One-dimensional Potential Energy Surface Research Articles

Electronic Structure Methods for Simulating Flavin's Spectroscopy and Photophysics: Comparison of Multi-reference, TD-DFT, and Single-Reference Wave Function Methods.

The use of flavins and flavoproteins in photocatalytic, sensing, and biotechnological applications has led to a growing interest in computationally modeling the excited-state electronic structure and photophysics of flavin. However, there is limited consensus regarding which computational methods are appropriate for modeling flavin's photophysics. We compare the energies of low-lying excited states of flavin computed with time-dependent density functional theory (TD-DFT), equation-of-motion coupled cluster (EOM-EE-CCSD), scaled opposite-spin configuration interaction [SOS-CIS(D)], multiconfiguration pair-density functional theory (MC-PDFT), and several multireference perturbation theory (MR-PT2) methods. In the first part, we focus on excitation energies of the first singlet excited state (S1) of five different redox and protonation states of flavin, with the goal of finding a suitable active space for MR-PT2 calculations. In the second part, we construct two sets of one-dimensional potential energy surfaces connecting the S0 and S1 equilibrium geometries (S0-S1 path) and the S1 (π,π*) and S2 (n,π*) equilibrium geometries (S1-S2 path). The first path therefore follows a Franck-Condon active mode of flavin while the second path maps crossings points between low-lying singlet and triplet states in flavin. We discuss the similarities and differences in the TD-DFT, EOM-EE-CCSD, SOS-CIS(D), MC-PDFT and MR-PT2 energy profiles along these paths. We find that (TD-)DFT methods are suitable for applications such as simulating the spectra of flavins but are inconsistent with several other methods when used for some geometry optimizations and when describing the energetics of dark (n,π*) states. MR-PT2 methods show promise for the simulation of flavin's low-lying excited states, but the selection of orbitals for the active space and the number of roots used for state averaging must be done carefully to avoid artifacts. Some properties, such as the intersystem crossing geometry and energy between the S1 (π,π*) and T2 (n,π*) states, may require additional benchmarking before they can be determined quantitatively.

High-resolution infrared spectroscopy of jet cooled cyclobutyl in the α-CH stretch region: large-amplitude puckering dynamics in a 4-membered ring radical.

Gas-phase cyclobutyl radical (c-C4H7) is generated at a rotational temperature of Trot = 26(1) K in a slit-jet discharge mixture of 70% Ne/30% He and 0.5-0.6% cyclobromobutane (c-C4H7Br). A fully rovibrationally resolved absorption spectrum of the α-CH stretch fundamental band between 3062.9 cm-1 to 3075.7 cm-1 is obtained and analyzed, yielding first precision structural and dynamical information for this novel radical species. The α-CH stretch band origin is determined to be 3068.7887(4) cm-1, which implies only a modest (≈0.8 cm-1) blue shift from rotationally unresolved infrared spectroscopic studies of cyclobutyl radicals in liquid He droplets [A. R. Brown, P. R. Franke and G. E. Douberly, J. Phys. Chem. A, 2017, 121, 7576-7587]. Of particular dynamical interest, a one-dimensional potential energy surface with respect to the ring puckering coordinate is computed at CCSD(T)/ANO2 level of theory and reveals a double minimum Cs puckered geometry, separated by an exceedingly shallow planar C2v transition state barrier (Ebarr ≈ 1 cm-1). Numerical solutions on this double minimum potential yield a zero-point energy for the ground state (Ezero-point ≈ 27 cm-1) greatly in excess of the interconversion barrier. This is indicative of highly delocalized, large amplitude motion of the four-membered ring structure, for which proper vibrationally averaging of the moment of inertia tensor reproduces the experimentally determined inertial defect remarkably well. Finally, intensity alternation in the experimental spectrum due to nuclear spin statistics upon exchange of three indistinguishable H atom pairs (IH = ½) matches Ka + Kc = even : odd = 36 : 28 predictions, implying that the unpaired electron in the radical center lies in an out-of-plane pπ orbital. Thus, high-resolution infrared spectroscopy provides first experimental confirmation of a shallow double minimum ring puckering potential with a highly delocalized ground state wave function peaked at a planar C2v transition state geometry consistent with a cyclobutyl π radical.

