Intersection Of Potential Energy Surfaces Research Articles

Intersection of Potential Energy Surfaces in Polyatomic Molecules by Gerhard Herzberg and H C Longuet-Higgins in Discuss. Faraday Soc., Vol.35, pp.77–82, 1963

Intersection of Potential Energy Surfaces in Polyatomic Molecules by Gerhard Herzberg and H C Longuet-Higgins in Discuss. Faraday Soc., Vol.35, pp.77–82, 1963

The multichannel i-propyl + O2 reaction system: A model of secondary alkyl radical oxidation.

The i-propyl + O2 reaction mechanism has been investigated by definitive quantum chemical methods to establish this system as a benchmark for the combustion of secondary alkyl radicals. Focal point analyses extrapolating to the abinitio limit were performed based on explicit computations with electron correlation treatments through coupled cluster single, double, triple, and quadruple excitations and basis sets up to cc-pV5Z. The rigorous coupled cluster single, double, and triple excitations/cc-pVTZ level of theory was used to fully optimize all reaction species and transition states, thus, removing some substantial flaws in reference geometries existing in the literature. The vital i-propylperoxy radical (MIN1) and its concerted elimination transition state (TS1) were found 34.8 and 4.4kcal mol-1 below the reactants, respectively. Two β-hydrogen transfer transition states (TS2, TS2') lie above the reactants by (1.4, 2.5) kcal mol-1 and display large Born-Oppenheimer diagonal corrections indicative of nearby surface crossings. An α-hydrogen transfer transition state (TS5) is discovered 5.7kcal mol-1 above the reactants that bifurcates into equivalent α-peroxy radical hanging wells (MIN3) prior to a highly exothermic dissociation into acetone + OH. The reverse TS5 → MIN1 intrinsic reaction path also displays fascinating features, including another bifurcation and a conical intersection of potential energy surfaces. An exhaustive conformational search of two hydroperoxypropyl (QOOH) intermediates (MIN2 and MIN3) of the i-propyl + O2 system located nine rotamers within 0.9kcal mol-1 of the corresponding lowest-energy minima.

Tensor-Train Split-Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations.

Numerically exact simulations of quantum reaction dynamics, including nonadiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank-adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including nonadiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need to construct the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor-train Fourier transforms.

Role of Multistate Intersections in Photochemistry.

It has been generally accepted that the intersection of potential energy surfaces can facilitate nonadiabatic transitions and plays a crucial role in photochemistry. Although most previous studies have focused on the conical intersection of two electronic states, multistate intersections are common in polyatomic molecules, and their key roles in photochemistry have been uncovered by electronic structure calculations and nonadiabatic dynamics simulations. In this Perspective, the algorithms for searching two- or three-state intersections are first examined with an emphasis on the latest development in a general algorithm for location of multistate intersections. Then, we focus on intersystem crossing (ISC) that occurs in the region of multistate intersection, paying more attention to how the state-specific spin-orbit coupling interaction influences nonadiabatic ISC processes. Finally, the interweaving of nonadiabatic dynamics simulation and electronic structure calculation has been recognized as a correct way to ascertain the vital roles of multistate intersections in photochemical reactions.

Do extra compactified dimensions of space cause a substructure underlying the expected eigenstates of a molecule?

Experimental results on NO2 are explained based on the ADD-model of large extra compactified dimensions of space. We assume that gravity is sufficiently strong in a compactification space of the size of the molecule to affect the vibrational motion of the nuclei by causing an asymmetric perturbation in the symmetric stretch vibrational motion of the optically excited state. At the same excitation energy, there are also other electronic states of different symmetry (conical intersection of potential energy surfaces), which may couple with the optically excited state. Due to the gravitational perturbation the nuclei being in the symmetric stretch vibration mode of the optically excited electronic state pass over into the asymmetric stretch vibration mode of an isoenergetic electronic state. This parity conserving change of the vibronic wave function enhances a small gravitational perturbation to an optically detectable signal. The perturbation is associated with a time constant of about 3 μs, which we attribute to fluctuations of the shape of the compactification space induced by a background cosmic field.

