Semiempirical Potential Surface Research Articles

Acceleration of Correlation-corrected Vibrational Self-consistent Field Calculation Times for Large Polyatomic Molecules

Acceleration of the correlation-corrected Vibrational self-consistent field (CC-VSCF) method for anharmonic calculations of vibrational states of polyatomic molecules is described. The acceleration assumes pairwise additive interactions between different normal modes, and employs orthogonality of the single-mode vibrational wavefunctions. This greatly reduces the effort in computing correlation effects between different vibrational modes, which is treated by second order perturbation theory in CC-VSCF. The acceleration can improve the scaling of the overall computational effort from N6 to N4, where N is the number of vibrational modes. Sample calculation times, using semi-empirical potential surfaces (PM3), are given for a series of glycine peptides. Large computational acceleration, and significant reduction of the scaling of the effort with system size, is found and discussed.

Ab initio/LD studies of chemical reactions in solution: Reference free-energy surfaces for acylation reactions occurring in serine and cysteine proteases

A systematic ab initio study of the reactions of amides with alcohols and thiols in aqueous solution is presented. This study is aimed at providing well-defined reference free-energy surfaces for the corresponding studies of the catalytic power of serine and cysteine protease. The applied methodology consists of the combined ab initio and Langevine dipoles (LD) solvent model, and a systematic calibration using the available experiments. The study of the base-catalyzed and general-base-catalyzed methanolysis of formamide, which serves as a reference reaction of serine protease, indicates that when a water molecule is the base the initial proton transfer is concerted with the RO− nucleophilic attack. However, with histidine as a general base this reaction is a stepwise process with a shallow surface that can allow also for a concerted path. It is also found that the protonation of the nitrogen of the oxyanion leads to breaking of the CN bond. The study of a reference reaction of cysteine protease indicates that the initial proton transfer to the general base occurs before the RS− attack on the amide. The nucleophilic attack may be concerted with the protonation of the amide nitrogen, but a stepwise process where the protonation occurs after the formation of the tetrahedral intermediate is also possible. The CN bond cleavage appears to be the last step of the reaction. The common belief that thiols have greater tendency to add to carbonyl groups than alcohols is revisited. It is found that this is probably true because the reactivity of thiols can involve unassisted proton transfer to the nitrogen or oxygen of the amide concerted with the nucleophilic attack. The possibility that thiolysis of amides in solution circumvents the general-base catalysis mechanism should thus be taken into account in comparing enzymatic reactions to uncatalyzed solution reactions. Having relatively reliable potential surfaces for the reference reactions of serine and cysteine proteases should allow one to calibrate potential surfaces for the corresponding enzymatic reactions. This can be very useful for calibrating empirical valence bond (EVB) potential surfaces or other hybrid quantum mechanical/molecular mechanical (QM/MM) semiempirical potential surfaces. In addition, our results will be useful for ab initio studies that use the EVB surfaces as reference potentials. Furthermore, any attempts to study these enzymatic reactions by quantum mechanical approaches should be validated by examining the corresponding solution reactions and the present study should be helpful in such validation studies. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 44–53, 2000

The generalized Heitler–London theory for the H3 potential energy surface

A systematic perturbation theory has been developed to analyze the terms contributing to the H3 potential energy surface. Group theory is used to find the irreducible representations of the Hamiltonian matrix elements which then are decoupled to their simplest level. In the case of diatomic molecules, this approach leads naturally to the Generalized Heitler–London (GHL) theory derived previously [K. T. Tang and J. P. Toennies, J. Chem. Phys. 95, 5918 (1991)]. Many previous semi-empirical potential surfaces for the H3 triatomic system including the well known LEPS surface are examined in the light of the present results. In particular, the Cashion–Herschbach (or diatomics-in-molecules without overlap) surface is shown to encompass far more information than previously recognized. The new theory now contains all the terms needed for an exact perturbation calculation of the potential energy surface.

