SCF Gradient Research Articles

Dual-Basis Analytic Gradients. 1. Self-Consistent Field Theory

Analytic gradients of dual-basis Hartree-Fock and density functional theory energies have been derived and implemented, which provide the opportunity for capturing large basis-set gradient effects at reduced cost. Suggested pairings for gradient calculations are 6-31G/6-31G**, dual[-f,-d]/cc-pVTZ, and 6-311G*/6-311 + +G(3df,3pd). Equilibrium geometries are produced within 0.0005 A of large-basis results for the latter two pairings. Though a single, iterative SCF response equation must be solved (unlike standard SCF gradients), it may be obtained in the smaller basis set, and integral screening further reduces the cost for well-chosen subsets. Total nuclear force calculations exhibit up to 75% savings, relative to large-basis calculations.

Comment on Dunning's correlation-consistent basis sets

The contraction in Dunning's correlation-consistent basis sets follows the original Raffenetti approach that uses (a) occupied SCF orbitals plus (b) uncontracted primitives. Without any loss of energy, (b) can be excluded from (a), leading to substantial savings of Cce:simple-paraU times for integral-limited computing steps such as SCF gradient geometry searches on large to very large molecules.

Combined Hartree-Fock and density functional theory: a distributed memory parallel implementation

The parallelisation of an ab initio, Kohn-Sham density functional code for direct SCF energy and gradient evaluation calculations is described. The implementation of the parallel Hartree-Fock method uses the PRISM algorithm for the calculation of the two-electron integrals. A Kohn-Sham density functional code has been written by us and interfaced to Gaussian 92. This code has also been parallelised and incorporated into a set of new ‘links’ for the Gaussian 92 package. The work, although performed using one particular type of workstation ‘cluster’ (the Hewlett-Packard 9000-7xx series), has been based upon P.V.M. (Parallel Virtual Machine), a portable communications package which is already available for a large number of systems including many UNIX workstations. The methods described are, thus, applicable to any system which is supported by both the Gaussian 92 program and the P.V.M. communications package with minimal changes required to the sequential code.

Ab initio molecular orbital study of the rearrangement of fluoroallene to singlet fluorovinylmethylene

The rearrangement of fluoroallene (FAL) to singlet fluorovinylmethylene (FVM) is studied by using ab initio closed-shell SCF gradient and Møller-Plesset perturbation methods. It is found from the present results that among 1,2 hydrogen migration pathways from FAL to singlet FVM, the pathway to 3-FVM has the lowest potential energy barrier height which is estimated to be 67.8 kcal mol -1, that is 3.8 kcal mol -1 lower than the barrier height for the 1,2 hydrogen migration pathway from allene (AL) to singlet vinylmethylene (VM), and that 1,2 fluorine migration is energetically less favorable than 1,2 hydrogen migration reactions.

Prescreening of two‐electron integral derivatives in SCF gradient and Hessian calculations

AbstractThe definition and implementation of a rigorous two‐electron integral bound based on Schwarz' inequality both for gradient and hessian calculations is presented. Tests demonstrate the advantages of this easily implemented and effective bound.

ChemInform Abstract: Computational Study of the Isomerizations and Fragmentations of the Singlet and Triplet CH2CH2NH Diradicals.

Pathways for the thermal unimolecular reactions of the CH2CH2NH diradicals, both singlet and triplet, have been investigated by ab initio MO calculations using 4-31G basis functions. The minimum-energy paths for possible isomerizations and fragmentations are traced by the SCF gradient procedure, and multireference double-excitation (MRD) CI calculations carried out for all the stationary structures located. The results of calculation show that the energetically most favorable unimolecular reaction possible to the triplet diradical is an α-hydrogen detachment giving rise to CH2=CH–NH (2A″), whereas that to the singlet diradical is a 1,2-hydrogen migration to give CH3CH=NH (1A′). The activation barrier heights calculated for the two processes are 103 and 74 kJ mol−1, respectively. It is concluded that, in the gas phase, CH3CN and HCN should be formed concurrently by the α-bond cleavages of the doublet radical CH3CH=N (2A′), which will arise most readily from the vibrationally hot CH3CH=NH (1A′).

