Interfacing Electronic Structure Theory with Dynamics

Multi-state Energy Landscape for Photoreaction of Stilbene and Dimethyl-stilbene

We have recently developed the reaction space projector (ReSPer) method, which constructs a reduced-dimensionality reaction space uniquely determined from reference reaction paths for a polyatomic molecular system and projects classical trajectories into the same reaction space. In this paper, we extend ReSPer to the analysis of photoreaction dynamics and relaxation processes of stilbene and present the concept of a "multi-state energy landscape," incorporating the ground- and excited-state reaction subspaces. The multi-state energy landscape successfully explains the previously established photoreaction processes of cis-stilbene, such as the cis-trans photoisomerization and photocyclization. In addition, we discuss the difference in the excited-state reaction dynamics between stilbene and 1,1'-dimethyl stilbene based on a common reaction subspace determined from the framework part of reference structures with different number of atoms. This approach allows us to target any molecule with a common framework, greatly expanding the applicability of the ReSPer analysis. The multi-state energy landscape provides fruitful insight into photochemical reactions, exploring the excited- and ground-state potential energy surfaces, as well as comprehensive reaction processes with nonradiative transitions between adiabatic states, within the stage of a reduced-dimensionality reaction space.

Reaction Space Projector (ReSPer) for Visualizing Dynamic Reaction Routes Based on Reduced-Dimension Space

To analyze chemical reaction dynamics based on a reaction path network, we have developed the "Reaction Space Projector" (ReSPer) method with the aid of the dimensionality reduction method. This program has two functions: the construction of a reduced-dimensionality reaction space from a molecular structure dataset, and the projection of dynamic trajectories into the low-dimensional reaction space. In this paper, we apply ReSPer to isomerization and bifurcation reactions of the Au₅ cluster and succeed in analyzing dynamic reaction routes involved in multiple elementary reaction processes, constructing complicated networks (called "closed islands") of nuclear permutation-inversion (NPI) isomerization reactions, and elucidating dynamic behaviors in bifurcation reactions with reference to bundles of trajectories. Interestingly, in the second application, we find a correspondence between the contribution ratios in the ability to visualize and the symmetry of the morphology of closed islands. In addition, the third application suggests the existence of boundaries that determine the selectivity in bifurcation reactions, which was discussed in the phase space. The ReSPer program is a versatile and robust tool to clarify dynamic reaction mechanisms based on the reduced-dimensionality reaction space without prior knowledge of target reactions.

Ab Initio Surface-Hopping Simulation of Femtosecond Transient-Absorption Pump-Probe Signals of Nonadiabatic Excited-State Dynamics Using the Doorway-Window Representation

An ab initio theoretical framework for the simulation of femtosecond time-resolved transient absorption (TA) pump-probe (PP) spectra with quasi-classical trajectories is presented. The simulations are based on the classical approximation to the doorway-window (DW) representation of third-order four-wave-mixing signals. The DW formula accounts for the finite duration and spectral shape of the pump and probe pulses. In the classical DW formalism, classical trajectories are stochastically sampled from a positive definite doorway distribution, and the signals are evaluated by averaging over a positive definite window distribution. Nonadiabatic excited-state dynamics is described by a stochastic surface-hopping algorithm. The method has been implemented for the pyrazine molecule with the second-order algebraic-diagrammatic construction (ADC(2)) ab initio electronic-structure method. The methodology is illustrated by ab initio simulations of the ground-state bleach, stimulated emission, and excited-state absorption contributions to the TA PP spectrum of gas-phase pyrazine.

Trajectory on-the-fly molecular dynamics approach to tunneling splitting in the electronic excited state: A case of tropolone

The semiclassical tunneling method is applied to evaluate the tunneling splitting of tropolone due to the intramolecular proton transfer in the electronic excited state, first time, in a framework of the trajectory on-the-fly molecular dynamics (TOF-MD) approach. To prevent unphysical zero-point vibrational energy transfer among the normal modes of vibration, quantum zero-point vibrational energies are assigned only to the vibrational modes related to intramolecular proton transfer, whereas the remaining modes are treated as bath modes. Practical ways to determine the tunnel-initiating points and tunneling path are introduced. It is shown that the tunneling splitting decreases as the bath-mode energy increases. The experimental tunneling splitting value is well reproduced by the present TOF-MD approach based on the Wentzel-Kramers-Brillouin (WKB) approximation.