Theoretical studies of energy transfer and reaction in H+H2O and H+D2O collisions

We present the results of a quasiclassical trajectory study of vibration–rotation excitation and reaction in H+H2O(000) and H+D2O(000) collisions, including detailed comparisons with experiment. All calculations have used a semiempirical potential surface due to Schatz and Elgersma, and the H2O initial and final states were numerically determined by solving for the good action variables associated with vibrational motions. Our studies of collisional excitation emphasize comparisons with recent experiments by Lovejoy, Goldfarb, and Leone [J. Chem. Phys. 96, 7180 (1992)] in which fast hydrogen atoms produce vibrationally and rotationally excited water. As in the experiments, we find a propensity for the production of rotational states in which the rotational angular momentum vector is predominantly aligned perpendicular to the water molecule plane (c-axis excitation). This propensity is found for all excited vibrational states of H2O, but it is significantly stronger in the experiments [where only the (001) state was studied] than in the calculations. An analysis of trajectory motions indicates that the primary excitation mechanism for states which show the c-axis propensity involves a nearly planar collision in which the incoming H impulsively strikes one of the water hydrogens. Failed reactive collisions associated with either abstraction or exchange as well as reactive exchange collisions give the same propensity but they are not the dominant mechanism for producing aligned water. In studies of the reaction H+D2O→OD+HD, we analyze product vibrational and rotational state distributions in detail, making comparison with recent studies of Adelman, Filseth, and Zare [preceding paper, J. Chem. Phys. 98, 4636 (1993)] as well as earlier work. The product HD energy partitioning is found to be in excellent average agreement with experiment, with the HD receiving much more of the available energy than does OD. There are, however, differences in some of the HD rotational distributions, with the experiment showing a much stronger inverse correlation between HD rotational and vibrational excitation than is found in the calculations.

Algorithmic tools in the study of semiempirical potential surfaces

AbstractThe most efficient optimization methods implemented in the semiempirical package AMPAC are presented. They concern the minimization of the energy or of the gradient norm by either pseudo‐Newton or quadratic procedures, the search for transition states, and the intrinsic reaction coordinate in conjunction with variational transition‐state theories. Nonlocal methods such as simulated annealing are also introduced. © 1992 John Wiley & Sons, Inc.

Computation of cross sections for the F+H2(v=0,j=0) ? FH(v?j)+H reaction by the hyperspherical method

A quantum mechanical calculation of cross sections for the reaction F+H2(v=0,j=0) → FH(v′j′)+H has been performed on the T5A semiempirical potential surface using hyperspherical coordinates. State-to-state integral and differential cross sections converge rapidly with the number of components of the total angular momentum projection onto the axis of least inertia. Thev′=3 differential cross section has a forward peak whose magnitude increases with energy whereas thev′=2 differential cross section has a backward maximum, in qualitative agreement with cross-beam experiments. Thev′=2 andv′=3 rotational distributions are in rather good agreement with experiment, but not the vibrational branching ratios.

A three dimensional quantum reactive scattering study of the I+HI reaction and of the IHI− photodetachment spectrum

In this paper, we present the results of coupled channel hyperspherical reactive scattering calculations on the reaction I+HI→IH+I using a semiempirical potential surface. Only the J=0 partial wave is considered. The bimolecular reaction probability is found to exhibit two sharp resonant peaks at energies below threshold for direct reaction. The resonances are associated with transition state quantum numbers (ν1ν2ν3)=(100) and (200), and their energies are in excellent agreement with the result of L2 calculations due to Clary and Connor, and to Bowman and Gazdy. At higher energy the reaction is dominated by rotational threshold effects, and then below the HI(ν=1) energetic threshold, additional resonances are found which correspond to quantum numbers (002), (102), (202), and (302). Franck–Condon factors associated with photodetachment of IHI− have also been calculated, and these show mainly direct scattering threshold behavior at low energies (E<0.30 eV), with the (100) and (200) resonances contributing only slightly. Resonant behavior is dominant at higher energies (0.3–0.4 eV) where the (002) resonance especially contributes. Agreement of our calculated photodetachment spectra with experimental results due to Neumark and co-workers is good provided that an 0.08 eV energy shift is made in the calculated spectra. This shift is probably due to an incorrect energy barrier on the semiempirical surface.

Energy transfer in Ne and Xe collisions with CO 2 at 1 eV

A semiclassical collision model has been used to calculate differential cross sections for rotational and vibrational excitation of CO 2 colliding with Ne and Xe. For NeCO 2 a previously determined semi-empirical potential surface was used. Recent electron-gas data were used to determine the short-range XeCO 2 interaction.

Pressure broadening of the O2 microwave spectrum

The pressure broadened half-widths of the 60 GHz microwave spectrum in O2 have been calculated for low pressures where the lines do not overlap. Both self-broadening and foreign gas broadening by noble gases have been calculated using various semiempirical potential surfaces. Agreement with experimental results is quite good. Differences with various other theoretical calculations are discussed.

