Including Polarization Functions Research Articles

Geometry optimization inab initioSCF calculations

Abstract The floating orbital geometry optimization (FOGO) described previously is applied to H2O2, NH3, HNC, HNO, HNCO, and CH3OH. In the FOGO method we apply two analytically calculated energy gradients in a variable metric method. Some orbitals are no longer fixed on the corresponding nuclei, but their position is optimized simultaneously with the nuclear coordinates. It is shown that relative energies (e.g. rotational barriers) are obtained with similar accuracy to basis sets including polarization functions. Further, it is confirmed that FOGO yields excellent dipole moments. The FOGO method involves a considerable time saving compared to conventional calculations with DZ + P basis sets.

The inversion barriers of NF3, NCl3, PF3, and PCl3. A theoretical study

The inversion barriers of NF3, NCl3, PF3, and PCl3 have been calculated from ab initio molecular orbital theory using large basis sets including polarization functions on the central atom. The calculated inversion barriers (in kcal/mole) are 78.5(NF3), 22.9(NCl3), 121.5(PF3), and 90.8(PCl3). The NF3 inversion barrier is clearly larger than the experimental first bond dissociation energy (∼57 kcal/mole), indicating that planar NF3 is not bound relative to NF2+F. For PF3 and PCl3, bond dissociation is energetically competitive with inversion, since the experimental first bond dissociation energies are 130±14 and 81±5 kcal/mole, respectively. The lowest energy closed shell electronic configuration for planar PF3 is shown to have the phosphorus nonbonding (lone pair) electrons in a A1′ type orbital, rather than the pure p orbital of A2″ symmetry usually assumed for molecules of this type. Limiting the description of inner shells to a minimum basis set is shown to have relatively small (0–3 kcal/mole) effects on the calculated barrier.

Ab initio MO calculation of force constants and dipole derivatives for formamide

Ab initio SCF MO calculations have been carried out for the equilibrium geometry, vibrational frequencies, force constants, dipole moment and its derivatives of formamide. The energy gradient method was employed and the 4-31G basis set was used. For in-plane vibrations: (1) Calculated normal frequencies were 10–20% greater than the observed fundamental frequencies. (2) Isotope shifts (− d 0, − d 1, − d 2, and − d 3 species) were well reproduced. (3) The calculated dipole moment derivatives showed a good correspondence with the infrared intensity pattern. (4) The NH 2 rocking—OCN bending cross term, which should be zero in the Urey—Bradley force field, came out to be as large as −0.18 mdyne A. For out-of-plane vibrations, especially for the NH 2 wagging, it was found to be essential to include polarization functions for N, C and O atoms.

Calculated inversion barrier of AsF 3

The inversion barrier of AsF 3 has been calculated using SCF theory with a moderately large basis set of Slater type orbitals, including polarization functions on the central atom. The calculated barrier is ≈ 112 kcal mole . The highest occupied molecular orbital in planar AsF 3 is shown to have A' 1 symmetry, rather than A″ 2 symmetry typical for molecules of this type.

Calculation of Raman intensities by a CNDO method

A variational method for calculation of Raman intensities within the polarizability theory is formulated. The CNDO approximation is inworked, and the basis set is extended to include polarization functions. The numerical results obtained for the ethylene molecule compare well with experiments.

The photodissociation of formaldehyde: Potential energy surface features

Features of the S0 potential energy surface of formaldehyde relevant to its dissociation to molecular products, H2+CO, to radical formation, H + HCO, and to rearrangement to hydroxycarbene, HCOH, have been studied by means of ab initio calculations. A gradient procedure was used to locate and to characterize both equilibrium and transition state geometries. Basis sets of at least double zeta (DZ) quality were employed throughout and many calculations involved more flexible basis sets including polarization functions. Force constants, normal modes and vibrational frequencies were calculated at the SCF level for stationary points on the surface. Extensive configuration interaction (CI) calculations were also carried out. For the molecular dissociation the energy barrier including the effects of polarization functions and electron correlation was 4.06 eV (93.6 kcal mole−1, 32 700cm−1). Correcting for changes in zero point vibrational energy gave an approximate activation energy of 3.76 eV (87 kcal mole−1, 30 300cm−1) with an estimated error of ±0.2 eV (±5 kcal mole−1, ±1700cm−1). The energy required for the rearrangement of formaldehyde to trans-hydroxycarbene was calculated to be 3.85 eV (89 kcal mole−1, 31 000cm−1) at the DZ + polarization + CI level with the inclusion of zero point corrections. The large imaginary frequencies associated with the reactive motion imply sharp and thin barriers through which tunneling is estimated to be of considerable importance. Based on the calculated features of the potential energy surface the mechanism of the photodissociation of formaldehyde is discussed.