Ab initio surface hopping excited-state molecular dynamics approach on the basis of spin-orbit coupled states: An application to the A-band photodissociation of CH3 I

Ab initio molecular dynamics approach has been extended to multi-state dynamics on the basis of the spin-orbit coupled electronic states that are obtained through diagonalization of the spin-orbit coupling matrix with the multi-state second-order multireference perturbation theory energies in diagonal elements and the spin-orbit coupling terms at the state-averaged complete active space self-consistent field level in off-diagonal elements. Nonadiabatic transitions over the spin-orbit coupled states were taken into account explicitly by a surface hopping scheme with utilizing the nonadiabatic coupling terms calculated by numerical differentiation of the spin-orbit coupled wavefunctions and analytical nonadiabatic coupling terms. The present method was applied to the A-band photodissociation of methyl iodide, CH₃ I + hv → CH₃ + I (² P_3/2 )/I* (² P_1/2 ), for which a pioneering theoretical work was reported by Amatatsu, Yabushita, and Morokuma. The present results reproduced well the experimental branching ratio and energy distributions in the dissociative products. © 2018 Wiley Periodicals, Inc.

Analyses of trajectory on-the-fly based on the global reaction route map

A methodology to analyze a trajectory on-the-fly (TOF) based on a global reaction route map consisting of intrinsic reaction coordinate (IRC) pathways is proposed. By using the distance functions in the configurational space, the location of each point on the trajectories is detected, providing a dynamical picture that the molecular system goes over several minima and transition states in the reaction path network. In its application to structural transformations of an Au₅ cluster, a variety of reaction routes are obtained, and the hopping from one IRC to another IRC (IRC-jump) is analyzed. The branching of trajectories over many minima on the potential energy surface via valley-ridge transition points is also discussed.

Roaming as the dominant mechanism for molecular products in the photodissociation of large aliphatic aldehydes

Photodissociation of isobutyraldehyde (C₃H₇CHO) at 248 nm is investigated using time-resolved Fourier-transform infrared emission spectroscopy to demonstrate the growing importance of the roaming pathway with increasing molecular size of aliphatic aldehydes.

Ab initio and semi-empirical Molecular Dynamics simulations of chemical reactions in isolated molecules and in clusters

Recent progress in “on-the-fly” trajectory simulations of molecular reactions, using different electronic structure methods is discussed, with analysis of the insights that such calculations can provide and of the strengths and limitations of the algorithms available.

Ab initio direct classical trajectory investigation on the SN2 reaction of F- with NH2F: nonstatistical central barrier recrossing dynamics

The bimolecular nucleophilic substitution (S(N)2) reaction of F(a)(-) with NH(2)F(b) has been investigated with the ab initio direct classical trajectory method. According to our trajectory calculations, a dynamic behavior of nonstatistical central barrier recrossing is revealed. Among the 64 trajectories calculated in this work, 45 trajectories follow the dynamic reaction pathways as assumed by statistical theory and other 19 trajectories with central barrier recrossings are nonstatistical. For the nonstatistical trajectories, the central barrier recrossings may originate from the inefficient kinetic energy transfer from the intramolecular modes of the NH(2)F(a) moiety in the dynamic F(b)(-)…H-NH-F(a) complex to the intermolecular modes of the dynamic F(b)(-)…H-NH-F(a) complex on the exit-channel potential energy surface. With respect to the dynamic behavior of the nonstatistical central barrier recrossing, the statistical theories such as the Rice-Ramsperger-Kassel-Marcus and transition state theories without further corrections cannot be used to model the reaction kinetics for this S(N)2 reaction.

