Shape Of Potential Energy Surface Research Articles

Independent trajectory mixed quantum-classical approaches based on the exact factorization.

Mixed quantum-classical dynamics based on the exact factorization exploits the "derived" electron-nuclear correlation (ENC) term, aiming for the description of quantum coherences. The ENC contains interactions between the phase of electronic states and nuclear quantum momenta, which depend on the spatial shape of the nuclear density. The original surface hopping based on the exact factorization (SHXF) [Ha et al., J. Phys. Chem. Lett. 9, 1097 (2018)] exploits frozen Gaussian functions to construct the nuclear density in the ENC term, while the phase of electronic states is approximated as a fictitious nuclear momentum change. However, in reality, the width of nuclear wave packets varies in time depending on the shape of potential energy surfaces. In this work, we present a modified SHXF approach and a newly developed Ehrenfest dynamics based on the exact factorization (EhXF) with time-dependent Gaussian functions and phases by enforcing total energy conservation. We perform numerical tests for various one-dimensional two-state model Hamiltonians. Overall, the time-dependent width of Gaussian functions and the energy conserving phase show a reliable decoherence compared to the original frozen Gaussian-based SHXF and the exact quantum mechanical calculation. In particular, the energy conserving phase is crucial for EhXF to reproduce the correct quantum dynamics.

Energy levels and electromagnetic transitions of some eveneven and even-odd Barium Isotopes

In this paper, the nuclear structure of Barium nuclei has been studied by interacting boson model. The properties of eigenstates and reduce probability of electric transition and potential energy surface have been calculated. The nuclei understudy has proton number equal 56 and neutron numbers 75 and 76. The results of energy states and B(E2) values have been compared with the experimental data. These comparisons show that acceptable between the calculations and experimental data. The parameters which used in the calculation have been estimated and give best approximation. The shape of potential energy surface show that the even-even nucleus have O(6) dynamical symmetry.

Examination of the performance of semiempirical methods in QM/MM studies of the SN2-like reaction of an adenylyl group transfer catalysed by ANT4′

Quantum mechanical (QM) semiempirical methods (SMs), combined with molecular mechanics (MM) force fields, are extensively used in theoretical studies of enzymatic reactions. Despite being several orders of magnitude faster than ab initio methods, their correctness is essential to be used in calculations requiring statistical simulations. Herein, a wide range of SMs are examined, from those based on s and p orbitals, sp-SMs (MNDO, AM1, PM3 and RM1), to those including d orbitals, spd-SMs, either based on approximations to the Hartree–Fock theory (MNDO/d, PM6 and AM1/d-PhoT) or derived from density functional theory (DFTB3). These QM Hamiltonians are used within a multiscale QM/MM additive scheme, to clarify their usefulness in mechanistic studies of phosphoryl-transfer reactions. The SN2-like reaction of the adenylyl group transfer catalysed by 4′-O-Nucleotidyltransferase (ANT4′) was selected as a benchmark. Geometrical characteristics of stationary structures, the shape of potential energy surfaces together with the barrier heights and kinetic isotope effects (KIEs), obtained with the different SMs/MM methods were compared with results obtained at higher M06-2X/MM level of theory. Critical limitations of the sp-SMs in the present mechanistic study were detected. The spd-SMs describe the reaction as a concerted process, same as the reference method M06-2X, but none of them is free of limitations. PM6 reproduces the biased trend of previous sp-SMs stabilizing structures of phosphorous atoms with certain pentavalent character, while AM1/d-PhoT and DFTB3 describe TSs more dissociative than M06-2X, which determines the lower quality of the computed primary and secondary 16O/18O KIEs. Efforts to improve the SMs can be guided by the exposure of their limitations, which were supported by the results of a second studied phosphoryl-transfer reactions; the hydrolysis of phosphodiester bond at the 3′-end of the viral DNA (vDNA). Thus, for instance, further increases in SMs accuracy can be achieved by improving the training and survey reference data sets, a more complete set of parameters for describing intermolecular interactions or further developments of spd-SMs.

NMR and XRD Study of Hydrogen Bonding in Picolinic Acid N-Oxide in Crystalline State and Solutions: Media and Temperature Effects on Potential Energy Surface.

