Engineering topics

Taylor, Peter R.

Publications and source records attributed to Taylor, Peter R..

At least 55 records · Page 3

NASA NTRS1990

Polyatomic molecular Dirac-Hartree-Fock calculations with Gaussian basis sets

Numerical methods have been used successfully in atomic Dirac-Hartree-Fock (DHF) calculations for many years. Some DHF calculations using numerical methods have been done on diatomic molecules, but while these serve a useful purpose for calibration, the computational effort in extending this approach to polyatomic molecules is prohibitive. An alternative more in line with traditional quantum chemistry is to use an analytical basis set expansion of the wave function. This approach fell into disrepute in the early 1980's due to problems with variational collapse and intruder states, but has recently been put on firm theoretical foundations. In particular, the problems of variational collapse are well understood, and prescriptions for avoiding the most serious failures have been developed. Consequently, it is now possible to develop reliable molecular programs using basis set methods. This paper describes such a program and reports results of test calculations to demonstrate the convergence and stability of the method.

Dyall, Kenneth G.↗

NASA NTRS1989

The polarizabilities of neon

The static dipole polarizability, second hyperpolarizability, quadrupole polarizability and dipole-dipole-quadrupole hyperpolarizability for the Ne atom are computed, using large Gaussian basis sets and coupled cluster wavefunctions. Correlation effects are substantial, ranging from 15 percent for the dipole polarizability to 40 percent for the second hyperpolarizability. It is confirmed by explicit calculation earlier hypotheses that g-type and higher angular momentum functions and core correlation effects make almost no contribution to these properties in Ne. Triple excitations, on the other hand, are very important, accounting for as much as 25 percent of the correlation contribution to the second hyperpolarizability. The best estimate of the second hyperpolarizability is 119 + or - 4 au, in good agreement with the recent calculations of Maroulis and Thakkar (1989) and the latest experimental result of Shelton (1989).

Taylor, Peter R.↗

NASA NTRS1989

Theoretical study of the dipole moment function of OH(X2Pi)

A theoretical study of the sensitivity of the dipole moment function (DMF) of the X2Pi ground state of OH to basis-set saturation and to refinements in the correlation treatment is presented. Emphasis is placed on determining the slope of the DMF at r(e) and the r value at which the maximum occurs. Consideration is given to the effect of oxygen polarization functions up through h type, expansion of the active orbital space to include the O 3d-delta orbital, the effect of higher excitations using the averaged coupled-pair functional method, and the effect of evaluating the dipole moment as an energy derivative rather than as an expectation value. The theoretical DMFs obtained here, which should be the most accurate to date, differ markedly from an empirical DMF of Turnbull and Lowe that is based on experimentally derived intensity ratios. The theoretical DMFs agree better with a recently published DMF of Nelson et al., but suggest that this empirical DMF is also inaccurate for r greater than 2.3 a0.

Langhoff, Stephen R.↗

NASA NTRS1989

On the electron affinities of the Ca, Sc, Ti and Y atoms

For the Ca, Sc, Ti, and Y atoms calculations are performed for the ground states of the neutrals and the ground and several low-lying excited states of the negative ions. Overall, the computed electron affinities are in good accord with experiment. The calculations show the rapid stabilization of the 3d orbital relative to the 4p as the nuclear charge increases. The 3F0 and 3D0 terms are found to be close in energy in Sc(-) and in Y(-). This confirms earlier speculation that some of the peaks in the photodetachment spectra of Y(-) originate from the bound excited 3F0 term of Y(-).

Bauschlicher, Charles W., Jr.↗

NASA NTRS1989

The effect of higher than double excitations on the F + H2 to FH + H barrier

The averaged coupled-pair functional (ACPF) method is used to calculate the barrier height and saddle-point geometry for the reaction F + H2 yields FH + H. The theoretical basis of the calculation method is outlined, and results for both 7-electron and 9-electron correlations are presented in tables and shown to be consistent with a barrier of 1.65 kcal/mol. The ACPF results are found to be in good agreement with the Davidson-corrected multireference CI computations of Bauschlicher et al. (1988) and with the results obtained by Scuseria and Schaefer (1988) using a CI method which accounts for all single, double, triple, and quadruple excitations.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1989