Ab initio study on the isomers HNO + and NOH +. vertical spectra and heat of formation

The equilibrium geometries, relative stabilities and dissociation energies in the respective ground states as well the vertical spectra up to 10 eV associated with these isomers have been reinvestigated using the MRD-CI method and including polarization functions in the AO basis set. In the case of HNO + a value of 1.65 eV is now found for the vertical transition 2A″ ← X 2A′, indicating the possibility that this species is responsible for the transition observed by Herzberg at 7200 A (1.73 eV). It is recommended for HNO + a D 298 (HNO +) value equal to 27.2 kcal/mole, while the corresponding value for the NOH + isomer is predicted to be lower by 17.5 kcal/mole (isomerization energy at room temperature). The heat of formation obtained in the case of HNO + (260.0 ± 2.0 kcal/mole) is in agreement with inferences based on experimental measurements. The corresponding frequencies of vibration and the rotational constants are also given. The possibility that these isomers could be present in the interstellar space is discussed on the basis of a limited reaction scheme.

Ab initiopotential energy surfaces for triplet states of NH2+

Ab initio configuration interaction calculations using Dunning's basis set augmented with polarization functions are presented for the 3Σ-, 3 A 2, 3 B 1, and 3 A″ surfaces for the reactions N+ + H2 and N + H2 +. The inclusion of polarization functions has little effect on the potential minima for the 3Σ- and 3 B 1 surfaces in contrast to the 3 A 2 surface. Surfaces of C ∞v and C 2v symmetry correlate as follows: 3Σ--13 A″-3 A 2, 3Π-23 A″-3 B 1. For collinear and near collinear collisions the reaction N+ + H2 is expected to occur by a direct mechanism on the 3Σ--1 3 A″ surfaces. For C 2v geometries motion will occur on the 3 A 2 surface which has a well depth of 2·6 eV. A low energy route to the deep potential well of 3 B 1 NH2 + is possible for C δ collisions of near C 2v geometry. Te triplet surfaces correlating with N + H2 + are repulsive and reaction at low energies is unlikely to occur on these surfaces.

Generalized valence-bond investigation of the reaction H+Br2 →HBr+Br

A b initio quantum mechanical calculations have been carried out to predict the H+Br2→HBr+Br potential energy surface. We used ab initio effective core potentials and an extended valence basis set including polarization functions on each center and carried out open-shell self-consistent-field calculations in the generalized valence bond–perfect-pairing (GVB–PP) approximation. The orbitals of this calculation were used as a starting point for eight-configuration–configuration-interaction (GVB–CI) calculations. The CI calculations not only bring in electron correlation effects but also make up to a large extent the inability of the GVB–PP calculation to adequately treat the recoupling of orbitals which occurs near the transition state. The classical barrier height is predicted to be about 12 kcal mole−1 by the GVB–PP calculations and about 3.0 kcal mole−1 by the GVB–CI calculations. The latter value is in reasonable agreement with the experimental Arrhenius activation energy. The saddle point is predicted from the GVB–CI calculations to occur for a linear geometry with an H–Br separation 46% greater than in HBr but a Br–Br separation only 6% greater than in Br2. The CI calculations lead to only 30% attractive energy release along a rectilinear path and predict that the energy increases only about 2.4 kcal mole−1 for a 25° bend near the saddle point. We present results for a wide range of geometries which illustrate the phenomenon of dual surfaces for a GVB–PP self-consistent-field calculation on a reactive system.

An a b i n i t i o study of the energies and structures of ketene, oxirene, and ethynol

The structures and relative energies of the lowest closed shell states of ketene, oxirene, and ethynol were studied with ab initio wavefunctions at several levels of theory. Geometries were optimized at the one-configuration self-consistent field (SCF) level of treatment using a double zeta (DZ) basis of 34 contracted Gaussian functions. The optimum structures were then refined with a basis including polarization functions (DZ+P). Correlation effects were included using the method of self-consistent electron pairs (SCEP) which variationally treats singly and doubly substituted configurations and an important subset of the quadruple substitutions. The results show that oxirene is about 80 kcal less stable than ketene, while ethynol is only 35 kcal above ketene.

CNDO calculation of polarizabilities including polarization functions in the basis set

AbstractElectric polarizabilities are calculated by solving the first‐ and second‐order perturbation equations through a variational procedure. Satisfactory numerical results are obtained for a number of molecules using the CNDO approximation with an extended basis set.

Influence of polarization functions on molecular electrostatic potentials

We study the effects of d-polarization functions, centered on the heavy atoms, on the SCF molecular electrostatic potentials calculated for some molecules. The positions and energies of the minima found are very sensitive to the inclusion of polarization functions in the basis set used. The variations depend on the heavy atom involved and on the possible anisotropy of its charge distribution. These variations are particularly important for second-row atoms.

Internal rotation in the ground electronic state of allene

The internal rotation potential of allene has been studied with ab initio self-consistent field (SCF) methods using a double-zeta basis set of 38 contracted Gaussian functions and an extended set of 65 functions including polarization functions, and with the method self-consistent electron pairs (SCEP) using the double-zeta set. The ground state of allene is a closed shell /sup 1/A/sub 1/ state in D/sub 2d/ symmetry. In the D/sub 2/ symmetry of the twisted form, this closed shell state mixes with a 2b/sub 3/ ..-->.. 3b/sub 3/ open shell /sup 1/A/sub 1/ state which correlates with a /sup 1/A/sub u/ state in the D/sub 2h/ symmetry of the planar form of the molecule. The planar closed shell state, /sup 1/A/sub g/, is higher in energy than the /sup 1/A/sub u/ state. Examination of pair correlation energies indicates that correlation effects will not reverse this order. The internal rotation barrier is predicted to be about 49 kcal, after geometry optimization, and there is little effect on relative energies from including polarization functions.