Solvent and temperature effects on H-bonding in crystalline picolinic acid N-oxide (PANO) and in solutions were studied by NMR (1H MAS and 1H-13C CP/MAS) and X-ray diffraction (XRD) methods. The single-crystal XRD experiments on β-polymorph were carried out at 105 and 299 K. 13C chemical shifts of PANO pyridine ring carbons were chosen as an effective diagnostic tool for the H-bond sensing. The crystal field in PANO forces the proton displacement from donor to acceptor atoms much stronger than the solvent reaction field, including that created by the most polar solvents. NMR and XRD data for crystalline PANO do not confirm any H-bond geometry changes in the studied temperature range. On the contrary, a considerable contraction of r(O-H) bond was observed for PANO in acetonitrile (ACN) solution upon heating. The relative contraction of r(O-H) bond with respect to R(O···O) perfectly fits the global dielectric scheme deduced for a vast set of common solvents and the dependence of the dielectric permittivity of ACN on temperature. The subtle H-bond changes can be explained by the temperature dependence of the shape of potential energy surface in the liquid state. Both factors, temperature and dielectric permittivity, are comparable in triggering this effect.

Structural Control of Nonadiabatic Photochemical Bond Formation: Photocyclization in Structurally Modified ortho-Terphenyls.

Understanding how molecular structure impacts the shapes of potential energy surfaces and prospects for nonadiabatic photochemical dynamics is critical for predicting and controlling the chemistry of molecular excited states. Ultrafast transient absorption spectroscopy was used to interrogate photoinduced, nonadiabatic 6π cyclization of a collection of ortho-terphenyls (OTP) modified with alkyl substituents of different sizes and electron-donating/withdrawing character positioned on its central and pendant phenyl rings. OTP alkylated at the 4,4″ and 4',5' positions of the pendant and central rings, respectively, exhibiting biphasic excited-state relaxation; this is qualitatively similar to relaxation of OTP itself, including a fast decrease in excited-state absorption (τ1 = 1-4 ps) followed by formation of metastable cyclized photoproducts (τ2 = 3-47 ps) that share common characteristic spectroscopic features for all substitutions despite variations in chemical nature of the substituents. By contrast, anomalous excited-state dynamics are observed for 3',6'dimethyl-OTP, in which the methyl substituents crowd the pendant rings sterically; time-resolved spectral dynamics and low photochemical reactivity with iodine reveal that methylation proximal to the pendant rings impedes nonadiabatic cyclization. Results from transient measurements and quantum-chemical calculations are used to decipher the nature of excited state relaxation mechanisms in these systems and how they are perturbed by mechanical, electronic, and steric interactions induced by substituents.

A road to a multiconfigurational ensemble density functional theory without ghost interactions

Ensemble density functional theory (DFT) is a theory potentially able to describe electronic states inaccessible to traditional time‐dependent DFT approaches, e.g. Rydberg and double excitations. When combined with ensemble wavefunction approaches through a range‐separation scheme of Stoll and Savin (Density Functional Methods in Physics, 1985, 177‐207), a resulting multiconfiguration ensemble DFT is able to address also such challenging phenomena as bond breaking in the electronically excited molecules. Ensemble DFT is, however, crippled by the so‐called “ghost interaction” error, analogous to the self‐interaction error in the ground‐state DFT. We are exploring ways to alleviate this effect. We also study the importance of spin polarization in the density functional, the self‐consistency effects and the impact of tunable parameters on the quality of shapes of potential energy surfaces. © 2016 Wiley Periodicals, Inc.

Intermolecular potential energy surface for CS2 dimer

A new four-dimensional intermolecular potential energy surface for CS(2) dimer is obtained by ab initio calculation of the interaction energies for a range of configurations and center-of-mass separation distances for the first time. The calculations were performed using the supermolecular approach at the Møller-Plesset second-order perturbation (MP2) level of theory with the augmented correlation consistent basis sets (aug-cc-pVxZ, x = D, T) and corrected for the basis-set superposition error using the full counterpoise correction method. A two-point extrapolation method was used to extrapolate the calculated energy points to the complete basis set limit. The effect of using the higher levels of theory, quadratic configuration interaction containing single, double, and perturbative triple excitations QCISD(T) and coupled cluster singles, doubles and perturbative triples excitations CCSD(T), on the shape of potential energy surface was investigated. It is shown that the MP2 level of theory apparently performs extremely poorly for describing the intermolecular potential energy surface, overestimating the total energy by a factor of nearly 1.73 in comparison with the QCISD(T) and CCSD(T) values. The value of isotropic dipole-dipole dispersion coefficient (C(6) ) of CS(2) fluid was obtained from the extrapolated MP2 potential energy surface. The MP2 extrapolated energy points were fitted to well-known analytical potential functions using two different methods to represent the potential energy surface analytically. The most stable configuration of the dimer was determined at R = 6.23 au, α = 90°, β = 90°, and γ = 90°, with a well depth of 3.980 kcal mol(-1) at the MP2 level of theory. Finally, the calculated second virial coefficients were compared with experimental values to test the quality of the presented potential energy surface.