Semiempirical potential surfaces and dynamical considerations for collisions between alkali metals and molecular oxygen: Li+O2 and Na+O2

The intermediates in both the inelastic and reactive collisions of alkali metals with molecular oxygen are the M+O−2 ion pairs. We develop here analytic forms for the lowest energy diabatic potential energy surfaces of both A′ and A″ electronic symmetry for the Li+O−2 and Na+O2− systems. An exponential–rational approximant functional form, which is found to provide an excellent description of the ionic alkali monoxide potential curves, is adapted to the alkali dioxide ion pairs. The degree of polarization of the O−2 charge distribution is modeled from available theoretical data for the homologous LiF2 system. With only a few variable parameters it is possibile to fit extremely well those features of the M+O−2 surfaces which are presently known either from experiments or ab initio calculations. The topologies of the A′ and A″ surfaces are substantially dissimilar. The lower energy surface (A″) for both LiO2 and NaO2 possesses a pronounced minimum in isoceles triangular geometry, as expected from the matrix isolation experiments; whereas the A′ surface displays little variation with the MOO angle. The fitted ion pair surfaces are used to discuss certain expected features of the M+O2 collision dynamics. Also, we show how it may be possible to relate the coupling matrix elements for the MO2 ionic–covalent surface crossings to equivalent matrix elements for the alkali monoxide systems, which are significantly easier to determine.

Semi-empirical potential surfaces for electron transfer reactions: The Li + FH and Li + F 2 reactions

A new semi-empirical method for calculating potential energy surfaces of triatomic molecules, requiring knowledge of only ground state potentials of diatomic molecules has been developed. The method is formulated for the M + XY → MX + Y class of reactions, M being an alkali-atom, X a halogen atom and Y either a halogen or a hydrogen atom. The method has been used to obtain excited state potentials of LiF and HF and potential energy surfaces of LiF 2 and LiHF. The results agree well with ab-initio studies. The resulting potential surfaces are analytic and are thus well suited for classical trajectory studies. The formula obtained can be used to construct surfaces for the heavier MXY analogues, the results of which are reported elsewhere.

Semi-Empirical Potential Surfaces for Some Mixed Alkali Trimers

Semi-Empirical Potential Surfaces for Some Mixed Alkali Trimers

Three-dimensional quantum mechanical studies of the H+H2 reactive scattering

A three-dimensional quantum mechanical study is made of H+H2 reactive scattering. The differential and total cross sections as well as the S-matrix elements are obtained from the adiabatic distorted wave model and the Porter–Karplus semiempirical potential surface. With the initial molecule in the ground rotational state, the energy dependence, rotational state dependence, and other properties of the reaction probabilities and of the cross sections for transitions to all possible states of the product molecule are determined. The reactive scattering from the threshold to 0.5 eV is predominantly backward. The 0→0 rotational transition contributes only a small fraction to the total reactive cross section; however, most product molecules prefer rotational states that are considerably lower than the highest one allowed by energy conservation. The reaction probability is found to be a smoothly decreasing function of the total angular momentum of the system. These results are very similar to our previous results for the D+H2 reaction except the threshold energy for the H+H2 is higher and the magnitude of the cross section for the reaction of the D+H2 is larger. A systematic study of the effects of the Pauli exclusion principle on cross sections of the scattering of three identical particles shows that in order to obtain the ’’observable’’ cross sections, the unsymmetrized results of the H+H2 and D+D2 reactions have to be multiplied by various ’’strange’’ numerical factors. These observable cross sections are compared with three different sets of close coupling results on the same potential surface. Our results are in close agreement with those of Kuppermann and Schatz and are in substantial disagreement with those of Wolken and Karplus. Our results near the threshold and at 0.5 eV are similar to those of Elkowitz and Wyatt but there are significant differences in energy dependence in the intermediate region. The present results are also compared with the three-dimensional classical trajectory results. The most significant quantum effect is caused by the spin statistics. Dynamically, there are excellent qualitative and quantitative agreements in many respects between the quantum and classical results, although the present quantum cross sections rise above the classical values at incident energies greater than 0.4 eV.