Ionization potentials of HCN and HNC by a Green's function method

The vertical valence ionization potentials of HCN and HNC have been calculated by a many-body Green's function method using extended basis sets including polarization functions. For HCN the agreement of the computed ionization potentials with experiment is very satisfactory. The ordering is 1π, 3σ, 2σ. The ionization potentials of HNC have not been measured yet. The calculated ordering is 3σ, 1π, 2σ. The electronic structure of the two molecules is seen to differ.

SCF-CI studies of the equilibrium structure and the proton transfer barrier H3O 2 ?

Large-scale configuration interaction (CI) calculations have been performed in order to study the effect of the correlation energy on the equilibrium geometrical structure, the stability, and on the energy barrier of the proton transfer reaction in the hydrogen bonded system HO− · HOH. An extended Gaussian basis set including polarization functions on each nuclear centre has been employed to approximate the molecular Orbitals. All possible single and double replacements resulting from a single determinant Hartree-Fock reference state have been taken into account in the CI wavefunction. Compared to the SCF results the equilibrium oxygen/oxygen distance has been obtained from the CI calculations to be smaller by about 0.08 A and the correlation energy has been found to stabilize the composed system by 3.6 kcal/mole. An almost symmetric equilibrium structure with the hydrogen bonding H-atom midway between the two oxygen centres has been obtained in the CI treatment, whereas SCF calculations yield an asymmetric geometrical configuration with a small energy barrier of 1.4 kcal/mole for the proton transfer process.

Extended basis set studies of hydrocarbon molecular orbital energies

Ab initio molecular orbital theory with three extended basis sets (4-31G, 6-31G, 6-31G *) has been used to study some simple hydrocarbons. Results are presented for propane, 1,3-butadiyne and several of the isomers of the C 4H 4 and C 4H 6 systems. The inclusion of polarization functions (basis 6-31G *) leads to relative energies within 3 kcal mol −1 of the available experimental data. Results are also presented for isodesmic energy comparisons, including bond separation energies.

A molecular orbital study of the cis- trans energy difference in glyoxal

The barrier to internal rotation around the C-C bond in glyoxal, and the energy difference between the cis and the trans form of the molecule have been estimated using (7, 3 4 ) and (9, 5 4 ) Gaussian basis sets including polarization functions. The predicted energy of the cis form relative the ground state trans form was found to be substantially higher (4.9–6.3 kcal mol −1) than the experimental value of 3.2 kcal mol −1.

All-valence-electron Cl calculations on the electronic spectrum of diborane

All-valence-electron Cl calculations have been carried out for diborane B 2H 6 and its positive ion employing a rather large double-zeta AO basis including polarization functions in order to study the electronic spectrum of this system. Transitions from four different valence MOs are found to lead to low-lying electronic transitions of both Rydberg and valence type in each case. Ad mixture of valence character in the otherwise Rydberg-like ( nx, 3s), ( ny, 3s) and (σ, 3pz) transitions calculated to lie between 11.0 and 11.6 eV is indicated as being primarily responsible for the highly intense shoulder found in this region of the B 2H 6 spectrum. The other strong feature with essentially continuous absorption peaking at 9.3 eV is suggested to result from superposition of several Rydberg-type transitions in the generally broad absorption pattern expected for the 1(π,π *) species at significantly higher vertical excitation energy. Quite good agreement is obtained between calculation and experiment for all of the six lowest IPs of diborane and also for the locations of the 1(n, π *) and 1(σ, π *) transitions previously assigned to the two weak features observed at 6.8 and 8.3 eV in this spectrum.

Calculation of the inversion barrier of ammonia with small optimized GTF basis sets

Two small GTF contracted basis sets including polarization functions on nitrogen have been partially optimized on the ammonia molecule. Basis set A (7,3,1;4/2,1,1;1) is found to yield an energy value less than 0.2 a.u. above the Hartree—Fock limit and a nitrogen inversion barrier fairly close to the experimental height. These results may make A an acceptable basis set for calculations on larger systems containing nitrogen. Basis set B (5,2,1;3/2,1,1;1) does not simultaneously yield acceptable values for the energy and the inversion barrier and should not be considered seriously for further calculations.

Calculation of electric polarizabilities within the CNDO framework including polarization functions in the basis set

A semi-empirical method within the CNDO framework is applied to the calculation of the electric polarizabilities for H2O, H2CO, NH3, CH3OH, C2H2, C2H4 and N2. The approach allows for the inclusion of different valence shell orbitals on the same atom and yields results which agree well with experiment. The main features of elaborate ab initio calculations are also reproduced. In most cases the polarization functions have been optimized and account well for the polarization of the molecule. It is shown that a judicious choice of these functions is intimately related with the environmental anisotropy of bonds and is indirectly connected with internal field effects.