CCSD(T)) has been developed and implemented. The approach, which is based on the gauge‐including atomic orbital (GIAO) ansatz, is illustrated by several numerical examples. These include a comparison of CCSD(T) and other highly correlated methods with full configuration interaction for the BH molecule, and a systematic comparison with experiment for HF, H2O,NH3, CH4, N2, CO, HCN, and F2. The results demonstrate the importance of triple excitations in establishing quantitative accuracy. Finally, the ability of GIAO‐CCSD(T) to make accurate predictions for difficult cases is explored in calculations for formaldehyde (CH2O), diazomethane(CH2NN), and ozone (O3).

Calculation of NMR chemical shifts at second-order many-body perturbation theory using gauge-including atomic orbitals

Abstract Formulas for calculating NMR chemical shifts at second-order many-body perturbation theory using the gauge-including atomic orbital method are presented and their implementation is discussed. The method is applied to study correlation effects on calculated 17 O chemical shifts.

The accurate determination of molecular equilibrium structures

Equilibrium structures have been determined for 19 molecules using least-squares fits involving rotational constants from experiment and vibrational corrections from high-level electronic-structure calculations. Equilibrium structures obtained by this procedure have a uniformly high quality. Indeed, the accuracy of the results reported here likely surpasses that reported in most experimental determinations. In addition, the accuracy of equilibrium structures obtained by energy minimization has been calibrated for the following standard models of ab initio theory: Hartree–Fock, MP2, CCSD, and CCSD(T). In accordance with previous observations, CCSD(T) is significantly more accurate than the other models; the mean and maximum absolute errors for bond distances of the 19 molecules are 0.09 and 0.59 pm, respectively, in CCSD(T)/cc-pCVQZ calculations. The maximum error is obtained for ROO in H2O2 and is so large compared with the mean absolute error that an experimental reinvestigation of this molecule is warra...

High-accuracy extrapolated ab initio thermochemistry. III. Additional improvements and overview

Effects of increased basis-set size as well as a correlated treatment of the diagonal Born-Oppenheimer approximation are studied within the context of the high-accuracy extrapolated ab initio thermochemistry (HEAT) theoretical model chemistry. It is found that the addition of these ostensible improvements does little to increase the overall accuracy of HEAT for the determination of molecular atomization energies. Fortuitous cancellation of high-level effects is shown to give the overall HEAT strategy an accuracy that is, in fact, higher than most of its individual components. In addition, the issue of core-valence electron correlation separation is explored; it is found that approximate additive treatments of the two effects have limitations that are significant in the realm of <1 kJ mol(-1) theoretical thermochemistry.

The prediction of molecular equilibrium structures by the standard electronic wave functions

A systematic investigation has been carried out of the accuracy of molecular equilibrium structures of 19 small closed-shell molecules containing first-row atoms as predicted by the following standard electronic ab initio models: Hartree–Fock (HF) theory, Mo/ller–Plesset theory to second, third, and fourth orders (MP2, MP3, and MP4), coupled-cluster singles and doubles (CCSD) theory; CCSD theory with perturbational triples corrections [CCSD(T)], and the configuration-interaction singles and doubles (CISD) model. For all models, calculations were carried out using the correlation-consistent polarized valence double-zeta (cc-pVDZ) basis, the correlation-consistent polarized valence triple-zeta (cc-pVTZ) basis, and the correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis. Improvements in the basis sets shorten the bond distances at all levels. Going from cc-pVDZ to cc-pVTZ, bond distances are on the average reduced by 0.8 pm at the Hartree–Fock level and by 1.6 pm at the correlated levels....

Open-shell analytical energy gradients for triple excitation many-body, coupled-cluster methods: MBPT(4), CCSD+T(CCSD), CCSD(T),and QCISD(T)

Abstract Equations are derived for the derivatives of the contribution of triple excitations to the energy for the fourth-order many-body perturbation theory (MBPT(4)), quadratic configuration interaction with singles, doubles, and noniterative triples (QCISD(T)), and coupled-cluster with singles, doubles, and noniterative triples (CCSD+T(CCSD) and CCSD(T)) methods. Based on these equations, analytical gradients have been efficiently implemented for the four aforementioned methods for unrestricted Hartree-Fock (UHF) reference functions. This is the first implementation of open-shell analytical gradients for the QCISD(T), CCSD+T(CCSD), and CCSD(T) methods. The new analytical gradient techniques have been used to compute the structure and some properties of the ground state of the HOO radical with extended basis sets.