Computational Study of the Isomerizations and Fragmentations of the Singlet and Triplet CH2CH2NH Diradicals

Abstract Pathways for the thermal unimolecular reactions of the CH2CH2NH diradicals, both singlet and triplet, have been investigated by ab initio MO calculations using 4-31G basis functions. The minimum-energy paths for possible isomerizations and fragmentations are traced by the SCF gradient procedure, and multireference double-excitation (MRD) CI calculations carried out for all the stationary structures located. The results of calculation show that the energetically most favorable unimolecular reaction possible to the triplet diradical is an α-hydrogen detachment giving rise to CH2=CH–NH (2A″), whereas that to the singlet diradical is a 1,2-hydrogen migration to give CH3CH=NH (1A′). The activation barrier heights calculated for the two processes are 103 and 74 kJ mol−1, respectively. It is concluded that, in the gas phase, CH3CN and HCN should be formed concurrently by the α-bond cleavages of the doublet radical CH3CH=N (2A′), which will arise most readily from the vibrationally hot CH3CH=NH (1A′).

AB initio calculations of structural features not easily amenable to experiment: Part 68. Structural trends in some substituted nitriles and acetylenes

The geometries of a number of alkynes, nitriles, and dinitriles were determined by SCF gradient optimization using the 4-21G, 4-21G ∗, 5-31G ∗, and 3-321G ∗ basis sets. The systems investigated include: YH3-C-C-X compounds, with Y = Si and C, and X = H, F, Cl, and CN; the geminally disubstituted systems, 1,4-pentadiyne, H 2C-(CCH) 2, and 1,1-dicyanocarbonyl, OC(CN) 2; X 2Z-(CN) 2 homologs with X = H, F, and Cl, and Z = Si and C; and various auxiliary structures (e.g. silylcyanide, methoxyacetylene, and S-methylacetylene) needed to establish structural trends with specific basis sets. The CC bond lengths in C C-X systems are found to decrease with increasing electronegativity of X. The Si-H bond lengths decrease in the series SiH 4, SiH 3-CN, SiH 2-(CN) 2 in contrast to C-H bond lengths in the methyl homologs. The characteristic non-linearity of the C-CC-H and Z-CN (Z = Si and C) moieties in geminally disubstituted Y 2Z(CX) 2 systems is considered in detail and found to depend on the electronegativity of Y. The calculated structures are in good agreement with previously published experimental geometries, some of which were derived from a limited number of experimental data.

Ab initio calculations on three isomers of LiC 2H 2

The LiC 2H 2 complex has been investigated with the analytical SCF gradient method and MRD-CI calculations have been carried out for the SCF optimized geometries. The vinyl-radical-like structure does not correspond to a minimum, but represents a transition state with one negative eigenvalue of its Hessian. The vinylidene-like structure, as well as the acetylene π-complex structure, are both local minima on the LiC 2H 2 SCF energy hypersurface with comparable energies. The vinylidene-like structure is found to be slightly favored, but the energy difference decreases with the improvement of the computational method used. The recently measured IR spectrum of matrix-isolated LiC 2H 2 is in good agreement with the calculated normal frequencies of the π-complex structure.

Vibrational energy transfer in collisions of He atoms with para-difluorobenzene

Vibrational energy transfer in the three-dimensional collisions of He atoms with para-difluorobenzene (pDFB) has been studied theoretically. A quantum-mechanical scattering method has been employed which uses the close-coupling method for the molecular vibrations and the infinite-order-sudden approximation for rotational motion. Both V–T and V–V processes are studied. The normal mode coefficients for pDFB were obtained from an SCF gradient program. The computations showed a strong propensity for excitation and relaxation of the v30 vibrational mode, which is the mode of lowest frequency. This finding is in agreement with molecular beam experiments of Gentry and co-workers, and laser-fluorescence measurements of Parmenter and co-workers. When the different vibrational modes were given the same frequency in the calculations, modes involving atomic displacements out of the molecular plane had distinctly larger vibrational excitation cross sections than those for in-plane modes.