Bifurcations on Potential Energy Surfaces of Organic Reactions

A single transition state may lead to multiple intermediates or products if there is a post-transition-state reaction pathway bifurcation. These bifurcations arise when there are sequential transition states with no intervening energy minimum. For such systems, the shape of the potential energy surface and dynamic effects, rather than transition-state energetics, control selectivity. This Minireview covers recent investigations of organic reactions exhibiting reaction pathway bifurcations. Such phenomena are surprisingly general and affect experimental observables such as kinetic isotope effects and product distributions.

Nucleophilic Substitution at C, Si and P: How Solvation Affects the Shape of Reaction Profiles

AbstractWe have studied how solvation affects the shape of potential energy surfaces (PES) of archetypal nucleophilic substitution reactions at carbon (SN2@C), silicon (SN2@Si) and phosphorus (SN2@P), using the generalized gradient approximation (GGA) of density functional theory (DFT) at OLYP/TZ2P. Our model systems cover nucleophilic substitution, in water and in the gas phase, at carbon in X– + CH3Y (SN2@C), at silicon in X– + SiH3Y (SN2@Si), at tricoordinate phosphorus in X– + PR2Y (SN2@P3), and at tetracoordinate phosphorus in X– + POR2Y (SN2@P4) with substituents R = H, F, Cl, CH3, OCH3. In the gas phase, particular types of SN2 reactions are characterized by different shapes of reaction profiles, such assingle‐, double‐ and triple‐well PESs. The main effect of solvation is to turn the PESs of the SN2@C but also of SN2@Si and SN2@P into unimodal reaction profiles which lead from the reactants via one single barrier to the products. The results are discussed in terms of differential solvation of reactants and transition states. We also address the question how the relative heights of reaction barriers are affected by solvation. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2008)

Biasing reaction pathways with mechanical force

During the course of chemical reactions, reactant molecules need to surmount an energy barrier to allow their transformation into products. The energy needed for this process is usually provided by heat, light, pressure or electrical potential, which act either by changing the distribution of the reactants on their ground-state potential energy surface or by moving them onto an excited-state potential energy surface and thereby facilitate movement over the energy barrier. A fundamentally different way of initiating or accelerating a reaction is the use of force to deform reacting molecules along a specific direction of the reaction coordinate. Mechanical force has indeed been shown to activate covalent bonds in polymers, but the usual result is chain scission. Here we show that mechanically sensitive chemical groups make it possible to harness the mechanical forces generated when exposing polymer solutions to ultrasound, and that this allows us to accelerate rearrangement reactions and bias reaction pathways to yield products not obtainable from purely thermal or light-induced reactions. We find that when placed within long polymer strands, the trans and cis isomers of a 1,2-disubstituted benzocyclobutene undergo an ultrasound-induced electrocyclic ring opening in a formally conrotatory and formally disrotatory process, respectively, that yield identical products. This contrasts with reaction initiation by light or heat alone, in which case the isomers follow mutually exclusive pathways to different products. Mechanical forces associated with ultrasound can thus clearly alter the shape of potential energy surfaces so that otherwise forbidden or slow processes proceed under mild conditions, with the directionally specific nature of mechanical forces providing a reaction control that is fundamentally different from that achieved by adjusting chemical or physical parameters. Because rearrangement in our system occurs before chain scission, the effect we describe might allow the development of materials that are activated by mechanical stress fields.

