Alistair P. Rendell

Analytic gradients for coupled‐cluster energies that include noniterative connected triple excitations: Application to cis‐ and trans‐HONO

An efficient formulation of the analytic energy gradient for the single and double excitation coupled‐cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted CCSD(T), is presented. The formulation presented here has a smaller computational cost than any previous formulation, and the algebraic manipulations that lead to the additional savings may be applied generally to the analytic gradient of Mo/ller–Plesset perturbation theory energies. The energy contribution from connected triple excitations scales as n3on4v+n4on3v, and the additional work needed for the gradient scales as 2n3on4v+2n4on3v, where no is the number of doubly occupied orbitals and nv is the number of unoccupied orbitals. The new formulation has been implemented in an efficient set of programs that utilize highly vectorized algorithms and has been used to investigate the equilibrium structures, harmonic vibrational frequencies, infrared intensities, and energy separation of cis‐ and tr...

Coupled-Cluster Theory Employing Approximate Integrals: An Approach to Avoid the Input/Output and Storage Bottlenecks

By representing orbital products in an expansion basis, certain classes of two‐electron integrals are approximated for use in CCSD(T) calculations (singles and doubles coupled‐cluster plus a perturbational estimate of the effects of connected triple excitations). This leads to a very large reduction in disk storage and input/output requirements, with usually only a modest increase in computational effort. The new procedure will allow very large CCSD(T) calculations to be undertaken, limited only by available processor time. Using the molecular basis as the expansion basis, explicit numerical comparisons of equilibrium geometries, harmonic frequencies, and energy differences indicate that the error due to the use of approximate integrals is less than the error associated with truncation of the molecular basis set.

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.

The potassium channel: Structure, selectivity and diffusion

We employ the entire experimentally determined protein structure for the KcsA potassium channel from Streptomyces lividans in molecular dynamics calculations to observe hydrated channel protein structure, ion solvation, selectivity, multiple ion configurations, and diffusion. Free energy perturbation calculations display a significant ion discrimination of ∼9 kT in favor of the larger K+ ion. The protein forming the channel is very flexible yet is unable to fully solvate the Na+ ion because of its smaller size and large solvation energy. There is evidence that acidic and basic sidechains may dissociate in the presence of multiple K+ ions to explain experimental ion density maps. K+ diffusion is found to vary from approximately 10%–90% of bulk, supporting the high channel currents observed experimentally.

The structure and energetics of the HCN→HNC transition state

Abstract The optimum geometries and quadratic force constants of HCN, HNC and the transition state connecting them have been determined at the single and double excitation coupled-cluster (CCSD) and CCSD(T) levels of theory. Energy differences were evaluated using the CCSD and CCSD(T) methods in conjunction with large atomic natural orbital basis sets containing g-type basis functions on the heavy atoms and f-type functions on hydrogen. The most reliable structure obtained for the transition state has bond distances of 1.194, 1.188 and 1.389 A for rCN, rCH and rNH, respectively. Including a correction for zero-point vibrational energies, the transition state is predicted to be 44.6 ± 1.0 kcal/mol above the HCN isomer, while HNC is predicted to be 14.4 ± 1.0 kcal/mol above HCN. The latter value is in excellent agreement with the most recent experimental determination (14.8 ± 2.0 kcal/mol).

The validity of electrostatic predictions of the shapes of van der Waals dimers

Abstract The interaction energies of the van der Waals dimers H 2 O-H 2 O, Cl 2 -HF, ClF-HF and N 2 O-HF have been calculated for a range of geometries using ab initio SCF techniques. The SCF binding energies have been decomposed into electrostatic, exchange, polarisation and charge-transfer contributions and the intermolecular angles optimised with respect to various combinations of the above components. The effects of exchange, polarisation and charge transfer on the shape of a given dimer are found approximately to cancel, so that in each case a purely electrostatic model is capable of predicting intermolecular angles that agree well with those of a full SCF treatment, as well as with experiment. These findings are consistent with the proposals and earlier calculations of Buckingham and Fowler.

Open‐shell restricted Hartree–Fock perturbation theory: Some considerations and comparisons

A comparative study is presented of the various recently developed open‐shell perturbation theories that are based on a restricted Hartree–Fock reference wave function. Included in this study are issues concerning spin contamination, implementational considerations, and numerical comparisons at the second‐order of perturbation theory for equilibrium geometries, vibrational frequencies, and singlet–triplet energy differences. Based on all of these considerations, it is concluded that the z‐averaged perturbation theory (ZAPT) method is to be preferred over the other recently devised spin–orbital perturbation theories, while the spin‐free OPT2 method possesses some advantages and disadvantages relative to the ZAPT method. In particular, it is shown that OPT2 energies are not invariant to rotations among singly‐occupied degenerate molecular orbitals.

Binding energies and bond distances of Ni(CO)x, x= 1-4 : an application of coupled-cluster theory

The accuracy of the single and double excitation coupled‐cluster (CCSD) method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), has been tested for some representative transition metal complexes. For both the binding energy and metal to ligand bond distance of NiCO and Ni(CO)2, the CCSD(T) method yields results in very good agreement with multireference averaged coupled‐pair functional (ACPF) calculations. The results are much better than those obtained using either the coupled‐pair functional (CPF) or modified CPF (MCPF) methods. The contribution of connected triples to the binding energy is significant for all Ni(CO)x, x=1–4 ranging from 15 kcal/mol for NiCO to 30 kcal/mol for Ni(CO)4. In contrast, for the geometries the connected triples are only of minor importance. In this case, the correct treatment of disconnected quadruple excitations appears to be more important. For Ni(CO)4, the calculated binding energy is 125 kcal/mol (expt. 140 kcal/mol) and the bond d...

An efficient formulation and implementation of the analytic energy gradient method to the single and double excitation coupled-cluster wave function - Application to Cl2O2

The analytic energy gradient for the single and double excitation coupled‐cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented. The relative energies of the three isomers are further investigated using large atomic natural orbital basis sets in conjunction with the CCSD(T) method, which includes a perturbational estimate of conne...

A parallel vectorized implementation of triple excitations in CCSD(T): application to the binding energies of the AlH3, AlH2F, AlHF2 and AlF3 dimers

Abstract An efficient method for evaluating various non-iterative estimates of connected triple excitations in coupled-cluster theory is outlined and related to a similar expression occurring in Moller-Plesset perturbation theory. The method is highly vectorized and capable of utilizing multiple processors on a shared-memory machine, leading to computational rates in excess of one billion floating-point operations per second on four processors of a CRAY Y-MP. Using the new procedure, the binding energies of the D 2h diborane-type dimers of AlH 3 , AlH 2 F, AlHF 2 and AlF 3 have been determined to be 32, 40, 20 and 47 kcal/mol, respectively. For Al 2 F 6 , the correlation procedure includes 232 molecular orbitals and over 1.5 × 10 6 single and double coupled-cluster amplitudes, effectively accounting for over 2 × 10 9 connected triple excitations.