Quantum trajectory simulation for nonadiabatic molecular dynamics

The mixed quantum-classical (MQC) molecular dynamics (MD) approaches are extremely important in practice since, with the increase of atomic degrees of freedom, a full quantum mechanical evaluation for molecular dynamics would quickly become intractable. Moreover, in some cases, the nonadiabatic effects are of crucial importance in the proximity of conical intersection of potential energy surfaces (PESs), where the energy separation between different PESs becomes comparable to the nonadiabatic coupling. In the past decades, there has been great interest in developing and improving various nonadiabatic MQC-MD protocols. The widely known nonadiabatic MD proposals include the so-called Ehrenfest or time-dependent-Hartree mean-field approach, the trajectory surface-hopping method, and their mixed scheme. Among the trajectory-based surface hopping methods, the most popular one is Tully's fewest switches surface hopping approach. In this approach, the nonadiabatic dynamics is treated by allowing hops from one PES to another, with the hopping probability determined by a certain artificial hopping algorithm. In our present work, we extend the study of a recent work on the nonadiabatic MQC-MD scheme, which is based on a view that the nonadiabatic MQC-MD actually implies an effective quantum measurement on the electronic states by the classical motion of atoms. The new protocol, say, the quantum trajectory (QT) approach, provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also connects two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. In our present study, we implement further the QT approach to simulate several typical potential-surface models, i.e., including the single avoided crossing, dual avoided crossing, extended coupling, dumbbell and double arch potentials. In particular, we simulate and compare three decoherence rates, which are from different physical considerations, i.e., the frozen Gaussian approximation, energy discrimination and force discrimination. We also design simulation algorithms to properly account for the energy conservation and force direction change associated with the surface hopping. In most cases, we find that the QT results are in good agreement with those from the full quantum dynamics, which is insensitive to the specific form of the decoherence rate. But for the model involving strong quantum interference, like other nonadiabatic MQC-MD schemes, the QT approach cannot give desirable results. Developing better method should be useful for future investigations in this research area.

Quantum-classical model of retinal photoisomerization reaction in visual pigment rhodopsin.

A quantum-classical model of photoisomerization of the visual pigment rhodopsin chromophore is proposed. At certain (and more realistic) parameter value combinations, the model is shown to accurately reproduce a number of independent experimental data on the photoreaction dynamics: the quantum yield, the time to reach the point of conical intersection of potential energy surfaces, the termination time of the evolution of quantum subsystem, as well as the characteristic low frequencies of retinal molecular lattice fluctuations during photoisomerization. In addition, the model behavior is in good accordance with experimental data about coherence and local character of quantum transition.

Performance of Tamm-Dancoff approximation on nonadiabatic couplings by time-dependent density functional theory

The Tamm-Dancoff approximation (TDA), widely used in physics to decouple excitations and de-excitations, is well known to be good for the calculation of excitation energies but not for oscillator strengths. In particular, the sum rule is violated in the latter case. The same concern arises within the TDA in the calculation of nonadiabatic couplings (NACs) by time-dependent density functional theory (TDDFT), due to the similarities in the TDDFT formulations of NACs and oscillator strengths [C. Hu, H. Hirai, and O. Sugino, J. Chem. Phys. 127, 064103 (2007)]. In this study, we present a systematic evaluation of the performance of TDDFT/TDA for the calculation of NACs. In the cases we considered, including a variety of systems possessing Jahn-Teller and Renner-Teller intersections, as well as an example with accidental conical intersections, it is found that the TDDFT/TDA performs better than the full TDDFT, contrary to the conjecture that the TDA might cause the NAC results to deteriorate and violate the sum rule. The surprisingly good performance of the TDA for NACs is probably because the TDA can partially compensate for the local-density-approximation error and give better excitation energies in the vicinity of intersections of potential energy surfaces. Our study also shows that it is important to use the TDA based on the rigorous full-TDDFT formulation of NACs, instead of using it based on an alternative approximate formulation.

ChemInform Abstract: Future Perspectives of Nonadiabatic Chemical Dynamics

AbstractReview: 50 refs.