Hybrid density functional study of ligand coordination effects on the magnetic couplings and the dioxygen binding of the models of hemocyanin

AbstractLigand coordination effects on the magnetic interaction and the reversible dioxygen binding process for the models of hemocyanin have been investigated with hybrid density functional theory. Hemocyanin is an oxygen transport protein found in mollusks and arthropods. The active site of hemocyanin contains a pair of copper atoms, each of which is coordinated by three histidine residues. We utilized NH3 (a), methylimidazole (b), and histidine (c) as the ligands of the models of hemocyanin, which coordinate to the binuclear copper core in the active site of oxygenated (1z) (z = a–c) and deoxygenated hemocyanin (2z). The difference of the ligand coordination in the magnetic couplings for the model of hemocyanin 1z complexed with peroxide (1z‐O) shows that the substitution from histidine to methylimidazole group is not serious, but that the substitution from imidazole to NH3 is influential. In the dioxygen binding process, the ligands influence the binding energy and the shapes of potential energy surfaces of the models of hemocyanin 1z and 2z with dioxygen due to the strength of the mixing between the ground state and the charge transfer one. The active dxy ± dxy orbitals of the copper core of 1b and 1c strongly interact with π and π orbitals of the dioxygen than those of 1a, leading to the larger binding energy of the model 1b (1c) with dioxygen. The orbital energies of the active orbitals for the synthetic model, [Cu(HB(3,5‐iPr2‐Pz)3)]2 (HB(3,5‐iPr2‐Pz)3 = hydrotris{3,5‐diisopropyl‐pyrazolyl}borate), imply that it irreversibly binds dioxygen because HB(3,5‐iPr2‐Pz)3 groups show stronger electron‐release character and raise the orbital energies nearer that to π* orbitals of O2. The effective bond‐order, localized electron density, and information entropy for 1z with dioxygen were calculated in terms of occupation numbers of the natural orbitals of the broken‐symmetry UB2LYP solution in order to elucidate the nature of the Cu2O2 bonding. These chemical indices indicate that the copper–oxygen bonds in Hc exhibit an intermediate covalent‐bonding character (half bonding), which is the origin of an active control of oxygen transport: addition and dissociation of O2 in hemocyanin by the conformational changes. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Rydberg–valence interactions in CH2Cl→CH2+Cl photodissociation: Dependence of absorption probability on ground state vibrational excitation

A strong enhancement of absorption to the lowest A12 state is observed for vibrationally excited chloromethyl radicals. It is demonstrated that this enhancement is due to a significant increase in both electronic and vibrational Franck–Condon factors. Electronic structure calculations of potential energy surfaces (PESs) and transition dipole moments for the ground and the two lowest excited states of A1 symmetry, the 1 2A1 valence and 22A1 Rydberg states, reveal the origin of this effect. The shelflike shape of the 1 2A1 PES in the Franck–Condon region and the strong dependence of the electronic transition dipole moment on C–Cl distance are responsible for the enhancement. Analysis of the shape of the electron density distribution demonstrates that Rydberg–valence interaction in the two lowest excited states causes the changes in the shape of PESs and transition dipoles with C–Cl distance.

Mechanisms of reactions between > Si=O groups and CO2, N2O, and HC≡CH molecules: An experimental and quantum chemical study

IR spectroscopy and quantum chemical calculations are used to study the directions and kinetics of reactions between silanone groups (≡Si-O)2Si=O and CO2, N2O, and acetylene molecules. IR bands are assigned on the basis of the calculation of vibrational spectra of model low-molecular systems. Quantum chemical methods are used to obtain the data on the shapes of potential energy surfaces of these systems (intermolecular complexes and transition states). These data are used to interpret kinetic data. The silanone group is inclined to the formation of relatively stable (~10 kcal/mol) intramolecular complexes with CO2, N2O, and acetylene molecules. Their geometries and electronic structures are determined.

Deciphering factors which determine the Ramachandran surface of peptides. The application of isodesmic surfaces, ΔEID(ϕ,ψ), to analyze the contribution of rotating moieties to the shape of potential energy surfaces

A series of double rotors of the following types have been investigated via potential energy surfaces, E=E(ϕ,ψ), generated by ab initio Hartree–Fock molecular computations. Series of triply substituted methyne (H–C) moieties are called upon to mimic, the conformational behaviour of peptides. In substituents Z1 and Z2 the “first atoms” were of sp3 and sp2 hybridization having Z1=−CH3, –CH2F and –NHCHO, as well as Z2=−CH3, –CH2F, –CHO and –CONH2. The R group was chosen to be –H or –F and in one case –CH3 in order to reproduce the alanine model peptide. All potential energy surfaces, E=E(ϕ,ψ), were generated in the form of grids where points were separated by 15° intervals along both ϕ and ψ variables. This led to a total of 625 SCF points (25×25) for each surface, since both the initial (0°) and final (360°) values of both periodic variables (ϕ and ψ) were included in the grid. The interaction between substituents introduced were monitored by isodesmic reactions computed at each of the 625 grid points leading to isodesmic energy surfaces: ΔEID(ϕ,ψ). Comparing the influence of the different Z1 and Z2 substituents, undoubtedly, the introduction of two adjacent peptide bonds led to the greatest effect on the conformational energy surface.