Collisional deactivation of Br(4 2P1/2) by hydrogen isotopes

The quenching of electronically excited bromine atoms Br(4 2P1/2) upon collision with H2, HD, and D2 has been studied at 300 °K. The temporal profile of the Br(4 2P1/2) concentration was monitored by observation of the time-resolved attenuation of bromine resonance radiation at 153.2 nm. The probabilities of deactivation by the hydrogen isotopes are presented and compared to theoretical treatments based either upon long-range coupling via mulitpolar interactions or explicit treatment of the nonadiabatic crossing probabilities computed using semiempirical potential surfaces. These results are then examined with a view toward assessing the importance of near-resonant electronic–vibrational energy transfer in such an elementary system.

Angular distributions in the elastic scattering and rotational excitation of molecular hydrogen by atomic hydrogen

view Abstract Citations (24) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Angular distributions in the elastic scattering and rotational excitation of molecular hydrogen by atomic hydrogen. Chu, S. -I. ; Dalgarno, A. Abstract The effective close-coupling method of Rabitz is tested and used to calculate the angular distributions of the elastic and inelastic scattering of molecular hydrogen in collision with atomic hydrogen when rotational transitions may occur. The interaction potential adopted is the Porter-Karplus semi-empirical potential surface, which was joined smoothly to the correct long-range potentials. Explicit calculations are reported for the differential elastic and total inelastic cross sections in the energy range from 0.1 to 1.5 eV. Publication: The Astrophysical Journal Pub Date: August 1975 DOI: 10.1086/153731 Bibcode: 1975ApJ...199..637C Keywords: Angular Distribution; Atomic Collisions; Hydrogen; Interstellar Matter; Molecular Excitation; Scattering Cross Sections; Elastic Scattering; Graphs (Charts); Hydrogen Atoms; Inelastic Scattering; Quantum Mechanics; Tables (Data); Wave Functions; Astrophysics full text sources ADS |

Molecular beam kinetics: Exchange reactions of deuterium atoms with hydrogen halides

A crossed-beam study finds the reactions of D atoms with HCl, HBr, and HI give large yields of DCl, DBr, and DI, corresponding to reaction cross sections of the order 1–10 Å2. This demonstrates that the exceptionally small steric factors or transmission coefficients previously inferred from analysis of chain reaction mechanisms are low by several orders of magnitude. The reactively scattered deuterium halides recoil predominantly into the backward hemisphere with respect to the incident D atoms. In each case, the reaction exoergicity is ∼1 kcal/mole and the mean initial collision energy is 9 kcal/mole (with the D beam at 2800 °K, the hydrogen halide at 250 °K). The most probable final relative translational energy of the products is ≳4 kcal/mole for the HCl and HBr reactions and 7 kcal/mole for the HI reaction. The magnitude of the reaction cross sections and the predominant backward recoil and translational energy of the products are consistent with recent classical trajectory calculations based on semiempirical potential surfaces.

Theoretical Studies of H + H2 Rotationally Inelastic Scattering

Rotationally inelastic H,H2 scattering, without rearrangement, was studied quantum mechanically in three dimensions. A close-coupling technique was employed with a basis set consisting of unperturbed molecular functions. The resulting coupled differential equations were solved numerically by a technique recently developed by Gordon. The Porter-Karplus semi-empirical potential surface was used to represent the H3 system. Cross sections were calculated for relative kinetic energies of 0.05 to 0.50 eV. Various approximations were investigated and their effect on the inelastic cross sections were computed; they include variation of the number of terms in the expansion of the exact wavefunction, exclusion of high-order asymmetry contributions to the potential surface, treating the H2 target as a rigid rotor fixed at some specified internuclear distance, and modifying the long-range behavior of the Porter-Karplus surface. Differential cross sections in the helicity representation were also computed for various energies.

Internal Energy of Reaction Products by Velocity Analysis. III. Center-of-Mass Angular Distribution and Product Excitation Function for K+Br2

A computer analysis of the product (KBr) velocity distribution experiments previously reported for the crossed molecular beam reaction K+Br2 is presented. The shape of the angular distribution of KBr in the center-of-mass (c.m.) system and the product internal energy (excitation) distribution function are evaluated, subject to the assumption of no coupling between the two distributions. In agreement with the conclusions of Herschbach, Datz, and their co-workers, the differential reaction cross section in the c.m. system is strongly forward peaked, characteristic of a ``stripping'' reaction. The maximum in the internal excitation function occurs near 100% of the total available energy. The results are in fair accord with the predictions of Karplus, Polanyi, and their co-workers, based on Monte Carlo trajectory analyses employing semiempirical potential surfaces.