Ab initio study of vibrational frequencies,force field and normal coordinate analysis of the cis- and trans-isomets of nitrosomethanol

In this paper, the equilibrium geometries of two isomers of the newly found compound — nitrosomethanol—have been optimized by ab initio SCF MO method with 3–21G basic set by gradient technique. And the second derivatives of potential energy (i. e. the force constant matrix elements) have been calculated analytically. Hence the entire force fields of the two isomers of nitrosomethanol have been obtained theoretically. The theoretical vibrational frequencies and the corresponding normal modes were obtained and compared with the experimental values, and the structures of two isomeric forms of nitrosomethanol are established.     

Transition structure modeling by intersecting potential energy surfaces

A previously proposed method of modeling force field transition structures as the lowest energy structure on the seam of two intersecting potential energy surfaces is improved with respect to the force field expression and the efficiency of the optimization algorithm. Comparison with ab initio and experimental results show that the force field method may have the potential of achieving almost quantitative results. It appears that the results from transition state modeling are currently limited by the accuracy of the underlying force field. © 1994 by John Wiley & Sons, Inc.     

Multiobjective evolutionary algorithm with many tables for purely ab initio protein structure prediction

This article focuses on the development of an approach for ab initio protein structure prediction (PSP) without using any earlier knowledge from similar protein structures, as fragment‐based statistics or inference of secondary structures. Such an approach is called purely ab initio prediction. The article shows that well‐designed multiobjective evolutionary algorithms can predict relevant protein structures in a purely ab initio way. One challenge for purely ab initio PSP is the prediction of structures with β‐sheets. To work with such proteins, this research has also developed procedures to efficiently estimate hydrogen bond and solvation contribution energies. Considering van der Waals, electrostatic, hydrogen bond, and solvation contribution energies, the PSP is a problem with four energetic terms to be minimized. Each interaction energy term can be considered an objective of an optimization method. Combinatorial problems with four objectives have been considered too complex for the available multiobjective optimization (MOO) methods. The proposed approach, called “Multiobjective evolutionary algorithms with many tables” (MEAMT), can efficiently deal with four objectives through the combination thereof, performing a more adequate sampling of the objective space. Therefore, this method can better map the promising regions in this space, predicting structures in a purely ab initio way. In other words, MEAMT is an efficient optimization method for MOO, which explores simultaneously the search space as well as the objective space. MEAMT can predict structures with one or two domains with RMSDs comparable to values obtained by recently developed ab initio methods (GAPF_CG, I‐PAES, and Quark) that use different levels of earlier knowledge. © 2013 Wiley Periodicals, Inc.     

An algorithm for geometry optimization without analytical gradients

A numerical algorithm for locating both minima and transition states designed for use in the ab initio program package GAUSSIAN 82 is presented. It is based on the RFO method of Simons and coworkers and is effectively the numerical version of an analytical algorithm (OPT = EF) previously published in this journal. The algorithm is designed to make maximum use of external second derivative information obtained from prior optimizations at lower levels of theory. It can be used with any wave function for which an energy can be calculated and is about two to three times faster than the default DFP algorithm (OPT = FP) supplied with GAUSSIAN 82.     

A theoretical study of the rotational isomers of nitrosomethanol by semiempirical (AM1) and ab initio methods

The conformational potential energy surface as a function of the two internal torsion angles in C-nitrosomethanol has been obtained using the semiempirical AM1 method. Optimized geometries are reported for the local minima on this surface and also for the corresponding points on the HF/6-31G, 6-31G*, and 6-31G** surfaces. All methods predict cis and trans minima which occur in degenerate pairs, each pair being connected by a transition state of C_s symmetry. The AM1 structures are found to compare well with the corresponding ab initio structures. Ab initio HF/6-31G and HF/6-31G* harmonic vibrational frequencies are reported for the cis and trans forms of nitrosomethanol. When scaled appropriately the calculated frequencies are found to compare well with experimental frequencies. The ab initio calculations predict the energy barrier for cis → trans isomerization to be between 5.8 and 6.5 kcal/mol with the trans → cis isomerization barrier lying between 2.3 and 6.5 kcal/mol. The corresponding AM1 energy barriers are around 1 kcal/mol lower in energy. The ab initio calculations predict the barrier to conversion between the two cis rotamers to be very small with the AM1 value being around 1 kcal/mol. Both AM1 and ab initio calculations predict interconversion between trans rotamers to require between 1.2 and 1.4 kcal/mol.     

Location of saddle points and minimum energy paths by a constrained simplex optimization procedure

Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplex optimization technique that avoids the evaluation of gradients or second derivative matrices. Three chemical reactions of increasing structural complexity are studied within the PRDDO SCF approximation. Predicted properties of reaction hypersurfaces are in good overall agreement with those determined by gradient minimization and gradient following algorithms in connection with various ab initio SCF methods. Computational efforts required by the new procedures are discussed.     