The role of coherence and time in the mechanism of dynamical symmetry breaking and localization

The formation of resonant photon emission following core electron excitation in symmetric systems is discussed within a time-dependent framework. The starting point of the discussion is an expression for the rate of photon or Auger electron emission intensity valid for general excitation light pulses and shapes of potential energy surfaces. The mechanism of dynamical symmery breaking via the excitation of symmetry breaking and localizing modes is illustrated by the example of a linear symmetric molecule, e.g., CO2. It is shown that the decay rates are proportional to the population of a coherent superposition of the localized core states. The coherence of the decaying localized core states governs the population flow between the |Φu〉 and |Φg〉 symmetry adapted core states and determines the amount of total photon emission intensity recorded for a final state of definite spatial symmetry. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 950–957, 2000

Characterization of Photoinduced Electron Transfer in Jet-Formed Acceptor Donor Complexes. 2. Photoinduced Electron Transfer: Rates and Mechanisms

The electron transfer (ET) rates induced by the electronic excitation of different isomers of anthracene complexes with aniline derivatives are deduced from their fluorescence and fluorescence excitation spectra. The shapes of potential energy surfaces of locally excited and ionic surfaces are calculated with a special interest for the crossing areas of both surfaces. The dependence of the ET rates on the initial configuration is discussed and the assignments of calculated configurations to isomeric species (E and R isomers) are proposed.

Desorption Induced by Electronic Transitions at Metal Surfaces.

An attempt is made to provide a physical basis for DIET (desorption induced by electronic transitions) at metal surfaces. For this purpose, a theoretical description for DIET is given from a microscopic point of view. From the calculation for the dependence of the DIET probability on the penetration depth of the laser light and on the band-width of the electron system of the metal substrate, it is suggested that the spatial locality of electronic excitations affects the probability significantly. It is shown, furthermore, that the DIET probability increases, as the shape of PES (potential energy surface) is changed such that the number of adsorbate bound-states in the PES is decreased. As an order of magnitude, the result of calculation for the DIET probability of NO from Cu(111) agrees with the probability estimated experimentally.

An examination of a density functional/molecular mechanical coupled potential

AbstractIn this article we describe the coupling of a density functional (DF) Hamiltonian with the molecular mechanics (MM) potential function AMBER. We examine a series of test cases in which we compare the binding energies and geometries of the complexes predicted by this coupled potential with those predicted by other theoretical methods and experiment to establish the relative accuracy of the DF/MM coupled potential. We find that the DF/MM coupled potential performs well in most cases studied and, in general, outperforms the semiempirical/MM approach. The interaction energies and structures obtained using this method appear to be insensitive to the use of nonlocal (NL) corrections to the DF method. The is fortuitous because the NL treatment is significantly more computationally expensive than the local treatment. However, NL corrections may be required to predict accurately the shape of potential energy surfaces that involve bond breaking and formation. The DF/MM method has also been applied to the determination of the solvation free energy for a series of ions using free‐energy perturbation methods. The results obtained are good and can be improved by a simple scaling of the Lennard‐Jones parameters for the ion in question. © 1995 by John Wiley & Sons, Inc.

Reaction of exciplex formation in the gas phase. Potential curve crossing approach

The reaction of molecular exciplex formation in the gas phase is treated within the framework of the Landau-Zener approximation. The rate constant of exciplex formation is calculated as a function of “system parameter” which depends on the coupling and shape of potential energy surfaces. For a series of model exciplex systems the role of intramolecular vibrations in the formation process and the influence of the coupling strength and the temperature on the formation rate constant is investigated.

General Potential-Energy Function for Exchange Reactions

A general potential-energy function for linear triatomic systems has been developed for use in connection with reaction kinetics calculations. The function is a generalization of the Morse function with a sufficient number of adjustable parameters to permit arbitrary fixing of the location and curvatures of the saddle point of the potential energy surface. The function reduces, of course, to the Morse function when one of the atoms is infinitely distant from the other two. Since the characteristics of the saddle region are adjustable, the function is particularly useful in connection with computations designed to test the effect of different shapes of potential energy surfaces upon reaction probabilities. The function is most readily used for symmetric reactions, but it can be further generalized to cover unsymmetric cases.