Role of positional disorder in the spectra of conjugated polymer aggregates: a conical intersection of potential energy surfaces

Here we have studied the effect of disorder on the luminescence spectra due to the orientational disposition of monomeric conjugated polymer chain units forming a dimer aggregate. The dipolar interchain interactions are described considering static as well as dynamic disorder created by the torsion or shearing degree of freedom. For static disorder, the shearing angle is treated parametrically for different frozen configurations of the positional defect. In the case of dynamical disorder the torsional motion is treated on an equal footing with the vibrational degree of freedom by including the shearing coordinate explicitly in the calculation. The inclusion of torsion angle dependence in the interchain interaction not only saves the 0–0 transition from total quenching but also generates a conical intersection in the adiabatic potential energy surfaces of the dimer aggregate. Due to the vanishing of the interchain coupling at the conical intersection point, the two chains become independent and the dimeric spectra pass through a monomeric pattern which can serve as an example of the presence of conical intersection in the aggregates of conjugated polymer chains. Also the presence of the low-frequency torsion mode explicitly considered in the case of dynamic disorder can be detected from a significant Stokes shift in the steady state spectra.

Control of Chemical Dynamics by Lasers: Theoretical Considerations

Theoretical ideas are proposed for laser control of chemical dynamics. There are the following three elementary processes in chemical dynamics: (i) motion of the wave packet on a single adiabatic potential energy surface, (ii) excitation/de-excitation or pump/dump of wave packet, and (iii) nonadiabatic transitions at conical intersections of potential energy surfaces. A variety of chemical dynamics can be controlled, if we can control these three elementary processes as we desire. For (i) we have formulated the semiclassical guided optimal control theory, which can be applied to multidimensional real systems. The quadratic or periodic frequency chirping method can achieve process (ii) with high efficiency close to 100%. Concerning process (iii) mentioned above, the directed momentum method, in which a predetermined momentum vector is given to the initial wave packet, makes it possible to enhance the desired transitions at conical intersections. In addition to these three processes, the intriguing phenomenon of complete reflection in the nonadiabatic-tunneling-type of potential curve crossing can also be used to control a certain class of chemical dynamics. The basic ideas and theoretical formulations are provided for the above-mentioned processes. To demonstrate the effectiveness of these controlling methods, numerical examples are shown by taking the following processes: (a) vibrational photoisomerization of HCN, (b) selective and complete excitation of the fine structure levels of K and Cs atoms, (c) photoconversion of cyclohexadiene to hexatriene, and (d) photodissociation of OHCl to O + HCl.

Future perspectives of nonadiabatic chemical dynamics

A variety of chemical phenomena are governed by non-adiabatic transitions at conical intersections of potential energy surfaces, if not directly, but indirectly in the midst of the processes. In other words, the non-adiabatic transition makes one of the most significant key mechanisms in chemical dynamics. Since the basic analytical theory is now available to treat the transitions, it is possible to comprehend the dynamics of realistic chemical and biological systems with the effects of transitions taken into account properly. Another important quantum mechanical effect of tunneling can also be taken into account. Furthermore, it becomes feasible to control chemical dynamics by controlling the non-adiabatic transitions at conical intersections, and also to develop new molecular functions by using peculiar properties of non-adiabatic transitions. These may be realized, if we apply appropriately designed laser fields. This perspective review article explains the above mentioned ideas based on the authors' recent activities. The non-adiabatic chemical dynamics is expected to open a new dimension of chemistry.

Multimode vibronic coupling effects in molecules

The multimode vibronic coupling problem is discussed and compared with the standard single-mode problem. It is demonstrated for two typical examples that the simultaneous consideration of two vibrational modes is essential to explain the experimental findings. The coupling of the involved electronic states via these modes gives rise to a conical intersection of the potential energy surfaces. The presence of the conical intersection strengthens considerably the nonadiabatic effects in the nuclear motion. Conical intersection of potential energy surfaces constitute a widespread phenomenon which should be considered when investigating vibronic coupling effects in realistic polyatomic molecules.

Single switch surface hopping for a model of pyrazine

The single switch trajectory surface hopping algorithm is tested for numerical simulations of a two-state three-mode model for the internal conversion of pyrazine through a conical intersection of potential energy surfaces. The algorithm is compared to two other surface hopping approaches, namely, Tully's method of the fewest switches [J. Chem. Phys. 93, 1061 (1990)] and the method by Voronin et al. [J. Phys. Chem. A 102, 6057 (1998)]. The single switch algorithm achieves the most accurate results. Replacing its deterministic nonadiabatic branching condition by a probabilistic accept-reject criterion, one obtains the method of Voronin et al. without momentum adjustment. This probabilistic version of the single switch approach outperforms the considered algorithms in terms of accuracy, memory requirement, and runtime.