An ab initio CI investigation of structure and bonding in LiC 2H 2 complexes

The structures and energies of various LiC 2H 2 complexes have been investigated by means of ab initio molecular orbital calculations. Analytic SCF gradients were employed with a double-ζ basis set to locate and characterize stationary points on the energy surface. Single-point CI calculations using a double-ζ + diffuse and polarization basis set have been carried out at the DZ + P SCF stationary points. With the highest-level theory, the Li—vinylidene complex and the cis bridged adduct are found to be the most favorable arrangements, the former complex being slightly more stable by about 2 kcal mol −1. These molecules are bound respectively by about 5 and 3 kcal mole −1 relative to infinitely separated lithium plus acetylene. Harmonic vibrational frequencies are also reported and confirm the existence of the cis LiC 2H 2 species recently observed in a solid argon matrix.

The diradical nature of ketocarbenes occurring in the Wolff rearrangement. An MC-SCF study

Using MC–SCF gradient optimisation techniques (at the 6–31G* basis-set level) the minima and transition structures occurring in the rearrangements of formylmethylene to oxirene have been characterised. The triplet-state and singlet-state surfaces and the crossing region have been studied. The results show that the lowest-energy singlet state of formylmethylene is a pure diradical. The related triplet state has a very similar geometrical structure and lies only slightly lower in energy. Further, both states have the two unpaired electrons in sigma orbitals and the minimum-energy singlet–triplet crossing point occurs very near singlet–triplet diradical minimum of formylmethylene.

A MCSCF study of homoaromaticity and the role of ion pairing in the stabilization of carbanions

The bicyclo[3.2.1]octa-3,6-dien-2-yl anion (I), the anion I lithium cation complex, the allyl anion (X), the allylradical, the allyl anion lithium cation complex, the ethene molecule, and the ethene lithium cation complex have been studiedby means of multiconfigurational SCF (MCSCF) and analytical gradients. The calculations have been confined to minimaland split-valence basis sets. The large distance between the C2 olefinic bridge and the C3 carbanionic bridge of anion I andthe short C6-C7 bond distance imply bishomoaromaticity to be negligible. According to these results, homoaromaticity isnot responsible for the observed stability in many potentially homoaromatic carbanions. The stability of anion I in the gasphase is instead explained in terms of a simple electrostatic model, where the quadrupole moment in the C2 olefinic bridgestabilizes the charge in the C, carbanionic bridge. This model agrees quantitatively with experiment. Calculations on theanion I lithium cation complex showed that in solution an additional attractive interaction between the C2 olefinic bridge andthe lithium cation can contribute. This additional interaction is estimated to stabilize the carbanion-lithium ion pair in thegas phase by about 16 kcal/mol. However, the stabilizing interactions of anion I in solution (quadrupole-charge andcounterion-anion interactions) will be reduced by solvent shielding. The relative ratios of the different stabilizing interactionsare therefore difficult to estimate. The geometrical findings of this paper have been verified by a recent X-ray experiment.

An efficient algorithm for the approximate location of transition structures in a diabatic surface formalism

An efficient algorithm is presented for the approximate location of a transition structure by finding the minimum of the seam of intersection of two diabatic surfaces. The algorithm is sufficiently stable that the optimization can be started from the product geometry. The procedure is illustrated with two examples. The approximate structures obtained are sufficiently close to the corresponding MC SCF optimized structures, that the subsequent MC SCF gradient optimizations, starting from these points, converge easily.