Spin-Orbit coupling in aromatic hydrocarbons: A semiempirical evaluation of the radiative lifetimes of naphtalene and anthracene

Singlet-triplet spin-orbit matrix elements, which govern the lowest ³B_1u ← ¹A_g transition in typical aromatic molecules like naphtalene and anthracene, are calculated with INDO molecular orbitals and the conventional spin-orbit one-electron hamiltonian. The correct order of magnitude of the triplet radiative lifetimes is obtained for the two molecules, when INDO MO coefficients are referred to a symmetrically orthogonalized basis. The possibility of using the semiempirical Hamiltonian is explored using ab initio wave-functions for a few test cases. Reasonably accurate doublet-doublet and singlet-triplet matrix elements have been computed.     

An ab initio molecular orbital study of the C2F2 species: The difluorovinylidene → difluoroacetylene rearrangement

An ab initio MO study, using medium size Gaussian basis sets has been made of vinylidene carbene, acetylene and the isomeric cyclic intermediate presumed to represent the transition state of their interconversion reaction, along with their perfluorinated analogs. The total energies of the acetylenes are lower than the vinylidenes and the estimated activation energy of their interconversion is considerably higher for the fluorinated molecules. The results are in line with experimental observations.     

A test of the new “integrated MO + MM” (IMOMM) method for the conformational energy of ethane and n-butane

Test calculations of the newly developed “Integrated Molecular Orbital + Molecular Mechanics” (IMOMM) method were performed for the optimized equilibrium and transition structures and energies of ethane and n-butane. In this method, the total energy of a large molecular system is expressed as a sum of the MO energy of the small “model” system and a modified MM energy of the “real” system, and full geometry optimization is carried out using the gradient of this total energy. Various schemes of partition of the system into the MO part and the MM part, including some not intended in the original design of the method, were examined and compared with the pure ab initio MO and the pure MM results. In most reasonable partition schemes, the IMOMM method can reproduce the pure ab initio and the pure MM geometries and energies quite well. © 1996 John Wiley & Sons, Inc.     

Constrained optimization in cartesian coordinates

Modifications are made to a previously published algorithm for constrained optimization in Cartesian coordinates (J. Comp. Chem., 13 , 240, 1992) to incorporate both fixed and dummy atoms. Standard distance and angle constraints can now be specified with respect to dummy atoms, greatly extending the range of constraints that can be handled. Fixed atoms can be eliminated from the optimization space and so there is no need to calculate their gradients resulting in potentially significant savings of CPU time in ab initio computations. Several examples illustrate the range and versatility of the modified algorithm. © John Wiley & Sons, Inc.     

Protein structure prediction using a combination of sequence homology and global energy minimization: II. Energy functions

A protein energy surface is constructed. Validation is through applications of global energy minimization to surface loops of protein crystal structures. For 9 of 10 predictions, the native backbone conformation is identified correctly. Electrostatic energy is modeled as a pairwise sum of interactions between anisotropic atomic charge densities. Model repulsion energy has a softness similar to that seen in ab initio data. Intrinsic torsional energy is modeled as a sum over pairs of adjacent torsion angles of 2-dimensional Fourier series. Hydrophobic energy is that of a hydration shell model. The remainder of hydration free energy is obtained as the energetic effect of a continuous dielectric medium. Parameters are adjusted to reproduce the following data: a complete set of ab initio energy surfaces, meaning one for each pair of adjacent torsion angles of each blocked amino acid; experimental crystal structures and sublimation energies for nine model compounds; ab initio energies over 1014 conformations of 15 small-molecule dimers; and experimental hydration free energies for 48 model compounds. All ab initio data is at the Hartree–Fock/6–31G* level. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 548–573, 1998     

Optimized Structures and Relative Stabilities of the Carboranes from Ab Initio Calculations

Ab initio calculations at the STO-3G level were performed on almost all of the possible isomers for the entire series of closo-carboranes, C₂B_n-2H_n, 5 ? n ? 12. Geometry optimizations using the gradient method were also included in all calculations. We report here the relative energies obtained for the various isomers as well as the optimized structures. These calculations confirm our previous predictions of relative stabilities obtained from topological charge stabilization. Comparisons of our structures with those from experimental data provide us with a measure of reliability for bond distances obtained using ab initio SCF MO calculations at the STO-3G level. Results from the geometry optimization substantiated the experimentally known fluxional behavior of the 8 and 11 atom polyhedra.     

Wellenmechanische Absolutrechnungen an Molekülen und Atomsystemen mit der SCF?MO?LC(LCGO) Methode. IV. Das Äthylen (C2H4)

The C₂H₄ was investigated ab initio for the equilibrium distance of the centers, taking all 16 electrons into account, using the Allgemeines Programmsystem/SCF ? MO ? LC (LCGO ) Methode. A total energy of ?76.77 a.u. and an ionization energy of 10.55 eV were found.     

Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part II. Accurate energy minimization

A method is described to perform ab initio energy minimization for crystals of flexible molecules. The intramolecular energies and forces are obtained directly from ab initio calculations, whereas the intermolecular contributions follow from a potential that had been parameterized earlier on highly accurate quantum‐chemical calculations. Glycol and glycerol were studied exhaustively as prototypes. Lists of hypothetical crystal structures were generated using an empirical force field, after which ab initio energy minimizations were performed for a few hundreds of these. The experimental crystal structures were found among the structures with lowest energy, provided that sufficiently large basis sets were used. Moreover, their crystal geometries were well reproduced. This approach enables a systematic comparison between the merits of force fields at various levels of sophistication. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 805–815, 2001     

On the convergence properties of the Rayleigh–Schrödinger and the Hirschfelder–Silbey perturbation expansions for molecular interaction energies

By applying the powerful direct optimization technique of conjugate gradients as adapted for the optimization of an open shell energy functional, a uniformly balanced (15^s 10^p) Gaussian basis set was obtained for the silicon atom. The quality of this basis set, as defined in terms of “exponent forces” or energy gradient |g|, is compatible with the quality of suitably chosen (10^s 5^p) carbon and (5^s) hydrogen basis sets. Contractions better than double zeta were determined for all three bases of Si, C, and H. Using the primitive and contracted bases, ab initio SCF MO calculations were carried out on molecules of SiH₄, CH₄, and H₂. Some of the computed results obtained for H₂C = SiH₂ are also included as an illustration for organo-silicon compounds.     

An optimum strategy for solution chemistry using semiempirical molecular orbital method: Importance of description of charge distribution

For the purpose to execute direct dynamics calculation in solution chemistry, we propose an optimum strategy for solution chemistry using semiempirical molecular orbital (MO) method with neglect of diatomic differential overlap (NDDO) approximation with specific solution reaction parameters (SSRP), i.e., the NDDO‐SSRP method. In this strategy, the empirical parameters of the semi‐empirical MO method were optimized individually for target molecule or ion by reference to the ab initio MO calculation data for many configurations on the potential energy surface near the reaction path. For demonstration, the NDDO‐SSRP method was applied to two molecules and two ions (OH^?, H₂O, NH₃, NH₄⁺) at their equilibrium states in aqueous solution, respectively. Accordingly, it was verified that both the potential energy surface and the charge distribution of these solutes in aqueous solution are dramatically improved to reproduce themselves accurately at ab initio MO calculation level. In conclusion, it is expected that the NDDO‐SSRP method should become quite useful for dynamic and statistical applications to chemical reaction systems in solution. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Ab initio conformational analysis of cyclooctane molecule

The potential energy surface (PES) for the cyclooctane molecule was comprehensively investigated at the Hartree–Fock (HF) level of theory employing the 3–21G, 6–31G, and 6–31G* basis sets. Six distinct true minimum energy structures (named B, BB, BC, CROWN, TBC, and TCC₁), characterized through harmonic frequency analysis, were located on the multidimensional PES. Two transition state structures were also located on the PES for the cyclooctane molecule. Electron correlation effects were accounted for using the Møller–Plesset second-order perturbation theory (MP2) approach. The predicted global minimum energy structure on the ab initio PES for the cyclooctane molecule is the BC conformer. A gas phase electron diffraction study at 300 K suggested a conformational mixture while an NMR study in solution at 161.5 K predicted the BC conformer as the predominant form. The equilibrium constants reported in the present study, which were evaluated from the ab initio calculated total Gibbs free energy change values, were in good agreement with both experimental investigations. The ab initio results showed that the low temperature condition significantly favored the BC conformer while above room temperature both BC and CROWN structures can coexist. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 524–534, 1998     

A theoretical study on the structure and properties of phenothiazine derivatives and their radical cations

Semiempirical CNDO, AM1, PM3 and ab initio HF/STO-3G, HF/3-21G(d), and HF/6-31(d) methods were employed in the geometry optimization of the phenothiazine and the corresponding radical cation. The results obtained from the PM3 performances were as good as those from the ab initio calculations in the structure optimization of both phenothiazine and phenothiazine radical cation. The PM3 method was used to optimize the structures of a series of N-substituted phenothiazine derivatives and their radical cations. The PM3-optimized results were then analyzed with the ab initio calculation at the 6-311G(d,p) level, which yielded the total energy, frontier molecular orbitals, dipole moments, and charge and spin density distributions of the phenothiazine derivatives and their radical cations.     

Theoretical studies on ammonia oxide and its unimolecular reactions

The unimolecular reactions of ammonia oxide H₃NO, isomerization and dehydrogenation, are investigated by ab initio MO calculations with the 4-31G basis set. The geometries and energies of the reactant, transition states and products have been determined on the singlet potential energy surface. The reaction ergodography along the intrinsic reaction coordinate (IRC) for the two reactions have been performed. The vibrational frequency correlation diagram of the two reactions are analyzed along the IRC.