OntoPESScan: An Ontology for Potential Energy Surface Scans.

In this work, a new OntoPESScan ontology is developed for the semantic representation of one-dimensional potential energy surface (PES) scans, a central concept in computational chemistry. This ontology is developed in line with knowledge graph principles and The World Avatar (TWA) project. OntoPESScan is linked to other ontologies for chemistry in TWA, including OntoSpecies, which helps uniquely identify species along the PES and access their properties, and OntoCompChem, which allows the association of potential energy surfaces with quantum chemical calculations and the concepts used to derive them. A force-field fitting agent is also developed that makes use of the information in the OntoPESScan ontology to fit force fields to reactive surfaces of interest on the fly by making use of the empirical valence bond methodology. This agent is demonstrated to successfully parametrize two cases, namely, a PES scan on ethanol and a PES scan on a localized π-radical PAH hypothesized to play a role in soot formation during combustion. OntoPESScan is an extension to the capabilities of TWA and, in conjunction with potential further ontological support for molecular dynamics and reactions, will further progress toward an open, continuous, and self-growing knowledge graph for chemistry.

Program Synthesis of Sparse Algorithms for Wave Function and Energy Prediction in Grid-Based Quantum Simulations.

We have recently shown how program synthesis (PS), or the concept of “self-writing code”, can generate novel algorithms that solve the vibrational Schrödinger equation, providing approximations to the allowed wave functions for bound, one-dimensional (1-D) potential energy surfaces (PESs). The resulting algorithms use a grid-based representation of the underlying wave function ψ(x) and PES V(x), providing codes which represent approximations to standard discrete variable representation (DVR) methods. In this Article, we show how this inductive PS strategy can be improved and modified to enable prediction of both vibrational wave functions and energy eigenvalues of representative model PESs (both 1-D and multidimensional). We show that PS can generate algorithms that offer some improvements in energy eigenvalue accuracy over standard DVR schemes; however, we also demonstrate that PS can identify accurate numerical methods that exhibit desirable computational features, such as employing very sparse (tridiagonal) matrices. The resulting PS-generated algorithms are initially developed and tested for 1-D vibrational eigenproblems, before solution of multidimensional problems is demonstrated; we find that our new PS-generated algorithms can reduce calculation times for grid-based eigenvector computation by an order of magnitude or more. More generally, with further development and optimization, we anticipate that PS-generated algorithms based on effective Hamiltonian approximations, such as those proposed here, could be useful in direct simulations of quantum dynamics via wave function propagation and evaluation of molecular electronic structure.

Molecular structure and quantum descriptors of cefradine by using vibrational spectroscopy (IR and Raman), NBO, AIM, chemical reactivity and molecular docking.

This study aims to investigate the structural and vibrational features of cefradine (the first-generation cephalosporin antibiotic) based on spectroscopic experiments and theoretical quantum chemical approach. The fundamental structural aspects of cefradine have been examined based on optimized geometry, spectroscopic behavior, intermolecular interaction, chemical reactivity, intramolecular hydrogen bonding, and molecular docking analysis. The most stable minimum energy conformer of the title molecule was identified by performing a one-dimensional potential energy surface scan along the rotational bonds at B3LYP/6-311++G (d,p) level of theory. The vibrational features of the molecule and information about the coupled modes were predicted. The chemical reactivity and stability of all the possible conformers of cefradine were estimated based on the HOMO-LUMO energy gap and NBO approach. The overall picture of accumulation of charges on individual atoms of the molecule was predicted by molecular electrostatic potential (MEP) surface map which in turn identifies the nucleophilic and electrophilic region or sites. The quantitative analysis of electrophilicity and nucleophilicity indices was done by Hirshfeld charge analysis and it was found that N8 atom is the most prominent site for nucleophilic attack while C14 atom is feasible for electrophilic attack. QTAIM study has also been performed to investigate the nature and strength of hydrogen bonding interactions. Besides, molecular docking studies were performed to examine the active binding residues of the target.