Searching for Conical Intersections of Potential Energy Surfaces with the ONIOM Method: Application to Previtamin D

We demonstrate that the ONIOM method can be used to optimize a conical intersection between the ground and first excited-state potential energy surfaces of previtamin D (precalciferol), with excitation localized in a small part of the molecule: the hexatriene chromophore. These calculations were up to 100 times faster with little loss of accuracy compared to a full non-ONIOM Target calculation. The most accurate ONIOM method combination was CASSCF/4-31G//ROHF/STO-3G(Triplet): in comparison to the Target (CASSCF/4-31G), bond lengths and angles in the hexatriene model region were calculated to within 0.02 A and 0.7 degrees , respectively, and the energy difference between the conical intersection and nearest associated S 1 minimum to within 0.5 kcal x mol (-1). All of the low-level methods selected produced accurate geometries, including the UFF molecular mechanics and AM1 semiempirical methods, suggesting a cheap and efficient way of initially optimizing conical intersections geometries. Furthermore, ONIOM allows for an assessment of the localization of excited states, providing some fundamental insight into the physical processes involved.

Single switch surface hopping for molecular dynamics with transitions

A trajectory surface hopping algorithm is proposed, which stems from a mathematically rigorous analysis of propagation through conical intersections of potential energy surfaces. Since nonadiabatic transitions are only performed when a classical trajectory attains one of its local minimal surface gaps, the algorithm is called single switch surface hopping. Numerical experiments for a two mode Jahn-Teller system are presented, which illustrate the asymptotic justification of the method as well as its good performance in the physically relevant parameter range.

RMDff: A smoothly transitioning, forcefield-based representation of kinetics for reactive molecular dynamics simulations

RMDff is a new forcefield that smoothly couples the reactive intersections of potential energy surfaces to model chemical reactions. The method uses switching functions to accomplish a smooth transition from reactant to product atom types. This paper demonstrates and tests RMDff for homolytic scissions. The reaction networks are described by localized events involving only a few atoms, so that the complex mechanisms employed in conventional kinetics modeling are not needed. Unlike quantum chemical calculations, which are feasible only for small molecules, this new valence-bond forcefield can be coupled with Reactive Molecular Dynamics to describe chemical reactions in large domains.

Scattering at the intersections of potentials

The scattering process influenced by the intersection of potential energy surfaces is studied. Exact quantum-mechanical solutions to the two-dimensional two- and three-state models have been found for the collision energy equal to the potential energy at the intersection point. The models considered are the Jahn-Teller and Renner-Teller intersections and the triple intersection of the double cone with a plane. Closed analytical expressions for the scattering amplitudes have been obtained. The results reveal the geometric phase effect and the nonadiabatic phase impact on the differential cross section.

Intersections of potential energy surfaces of short-lived states: the complex analogue of conical intersections.

Whereas conical intersections between potential energy surfaces of bound states are well known, the interaction of short-lived states has been investigated only rarely. Here, we present several systematically constructed model Hamiltonians to study the topology of intersecting complex potential energy surfaces describing short-lived states: We find the general phenomenon of doubly intersecting complex energy surfaces, i.e., there are two points instead of one as in the case of bound states where the potential energy surfaces coalesce. In addition, seams of intersections of the respective real and imaginary parts of the potential energy surfaces emanate from these two points. Using the Sigma* and Pi* resonance states of the chloroethene anion as a practical example, we demonstrate that our complete linear model Hamiltonian is able to reproduce all phenomena found in explicitly calculated ab initio complex potential energy surfaces.

Singular nonadiabatic coupling at intersections of potential-energy surfaces by infinite-order perturbation theory

A general model for an intersection of two electronic states dependent on one nuclear coordinate is considered. A perturbational series expansion resulting from the inclusion of the nonadiabatic coupling starting from the Born-Oppenheimer approximation in zeroth order is set up. It is proven that the series has a finite radius of convergence and that it can be summed up exactly.