A diagnostic for determining the quality of single-reference electron correlation methods

It was recently proposed that the Euclidian norm of the t sub 1 vector of the coupled cluster wave function (normalized by the number of electrons included in the correlation procedure) could be used to determine whether a single-reference-based electron correlation procedure is appropriate. This diagnostic, T sub 1, is defined for use with self consistent field molecular orbitals and is invariant to the same orbital rotations as the coupled cluster energy. T sub 1 is investigated for several different chemical systems which exhibit a range of multireference behavior, and is shown to be an excellent measure of the importance of nondynamical electron correlation and is far superior to C sub 0 from a singles and doubles configuration interaction wave function. It is further suggested that when the aim is to recover a large fraction of the dynamical electron correlation energy, a large T sub 1 (i.e., greater than 0.02) probably indicates the need for a multireference electron correlation procedure.

Lee, Timothy J.↗

NASA NTRS1989

Chemical calculations on Cray computers

The influence of recent developments in supercomputing on computational chemistry is discussed with particular reference to Cray computers and their pipelined vector/limited parallel architectures. After reviewing Cray hardware and software the performance of different elementary program structures are examined, and effective methods for improving program performance are outlined. The computational strategies appropriate for obtaining optimum performance in applications to quantum chemistry and dynamics are discussed. Finally, some discussion is given of new developments and future hardware and software improvements.

Taylor, Peter R.↗

NASA NTRS1989

Lowest ionization potentials of Al2

Potential curves for the lowest two electronic states, X 2Sigma(+)g and A 2Pi(u), of Al2(+) were computed using complete active space SCF/multireference CI wave functions and large Gaussian basis sets. The lowest observable vertical ionization potential, to Al2(+) X 2Sigma(+)g, of the Al2 X 3 Pi(u) ground state is calculated to occur around 6.1 eV, in excellent agreement with the experimental range of 6.0 to 6.42 eV obtained in recent cluster ionization studies by Cox and co-workers. The second vertical ionization potential, to Al2(+) A 2Pi(u), occurs near 6.4 eV, also within the experimental range. The adiabatic IP of 5.90 eV is in good agreement with the value of 5.8 to 6.1 eV deduced by Hanley and co-workers from the difference in thresholds between collision induced dissociation processes of Al3(+). The computed IP values are somewhat larger than those deduced from branching ratios in cluster fragmentation experiments by Jarrold and co-workers. The observation of an ionization threshold below 6.42 eV is shown to be incompatible with an Al2 ground electronic state assignment of 3Sigma(-)g, but the separation between the two lowest states of Al2 is so small that it is likely that both are populated in the experiments, so that this does not provide unambiguous support for the recent theoretical assignment of the ground state as 3Pi(u).

Bauschlicher, Charles W., Jr.↗

NASA NTRS1989

A diagnostic for determining the quality of single-reference electron correlation methods

It was recently proposed that the Euclidian norm of the t(sub 1) vector of the coupled cluster wave function (normalized by the number of electrons included in the correlation procedure) could be used to determine whether a single-reference-based electron correlation procedure is appopriate. This diagnostic, T(sub 1) is defined for use with self-consistent-field molecular orbitals and is invariant to the same orbital rotations as the coupled cluster energy. T(sub 1) is investigated for several different chemical systems which exhibit a range of multireference behavior, and is shown to be an excellent measure of the importance of non-dynamical electron correlation and is far superior to C(sub 0) from a singles and doubles configuration interaction wave function. It is further suggested that when the aim is to recover a large fraction of the dynamical electron correlation energy, a large T(sub 1) (i.e., greater than 0.02) probably indicates the need for a multireference electron correlation procedure.

Lee, Timothy J.↗

NASA NTRS1989

The dissociation energy of N2

The requirements for very accurate ab initio quantum chemical prediction of dissociation energies are examined using a detailed investigation of the nitrogen molecule. Although agreement with experiment to within 1 kcal/mol is not achieved even with the most elaborate multireference CI (configuration interaction) wave functions and largest basis sets currently feasible, it is possible to obtain agreement to within about 2 kcal/mol, or 1 percent of the dissociation energy. At this level it is necessary to account for core-valence correlation effects and to include up to h-type functions in the basis. The effect of i-type functions, the use of different reference configuration spaces, and basis set superposition error were also investigated. After discussing these results, the remaining sources of error in our best calculations are examined.