Computational evaluation on molecular stability, reactivity, and drug potential of frovatriptan from DFT and molecular docking approach

Molecular stability, fundamental chemical reactive sites, global reactivity descriptors in frovatriptan molecule have been investigated by using computational evaluation and molecular docking approach. The density functional theory has been employed with standard functional B3LYP/6–311++G(d,p). The possible minimum energy structure has been predicted by implementing one-dimensional potential energy surface (PES) scan. The charge delocalization for stability of the molecule with natural bond orbital (NBO) analysis and molecular electrostatic potential (MEP) surface analysis to observe the active region for further chemical reaction with surrounding species have been performed. The chemical reactivity and hardness of the molecule in terms of HOMO-LUMO energy gap (ΔEL-H) have been implemented in terms of reactivity parameters. The potential use of frovatriptan as non-linear optical (NLO) material and its thermodynamical studies have also been performed. Moreover, the molecular docking with a predicted target has been performed to check the binding interaction as well as sites of the molecule.

First-principles description of intra-chain exciton migration in an oligo(para-phenylene vinylene) chain. I. Generalized Frenkel-Holstein Hamiltonian.

A generalized Frenkel-Holstein Hamiltonian is constructed to describe exciton migration in oligo(para-phenylene vinylene) chains, based on excited state electronic structure data for an oligomer comprising 20 monomer units (OPV-20). Time-dependent density functional theory calculations using the ωB97XD hybrid functional are employed in conjunction with a transition density analysis to study the low-lying singlet excitations and demonstrate that these can be characterized to a good approximation as a Frenkel exciton manifold. Based on these findings, we employ the analytic mapping procedure of Binder et al. [J. Chem. Phys. 141, 014101 (2014)] to translate one-dimensional (1D) and two-dimensional (2D) potential energy surface (PES) scans to a fully anharmonic, generalized Frenkel-Holstein (FH) Hamiltonian. A 1D PES scan is carried out for intra-ring quinoid distortion modes, while 2D PES scans are performed for the anharmonically coupled inter-monomer torsional and vinylene bridge bond length alternation modes. The kinetic energy is constructed in curvilinear coordinates by an exact numerical procedure, using the TNUM Fortran code. As a result, a fully molecular-based, generalized FH Hamiltonian is obtained, which is subsequently employed for quantum exciton dynamics simulations, as shown in Paper II [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)].

Vibrational spectroscopic, NBO, AIM, and multiwfn study of tectorigenin: A DFT approach

Tectorigenin (5,7-dihydroxy-3-(4-hydroxyphenyl)-6-methoxy-4H-chromen-4-one), a plant isoflavonoid, is a potential bioactive compound having antioxidant, anti-inflammatory, anti-osteoarthritis, anti-microbiotic, and antiplatelet activity. A combined experimental and theoretical approach was used to investigate the structural properties of the title compound. The optimized structure was obtained using B3LYP with 6–311++G(d,p) basis set. Two stable structural motifs in addition to the initially optimized form were obtained by the one-dimensional potential energy surface scan. The calculated 1H and 13C nuclear magnetic resonance spectra revealed good agreement with the available experimental data. Stability of the structure has been predicted by natural bond orbital analysis, which also confirmed the presence of lone pair and bonding to antibonding orbital interactions in the molecule. The reactive sites of the molecule were predicted using the molecular electrostatic potential surface. The weak and strong hydrogen bonds between non bonded atoms of the molecule have been analyzed by the quantum theory of atom in molecule. The reduced density gradient (RDG) and iso-surface defining long-range forces such as van der Waal and steric effect have been plotted and explained using multiwave function (Multiwfn) program. The vibrational assignment and interpretation of the spectra (FT-IR and FT-Raman) have been performed with the potential energy distribution (PED) analysis.

Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems

Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and shells, as well as molecular reconfigurations in chemical reactions. The criteria and routes of escape in one-degree of freedom systems have been well studied theoretically with reasonable agreement with experiment. The trajectory can only transit from the hilltop of the one-dimensional potential energy surface. The situation becomes more complicated when the system has higher degrees of freedom since the system state has multiple routes to escape through an equilibrium of saddle-type, specifically, an index-1 saddle. This paper summarizes the geometry of escape across a saddle in some widely known physical systems with two degrees of freedom and establishes the criteria of escape providing both a methodology and results under the conceptual framework known as tube dynamics. These problems are classified into two categories based on whether the saddle projection and focus projection in the symplectic eigenspace are coupled or uncoupled when damping and/or gyroscopic effects are considered. For simplicity, only the linearized system around the saddle points is analyzed, but the results generalize to the nonlinear system. We define a transition region, Th, as the region of initial conditions of a given initial energy h which transit from one side of a saddle to the other. We find that in conservative systems, the boundary of the transition region, ∂Th, is a cylinder, while in dissipative systems, ∂Th is an ellipsoid.

Structure and vibrations of 2-fluoro-N-methylaniline in the S0, S1 and D0 states: REMPI and MATI spectroscopy and theoretical calculations

Theoretical calculations predicted that there are only two stable conformers, trans and cis, for 2-fluoro-N-methylaniline (2FNMA) in the S0, S1 and D0 states. Compared to the cis conformer, the trans one is more stable, and has a population more than 99% at room temperature. The optimized molecular skeleton of trans and cis 2FNMA are both non-planar in the S0 state, but planar in the S1 and D0 states. The one-dimensional potential energy surface of 2FNMA in the S0 state is obtained. The Resonance-enhanced two-photon ionization (R2PI) and Mass-analyzed threshold ionization (MATI) spectra of trans 2FNMA are obtained. The first electronic excitation energy (E1) and the adiabatic ionization energy (IE) of trans 2FNMA are determined. The substitution effect on the molecular structures, transition energies and vibrations of 2FNMA are discussed.

Evaluation of one-dimensional potential energy surfaces for prediction of spectroscopic properties of hydrogen bonds in linear bonded complexes.

This work evaluated the reliability of the one-dimensional potential energy surface for calculating the spectroscopic properties (rovibrational constants and rotational line energies) of hydrogen bonds in linear bonded complexes by comparing theoretical results with the corresponding experimental results. For this purpose, two hydrogen bonded complexes were selected: the HCN···HCN homodimer and the HCN···HF heterodimer. The one-dimensional potential energy surfaces related to the hydrogen bonds in these complexes were calculated using different computational methods and basis sets. The calculated potential curve of each complex was fitted to an analytical one-dimensional potential function to obtain the potential parameters. The obtained analytical potential function of each complex was used in a two-particle Schrödinger equation to obtain the rovibrational energy levels of the hydrogen bond. Using the calculated rovibrational levels, the rovibrational spectra and constants of each complex were calculated and compared with experimental data available from the literature. Compared with experimental data, the calculated one-dimensional potential energy surface at the QCISD/aug-cc-pVDZ level of theory was found to predict the spectroscopic properties of hydrogen bonds better than the potential curves obtained using other computational methods, especially for the HCN···HCN homodimer complex. Generally, the results obtained for the HCN···HCN homodimer complex were closer to experimental data than those obtained for the HCN···HF heterodimer complex. The investigation performed in this work showed that the one-dimensional potential curve related to the hydrogen bond between two linear molecules can be used to predict the spectroscopic constants of hydrogen bonds. Graphical abstract Potential energy curves of HCN···HCN and HCN···HF complexes calculated at the different computational levels.

Analytic ab initio-based molecular interaction potential for the BrO⋅H2O complex.

Radical halogen oxide species play important roles within atmospheric processes, specifically those responsible for the removal of O3. To facilitate future investigations on this family of compounds, RCCSD(T)/aug-cc-pVQZ-level electronic structure calculations were employed to generate individual-molecule optimized geometries, as well as to determine the global minimum energy structure for the BrO⋅H2O complex. This information facilitated the generation of several one-dimensional potential energy surface (PES) scans for the BrO⋅H2O complex. Scans were performed for both the ground state and the first excited state; this inclusion is due to a low-lying first electronic excited-state energy. These rigid-geometry PES scans were used both to generate a novel analytic interaction potential by modifying the existing Thole-type model used for water and to the fitted potential function. This interaction potential features anisotropic atomic polarizabilities facilitating appropriate modeling of the physics regarding the unpaired electron residing within the p-orbitals of the oxygen atom of the bromine oxide radical. The intention of this work is to facilitate future molecular dynamics simulations involving the interaction between the BrO radical and water clusters as a first step in devising possible novel chemistries taking place at the water interface of clouds within the atmosphere.