Theoretical study of structures and energies of [HCOO] + and [COOH] + and their rearrangement

The structures of [HCOO] +, [COOH] + and the transition state on the rearrangement path are obtained by the MC SCF gradient method with a 6-31G ★ basis set. The energy barrier of the singlet rearrangement reaction, 8.47 kcal mol , calculated by the MC SCF MRSDQ CI method with a 6-311G ★★ basis set suggests that [HCOO] + is a stable biradical and experimentally observable.

ChemInform Abstract: The Conformation of 2‐Cyclopropylpropene and 1,1‐Dicyclopropyl Ethylene by Means of ab initio SCF Calculations.

Abstract The geometrical structure of 2-cyclopropylpropene and 1,1-dicyclopropyl ethylene has been determined by means of the ab initio SCF gradient method. The most stable conformation of 2-cyclopropylpropene has a gauche structure and the internal rotation angle between the cyclopropyl ring and the vinyl group is calculated to be 62°. The most stable conformation of 1,1-dicyclopropyl ethylene also has a gauche structure and the internal rotation angles between one of two cyclopropyl rings and the vinylidene group are 64°.

The conformation of 2-cyclopropylpropene and 1,1-dicyclopropyl ethylene by means of ab initio SCF calculations

The geometrical structure of 2-cyclopropylpropene and 1,1-dicyclopropyl ethylene has been determined by means of the ab initio SCF gradient method. The most stable conformation of 2-cyclopropylpropene has a gauche structure and the internal rotation angle between the cyclopropyl ring and the vinyl group is calculated to be 62°. The most stable conformation of 1,1-dicyclopropyl ethylene also has a gauche structure and the internal rotation angles between one of two cyclopropyl rings and the vinylidene group are 64°.

Theoretical studies on pteridines: Part V. comparison of STO-3G, 3-21G and experimental geometries

Full geometry optimisations using ab initio SCF gradient techniques are reported for pteridine, quinazoline, 2,4-diaminopteridine, pterin and its enol form with the 3-21G basis, and for quinazoline with the STO-3G basis. The results are compared with experiment and previously obtained STO-3G geometries for the pteridines, and literature data for pyrimidine, uracil and cytosine. The main finding is that the minimal basis substantially underestimates Π-electron delocalisation effects in these extended heterocycles, a deficiency mostly corrected by use of the extended basis set. The average absolute deviation from experiment of the 3-21G CC and CN bond lengths in the pteridines is ≈0.012 Å.

Critical comparison of the ab initio and spectroscopic methyl‐CH bond length difference in acetyl compounds, CH3C(O) X

AbstractIn order to provide additional data for the relative lengths of methyl‐CH bond distances in acetyl derivatives, which are difficult to determine accurately by the conventional tools of structural chemistry, the geometries of CH3COH, CH3COF, CH3COCH3, CH3COOH, and CH3CONH2 were determined by ab initio SCF gradient optimization at the 5‐31G** level and compared with previous 4‐21G results. For acetaldehyde 6‐311G4* calculations were also performed and the correlated methyl‐CH stretching potential energy functions were determined. It is found that the calculated differences between the in‐plane and out‐of‐plane methyl‐CH bonds are practically independent of the computational scheme. The calculated results are in contrast to relative bond lengths obtained by some vibrational overtone spectroscopic studies, but are in perfect agreement with CH bond length differences determined from isolated CH stretching frequencies of partially deuterated compounds. The reliability of the latter, and other spectroscopic data concerning the assignment of the methyl‐CH vibrations are critically analyzed. On the basis of the available evidence we conclude: (1) the methyl groups of the CH3C(O)X systems here discussed contain one strong (in‐plane) and two weak (out‐of‐plane) CH bonds; (2) intensities of CH local mode spectra do not provide a reliable basis for assignment to individual bonds.

The structure of the singlet tetramethylene diradical intermediate

Ab initio MC SCF geometry optimizations of the gauche and trans conformers of the singlet tetramethylene diradical have been carried out using MC SCF gradients with a minimal (STO-3G) and extended (4-31G) basis set. At both computational levels, it has been found that the tetramethylene diradical exists as a stable species in two different conformations, a gauche and a trans.