Almloef, Jan↗

NASA NTRS1989

General contraction of Gaussian basis sets. Part 2: Atomic natural orbitals and the calculation of atomic and molecular properties

A recently proposed scheme for using natural orbitals from atomic configuration interaction (CI) wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outmost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital (ANO) sets.

Almloef, Jan↗

NASA NTRS1989

Theoretical investigations of the structures and binding energies of Be(sub n) and Mg(sub n) (n = 3-5) clusters

Researchers determined the equilibrium geometries and binding energies of Be and Mg trimers, tetramers and pentamers using single and double excitation coupled cluster (CCSD) and complete active space self-consistent-field (CASSCF) multireference configuration interaction (MRCI) wave functions in conjunction with extended atomic basis sets. Best estimates of the cluster binding energies are 24, 83 and 110 kcal/mole for Be3, Be4 and Be5; and 9, 31 and 41 kcal/mole for Mg3, Mg4 and Mg5, respectively. A comparison of the MRCI and CCSD results shows that even the best single-reference approach (limited to single and double excitations) is not capable of quantitative accuracy in determining the binding energies of Be and Mg clusters.

Lee, Timothy J.↗

NASA NTRS1989

Accurate quantum chemical calculations

An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1989

Chemical calculations on Cray computers

Taylor, Peter R.↗

NASA NTRS1989

The dissociation energy of N2

Almlof, Jan↗

NASA NTRS1989

The determination of accurate dipole polarizabilities alpha and gamma for the noble gases

The static dipole polarizabilities alpha and gamma for the noble gases helium through xenon were determined using large flexible one-particle basis sets in conjunction with high-level treatments of electron correlation. The electron correlation methods include single and double excitation coupled-cluster theory (CCSD), an extension of CCSD that includes a perturbational estimate of connected triple excitations, CCSD(T), and second order perturbation theory (MP2). The computed alpha and gamma values are estimated to be accurate to within a few percent. Agreement with experimental data for the static hyperpolarizability gamma is good for neon and xenon, but for argon and krypton the differences are larger than the combined theoretical and experimental uncertainties. Based on our calculations, we suggest that the experimental value of gamma for argon is too low; adjusting this value would bring the experimental value of gamma for krypton into better agreement with our computed result. The MP2 values for the polarizabilities of neon, argon, krypton and zenon are in reasonabe agreement with the CCSD and CCSD(T) values, suggesting that this less expensive method may be useful in studies of polarizabilities for larger systems.

Rice, Julia E.↗

NASA NTRS1989

The computation of C-C and N-N bond dissociation energies for singly, doubly, and triply bonded systems

The bond dissociation energies (D sub e) of C2H2, C2H4, C2H6, N2, N2H2, and N2H4 are studied at various levels of correlation treatment. The convergence of D sub e with respect to the one particle basis is studied at the single reference modified coupled-pair functional (MCPF) level. At all levels of correlation treatment, the errors in the bond dissociation energies increase with the degree of multiple bond character. The multireference configuration interaction (MRCI) D sub e values, corrected for an estimate of higher excitations, are in excellent agreement with those determined using the size extensive averaged coupled pair functional (ACPF) method. It was found that the full valence complete active space self consistent field (CASSCF)/MRCI calculations are reproduced very well by MRCI calculations based on a CASSCF calculation that includes in the active space only those electrons involved in the C-C or N-N bonds. To achieve chemical accuracy (1 kcal/mole) for the D sub e values of the doubly bonded species C2H4 and N2H2 requires one particle basis sets including up through h angular momentum functions (l = 5) and a multireference treatment of electron correlation: still higher levels of calculation are required to achieve chemical accuracy for the triply bonded species C2H2 and N2.

Langhoff, Stephen R.↗

NASA NTRS1989

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F + H2 yields HF + H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces.

Bauschlicher, Charles W., Jr.↗