Selected cis- and trans-3-fluorostyrene rotamers studied by two-color resonant two-photon mass-analyzed threshold ionization spectroscopy

We applied two-color resonant two-photon ionization and mass-analyzed threshold ionization techniques to record the vibronic, photoionization efficiency, and cation spectra of the selected rotamers of 3-fluorostyrene. The adiabatic ionization energies of cis- and trans-3-fluorostyrene were determined to be 69 960±5 and 69 856±5cm−1, respectively. Cation vibrations 10a, 15, 6b, and 12 of both rotamers have been found to have frequencies of 218, 404, 452, and 971cm−1, respectively. This finding shows that the relative orientation of the vinyl group with respect to the F atom does not affect these vibrations of the 3-fluorostyrene cation. Our one-dimensional potential energy surface calculations support that the cis–trans isomerization of 3-fluorostyrene does not occur under the present experimental conditions.

The molecular dynamics of adsorption and dissociation of O2 on Pt(553).

Molecular adsorption and dissociation of O2 on the stepped Pt(553) surface have been investigated using supersonic molecular beam techniques and temperature programmed desorption. The initial and coverage-dependent sticking probability was determined with the King and Wells technique for various combinations of incident kinetic energy, surface temperature, incident angle, and surface coverage. A comparison with similar data for Pt(533) and Pt{110}(1 × 2) shows quantitatively the same high step-induced sticking at low incident energies compared to Pt(111). The enhancement is therefore insensitive to the exact arrangement of atoms forming surface corrugation. We consider energy transfer and electronic effects to explain the enhanced sticking. On the other hand, dissociation dynamics at higher incident kinetic energies are strongly dependent on step type. The Pt(553) and Pt(533) surfaces are more reactive than Pt(111), but the (100) step shows higher sticking than the (110) step. We relate this difference to a variation in the effective lowering of the barrier to dissociation from molecularly adsorbed states into atomic states. Our findings are in line with results from experimental desorption studies and theoretical studies of atomic binding energies. We discuss the influence of the different step types on sticking and dissociation dynamics with a one-dimensional potential energy surface.

Intricate internal rotation surface and fundamental infrared transitions of the n-propyl radical.

The potential energy surface for methylene hindered internal rotation is examined for the n-propyl radical, a molecule fundamental to combustion chemistry. Six stationary points are identified, and four of them are unique: 1, 2, TS1, and TS2. The remaining two structures 1' and TS1' are mirror images with respect to 1 and TS1. Focal point analysis, converged to the complete basis set limit of coupled-cluster theory with single, double, triple, and perturbative quadruple excitations [CCSDT(Q)], is employed to obtain the relative energies of these structures. A one-dimensional potential energy surface (PES) is constructed by explicitly mapping out a distinguished reaction path via constrained geometry optimizations. A "double-well" feature is observed on the electronic PES, but under the adiabatic approximation, the enthalpic (0 K) PES becomes a regular single-well potential with the expected 180° periodicity. The corresponding one-dimensional vibrational Schrödinger equation is solved using the Cooley-Numerov approach to obtain vibrational states of the methylene torsional motion. The predicted barrier for internal rotation is 105.5 and 137.2 cm(-1) for the electronic and enthalpic surfaces, respectively. Anharmonic (fundamental) vibrational frequencies are predicted for structure 1 using second-order vibrational perturbation theory, and the band origins for 11 modes are reported. Comparison with previous electron spin resonance and infrared spectroscopic work, in addition to other theoretical investigations, is made where possible.

Probing quantum and dynamic effects in concerted proton-electron transfer reactions of phenol-base compounds.