CONSTRUCTION OF A GLOBAL POTENTIAL ENERGY SURFACE FROM NOVEL AB INITIO MOLECULAR DYNAMICS FOR THE O(3P) + C3H3 REACTION

We present a global potential energy surface (PES) for the 2 A state of the O (3 P ) + C 3 H 3 radical reaction. The global PES is constructed mainly using direct ab initio molecular dynamics and further sampling is done using the Diffusion Monte Carlo method. The potential is fully invariant with respect to permutational symmetry of like atoms. Special techniques, based on invariant theory of finite groups, have been used to develop basis functions for fitting that display this symmetry. The resultant potential energy surface shows multiple reaction paths with six different product channels. The products of the reactions are CO + C 2 H 3 radicals H + C 3 H 2 O radicals (with two isomers, propynal and propa-1,2-dien-1-one) and OH + C 3 H 2 radicals (with three isomers, vinylidenecarbene, propargylene and cyclopropenylidene). Energies of the PES are in excellent agreement with ab initio energies for each stationary point, the reactants and the products. Most stationary points are fitted at the sub Kcal/mol level. The global potential surface represents all the stationary points and six different product channels correctly. Preliminary dynamics calculations show abstraction and insertion mechanisms for the OH + vinylidenecarbene channel and the H + propynal channel, respectively.

Conformational transitions of glycine induced by vibrational excitation of the O-H stretch

Vibrational energy flow and conformational transitions following excitation of the OH stretching mode of the most stable conformer of glycine are studied by classical trajectories. "On the fly" simulations with the PM3 semiempirical electronic structure method for the potential surface are used. Initial conditions are selected to correspond to the ν=1 excitation of the OH stretch. The main findings are: (1) An an equilibrium-like ratio is established between the populations of the 3 lowest-lying conformers after about 10 picoseconds. (2) There is a high probability throughout the 150 ps of the simulations for finding the molecule in geometries far from the equilibrium structures of the lowest-energy conformers. (3) Energy from the initial excited OH (ν=1) stretch flows preferentially to 5 other vibrational modes, including the bending motion of the H atom. (4) RRK theory yields conformational transition rates that deviate substantially from the classical trajectory results. Possible implication of these results for vibrational energy flow and conformational transitions in small biological molecules are discussed.

Systematic fragmentation method and the effective fragment potential: an efficient method for capturing molecular energies

The systematic fragmentation method fragments a large molecular system into smaller pieces, in such a way as to greatly reduce the computational cost while retaining nearly the accuracy of the parent ab initio electronic structure method. In order to attain the desired (sub-kcal/mol) accuracy, one must properly account for the nonbonded interactions between the separated fragments. Since, for a large molecular species, there can be a great many fragments and therefore a great many nonbonded interactions, computations of the nonbonded interactions can be very time-consuming. The present work explores the efficacy of employing the effective fragment potential (EFP) method to obtain the nonbonded interactions since the EFP method has been shown previously to capture nonbonded interactions with an accuracy that is often comparable to that of second-order perturbation theory. It is demonstrated that for nonbonded interactions that are not high on the repulsive wall (generally >2.7 A), the EFP method appears to be a viable approach for evaluating the nonbonded interactions. The efficacy of the EFP method for this purpose is illustrated by comparing the method to ab initio methods for small water clusters, the ZOVGAS molecule, retinal, and the alpha-helix. Using SFM with EFP for nonbonded interactions yields an error of 0.2 kcal/mol for the retinal cis-trans isomerization and a mean error of 1.0 kcal/mol for the isomerization energies of five small (120-170 atoms) alpha-helices.

Chlorine activation indoors and outdoors via surface-mediated reactions of nitrogen oxides with hydrogen chloride

Gaseous HCl generated from a variety of sources is ubiquitous in both outdoor and indoor air. Oxides of nitrogen (NO(y)) are also globally distributed, because NO formed in combustion processes is oxidized to NO(2), HNO(3), N(2)O(5) and a variety of other nitrogen oxides during transport. Deposition of HCl and NO(y) onto surfaces is commonly regarded as providing permanent removal mechanisms. However, we show here a new surface-mediated coupling of nitrogen oxide and halogen activation cycles in which uptake of gaseous NO(2) or N(2)O(5) on solid substrates generates adsorbed intermediates that react with HCl to generate gaseous nitrosyl chloride (ClNO) and nitryl chloride (ClNO(2)), respectively. These are potentially harmful gases that photolyze to form highly reactive chlorine atoms. The reactions are shown both experimentally and theoretically to be enhanced by water, a surprising result given the availability of competing hydrolysis reaction pathways. Airshed modeling incorporating HCl generated from sea salt shows that in coastal urban regions, this heterogeneous chemistry increases surface-level ozone, a criteria air pollutant, greenhouse gas and source of atmospheric oxidants. In addition, it may contribute to recently measured high levels of ClNO(2) in the polluted coastal marine boundary layer. This work also suggests the potential for chlorine atom chemistry to occur indoors where significant concentrations of oxides of nitrogen and HCl coexist.

