Configuration Interaction Singles And Doubles Research Articles

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 experimental results, and it is found that the CCSD predictions are most comparable to those of CISDTQ for this particular system. For the case of H2CO, the CCSD results are compared to CISD and experimental predictions. In general, the CCSD results and timings are encouraging.

The description of N2 and F2 potential energy surfaces using multireference coupled cluster theory

The ground state potential energy surfaces (PES’s) for diatomic nitrogen and fluorine are examined using a version of our recently published linearized multireference coupled cluster method (MR-LCCM). Comparison calculations employing a variety of standard ab initio techniques such as single reference configuration interaction singles and doubles (CISD), many-body perturbation theory (MBPT), coupled cluster single and doubles (CCSD), and multireference (MR)-CISD were also performed. In addition, the PES’s were also investigated using the newly developed CCSDT-1 method, which includes the dominant effect of T̂3. These single reference procedures fail in various ways (with the possible exception of the CCSDT-1 method), while the MR-LCCM method is shown to compare favorably to the more traditional MR-CI techniques. Like the MR-CIs, the MR-LCCM energy curves dissociate correctly and the two are nearly parallel.

Geometrical structures, force constants, and vibrational spectra of SiH, SiH 2, SiH 3, and SiH 4

This paper reports a comprehensive theoretical examination of the r e and r 0 geometrical structures, harmonic and anharmonic vibrational frequencies, and infrared intensities ofX̃ 2Π SiH, X̃ 1A 1, ã 3B 1, and à 1B 1 SiH 2, X̃ 2A 1 SiH 3, and X̃ 1A 1 SiH 4. Both self-consistent-field (SCF) and configuration interaction singles and doubles (CISD) methods have been employed with two basis sets (B1 and B2) of double-zeta plus polarization (DZ +P) and triple-zeta plus double polarization (TZ+2P) quality. For SiH the B2 CISD parameters r e = 1.5214 Å, r 0 = 1.5326 Å, ω e = 2062 cm −1, and v 0 = 1985 cm −1 are in excellent agreement with the experimental values r e = 1.5201 Å, r 0 = 1.5313 Å, ω e = 2042 cm −1, and v 0 = 1971 cm −1. The B2 CISD α i rovibrational constants for SiH 2D 2, SiH 4, SiD 4, and SiHD 3 when utilized to correct experimental A 0, B 0, and C 0 rotational constants give r e = 1.4735 Å for SiH 4. With the same procedure, r e(SiH) = 1.5141 Å and θ e (HSiH) = 92.0° are found for X̃ 1A 1 SiH 2, and r e(SiH) = 1.4871 Å and θ e(HSiH) = 121.8° are found for à 1B 1 SiH 2. All of these experimentally derived r e parameters are in excellent agreement with the B2 CISD r e structures for X̃ 1A 1 SiH 4, X̃ 1A 1 SiH 2, and à 1B 1 SiH 2. For ã 3B 1 SiH 2, r e = 1.4768 Å, θ e = 118.3°, and T e = 19.6 kcal/mol are predicted. The B2 CISD harmonic vibrational frequencies for the SiH stretches of SiH 4 are only 1–2% too large, and the corresponding theoretical anharmonicities are in error by less than 7 cm −1. Using the SiH 4 data to separately scale the B2 CISD ω 3 and x 3 values for X̃ 1A 1 SiH 2, ν 3 = 1981 cm −1 is obtained, which confirms the recent experimental frequencies of Fredin, Hauge, Kafafi, and Margrave. In a similar fashion ν 1 = 2117 cm −1, ν 2 = 892 cm −1, and ν 3 = 2180 cm −1 are predicted for ã 3B 1 SiH 2 and ν 1 = 2016 cm −1 and ν 3 = 2115 cm −1 for à 1B 1 SiH 2. The B2 CISD geometrical parameters for X̃ 2A 1 SiH 3 are r e(SiH) = 1.4768 Å and θ e(HSiH) = 111.1°, and the final (scaled) B2 CISD fundamental frequencies are ν 1 = 2150 cm −1, ν 2 = 773 cm −1, ν 3 = 2180 cm −1, and ν 4 = 933 cm −1. These frequencies definitely show that the 1999, 1955, and 996 cm −1 IR absorptions of Milligan and Jacox are not attributable to SiH 3. Finally, at the highest level of theory used here, a classical inversion barrier of 5.8 kcal/mol is obtained for SiH 3.

A b i n i t i o studies of the low-lying electronic states of ketene

Features of the potential energy surfaces of the X̃ 1A1, 3A2(3A″), 1A2(1A″), 3A1(3A′), 1B1, and 2 1As1 low-lying electronic states of ketene have been investigated using self-consistent-field (SCF) and configuration interaction singles and doubles (CISD) methods with double zeta plus polarization (DZP) and DZP+Rydberg (DZP+R) basis sets. The DZP+R CISD vertical excitation energies are in excellent agreement with observed transition energies and suggest assignments for the X̃ 1A1→1B1 and X̃ 1A1→2 1A1 transitions in the electronic spectrum of ketene. Stationary points have been located at the DZP SCF level of theory for the first four states listed above, and SCF quadratic force constants and harmonic vibrational frequencies have been computed analytically at these stationary points. The X̃ 1A1 geometry and vibrational frequencies compare favorably with experimental values, the agreement being typical of DZP SCF results. Due to curve crossings and conical intersections of potential surfaces, the four lowest theoretical excited state surfaces have only two valid (double) minima, corresponding to 3A″ and 1A″ electronic states. At the DZP SCF geometries, Davidson-corrected CISD adiabatic excitation energies of 16 700 and 19 000 cm−1 have been obtained for the 3A″ and 1A″ states, supporting the previous experimental T0 upper bounds of Laufer and Keller. Finally, the X̃ 1A1 state is predicted to lie only 5500–7000 cm−1 below the 1A″ state at the 1A″ optimum geometry and appears to have a significant effect on the 1A″ out-of-plane frequencies.