The oxidation of three phenols, which contain an intramolecular hydrogen bond to a pendent pyridine or amine group, has been shown, in a previous experimental study, to undergo concerted proton-electron transfer (CPET). In this reaction, the electron is transferred to an outer-sphere oxidant, and the proton is transferred from the oxygen to nitrogen atom. In the present study, this reaction is studied computationally using a version of Hammes-Schiffer's multistate continuum theory where CPET is formulated as a transmission frequency between neutral and cation vibrational-electronic states. The neutral and cation proton vibrational wave functions are computed from one-dimensional potential energy surfaces (PESs) for the transferring proton in a fixed heavy atom framework. The overlap integrals for these neutral/cation wave functions, considering several initial (i.e., neutral) and final (i.e., cation) vibrational states, are used to evaluate the relative rates of oxidation. The analysis is extended to heavy atom configurations with various proton donor-acceptor (i.e., O-N) distances to assess the importance of heavy atom "gating". Such changes in d(ON) dramatically affect the nature of the proton PESs and wave functions. Surprisingly, the most reactive configurations have similar donor-acceptor distances despite the large (~0.2 Å) differences in the optimized structures. These theoretical results qualitatively reproduce the experimental faster reactivity of the reaction of the pyridyl derivative 1 versus the CH(2)-pyridyl 2, but the computed factor of 5 is smaller than the experimental 10(2). The amine derivative is calculated to react similarly to 1, which does not agree with the experiments, likely due to some of the simplifying assumptions made in applying the theory. The computed kinetic isotope effects (KIEs) and their temperature dependence are in agreement with experimental results.

Vibrational assignment and proton tunneling in pyridine–pyridinium complexes

The pyridine–pyridinium cationic complexes [(Py 2H) +], with two different counterions (perchlorate and bromide), were prepared. The vibrational spectra of the complexes have been recorded. We then performed theoretical calculations to aid our understanding of the experimental data. To include the proton tunneling effect in our study, we adopted a simple one-dimensional potential energy surface (PES) for the motion of the hydrogen atom (at the center). This PES was derived from quantum mechanical calculations at the B3LYP/6-311++G ** level of theory for a fixed skeleton geometry. Based on such a PES, we computed the vibrational energy levels, from which a tunneling splitting of 487 ± 2 and 242 ± 2 cm −1 was obtained in the gas and solution phases, respectively. The calculated barrier height was about 2.0–2.3 and 4.0–4.2 kcal/mol in the gas and solution phases, respectively. After all things considered, our calculations assign the bands at 138, 1255, and 1665 cm −1 to the N⋯N stretching, N–H out-of-plane bending, and N–H in-plane bending modes, respectively.

Molecular Property Investigations of anortho-Hydroxy Schiff Base Type Compound with the First-Principle Molecular Dynamics Approach

The structure, proton transfer, and vibrational dynamics under ambient conditions of a selected ortho-hydroxy Schiff base type compound, 2-(N-methyl-alpha-iminoethyl)-4-chlorophenol, containing a very short intramolecular hydrogen bond, were investigated computationally in the gas phase and in the crystal by density functional theory (DFT) based first-principle molecular dynamics (FPMD). It is found that the proton is well localized on the nitrogen side of the O...H...N bridge in the crystal phase, in agreement with X-ray diffraction experiments, while a more labile proton is located most of the time on the oxygen side in a vacuum. Environmental effects on this very strong hydrogen bond thus appear crucial and lead to drastic changes of the infrared (IR) spectrum: The computed gas-phase IR spectrum shows a very broad absorption band that covers frequencies from about 1000 to 3000 cm(-1) assigned to the labile proton. In mere contrast, a much more localized absorption band around 2600-2700 cm(-1) is predicted in the crystal phase. Finally, effects of the quantization of the proton motion on the hydrogen bond structure were estimated in two ways. First, we constructed the one-dimensional (1D) potential energy surface (PES) for the proton along the O...H...N bridge in a vacuum. The 1D Schrodinger equation was then solved. Next, path integral molecular dynamics (PIMD) was performed in the solid state. Inclusion of quantum effects does not affect the observed change of the most probable tautomer, upon going from the gas phase to the crystal.

Calculation of the O−H Stretching Vibrational Overtone Spectrum of the Water Dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.

Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag-Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.