Classical Trajectory Simulations of Photoionization Dynamics of Tryptophan: Intramolecular Energy Flow, Hydrogen-Transfer Processes and Conformational Transitions

One-photon and two-photon ionization dynamics of tryptophan is studied by classical trajectory simulations using the semiempirical parametric method number 3 (PM3) potential surface in "on the fly" calculations. The tryptophan conformer is assumed to be in the vibrational ground state prior to ionization. Initial conditions for the trajectories are weighted according to the Wigner distribution function computed for that state. Vertical ionization in the spirit of the classical Franck-Condon principle is assumed. For the two-photon ionization process the ionization is assumed to go resonantively through the first excited state. Most trajectories are computed, and the analysis is carried out for the first 10 ps. A range of interesting effects are observed. The main findings are as follows: (1) Multiple conformational transitions are observed in most of the trajectories within the ultrafast duration of 10 ps. (2) Hydrogen transfer from the carboxyl group to the amino group and back has been observed. A zwitterion is formed as a transient state. (3) Two new isomers are formed during the dynamics, which have apparently not been previously observed. (4) Fast energy flow between the ring modes and the amino acid backbone is observed for both one- and two-photon ionization. However, the effective vibrational temperatures only approach the same value after 90 ps. The conformation transition dynamics, the proton-transfer processes and the vibrational energy flow are discussed and analyzed.

Advances in methods and algorithms in a modern quantum chemistry program package

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Different chemical dynamics for different conformers of biological molecules: Photoionization of glycine

Single-photon ionization dynamics of two conformers of glycine is studied by classical trajectory simulations using the semiempirical PM3 potential surface in "on the fly" calculations. Initial conditions for the trajectories are weighted according to the Wigner distribution function computed for the initial vibrational ground state. Vertical ionization in the spirit of the classical Franck-Condon principle is assumed. The dynamics of the two conformers are compared during the first 10 ps. The comparison shows very different dynamical behavior for the two conformers. In particular, the chemical fragmentation pathways differ in part. Also, one of the conformers gives much higher rates of conformational transitions, while the other conformer gives larger chemical fragmentation yields. The example shows significantly different chemical dynamics for two conformers close in energy and separated by a low barrier.

Photoionization dynamics of glycine adsorbed on a silicon cluster: “On-the-fly” simulations

Dynamics of glycine chemisorbed on the surface of a silicon cluster is studied for a process that involves single-photon ionization, followed by recombination with the electron after a selected time delay. The process is studied by "on-the-fly" molecular dynamics simulations, using the semiempirical parametric method number 3 (PM3) potential energy surface. The system is taken to be in the ground state prior to photoionization, and time delays from 5 to 50 fs before the recombination are considered. The time evolution is computed over 10 ps. The main findings are (1) the positive charge after ionization is initially mostly distributed on the silicon cluster. (2) After ionization the major structural changes are on the silicon cluster. These include Si-Si bond breaking and formation and hydrogen transfer between different silicon atoms. (3) The transient ionization event gives rise to dynamical behavior that depends sensitively on the ion state lifetime. Subsequent to 45 fs evolution in the charged state, the glycine molecule starts to rotate on the silicon cluster. Implications of the results to various processes that are induced by transient transition to a charged state are discussed. These include inelastic tunneling in molecular devices, photochemistry on conducting surfaces, and electron-molecule scattering.

Ab initiovibrational state calculations with a quartic force field: Applications to H2CO, C2H4, CH3OH, CH3CCH, and C6H6

For polyatomic molecules, n-mode coupling representations of the quartic force field (nMR-QFF) are presented, which include terms up to n normal coordinate couplings in a fourth-order polynomial potential energy function. The computational scheme to evaluate third-and fourth-order derivatives by finite differentiations of the energy is fully described. The code to generate the nMR-QFF has been implemented into GAMESS program package and interfaced with the vibrational self-consistent field (VSCF) and correlation corrected VSCF (cc-VSCF) methods. As a demonstration, fundamental frequencies have been calculated by the cc-VSCF method based on 2MR-QFF for formaldehyde, ethylene, methanol, propyne, and benzene. The applications show that 2MR-QFF is a highly accurate potential energy function, with errors of 1.0-1.9% relative to the experimental value in fundamental frequencies. This approach will help quantitative evaluations of vibrational energies of a general molecule with a reasonable computational cost.

On-the-flyab initiotrajectory calculations of the dynamics of Cl atom reactions with methane, ethane and methanol

The dynamics of Cl atom reactions with methane, ethane, and methanol have been studied by calculation of quasi-classical trajectories, with computation of potential energies and gradients only at the geometries through which the trajectories pass. Trajectories were started from the transition state, with 2 kcal mol(-1) of energy given to the mode with an imaginary frequency (representing the reaction coordinate at the transition state) and inclusion of zero-point energy in some or all of the remaining vibrational modes. The trajectories were propagated as far as separated products, with the majority of potential energy calculations performed at the HF/6-31G level of theory. The rotational quantum state population distributions of the HCl products from the reactions of Cl atoms with methane, ethane and methanol peaked at J'=1, 2, and 6, respectively. The calculations thereby exhibit somewhat greater rotational excitation than is found experimentally, but correctly describe the trend of increasing HCl product rotation for the three respective reactions. In agreement with previous observations, only 4% of the energy available to the products of the reaction of Cl atoms with methane was channeled into CH3 radical internal energy, and 1% into HCl rotation, with 92% ending up as translational energy. For the reaction of Cl atoms with ethane and with methanol, the corresponding values for radical internal energy, HCl rotation and product translation are 21, 3, and 78%, and 46, 13, and 42%, respectively. For the latter two reactions, the radical internal energy is mostly accounted for by rotational motion. The clear increase in rotational excitation of the HCl products from the Cl atom reaction with methanol is explained in terms of a dipole-dipole interaction between the departing polar fragments. A smaller set of more computationally expensive trajectory calculations using potentials and gradients from the MP2/6-311G(d,p) level of theory were performed for reactions of Cl atoms with methanol, and give results in better agreement with experimentally measured HCl rotational excitation, consistent with the model of dipole-induced product rotation because the MP2/6-311G(d,p) calculations give smaller dipole moments for both products than the HF/6-31G calculations. The calculated angles between the rotational angular momentum vectors and recoil velocities of the radical peak sharply at 90 degrees for the reactions of Cl atoms with ethane and methanol, but exhibit a much broader distribution for reaction with methane.

Exploring potential energy surfaces for chemical reactions: an overview of some practical methods

Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.

A single transition state serves two mechanisms: an ab initio classical trajectory study of the electron transfer and substitution mechanisms in reactions of ketyl radical anions with alkyl halides

Molecular dynamics has been used to investigate the reaction of a series of ketyl anion radicals and alkyl halides, CH2O(*)(-) + CH3X (X = F, Cl, Br) and NCCHO(*)(-) + CH3Cl. In addition to a floppy outer-sphere transition state which leads directly to ET products, there is a strongly bound transition state that yields both electron transfer (ET) and C-alkylated (SUB(C)) products. This common transition state has significant C-- C bonding and gives ET and SUB(C) products via a bifurcation on a single potential energy surface. Branching ratios have been estimated from ab initio classical trajectory calculations. The SUB(C) products are favored for transition states with short C--C bonds and ET for long C--C bonds. ET reactivity can be observed even at short distances of r(C)(-)(C) = ca. 2.4 A as in the transition state for the reaction NCCHO(*)(-) + CH3Cl. Therefore, the ET/SUB(C) reactivity is entangled over a significant range of the C--C distance. The mechanistic significance of the molecular dynamics study is discussed.