Multidimensional Potential Energy Surfaces Research Articles

Canonical Approach To Generate Multidimensional Potential Energy Surfaces.

A new force-based canonical approach for the accurate generation of multidimensional potential energy surfaces is demonstrated. Canonical transformations previously developed for diatomic molecules are used to construct accurate approximations to the 3-dimensional potential energy surface of the water molecule from judiciously chosen (adopting the right coordinate system) 1-dimensional planar slices that are shown to have the same canonical shape as the classical Lennard-Jones potential curve. Spline interpolation is then used to piece together the 1-dimensional canonical potential curves, to obtain the full 3-dimensional potential energy surface of a water molecule with a relative error less than 0.01. This work provides an approach to greatly reduce the computational cost of constructing potential energy surfaces in molecules from ab initio calculations. The canonical transformation techniques developed in this work illuminate a pathway to deepening our understanding of chemical bonding.

Dinitrogen Coupling to a Terpyridine-Molybdenum Chromophore Is Switched on by Fermi Resonance

Summary The traditional view of a chemical change is inherently local and classical, and such a change relies on a mix of thermodynamic and kinetic parameters to control reactivity. Often, the thermodynamic stability of chemical bonds necessitates significant energy input for activation. One fundamental question is potentially transformative: can quantum mechanics enable selective bond activation? A possible approach involves strategic input of energy to reaction-specific vibrational levels. Toward this goal, our work describes the coupling of vibrational motions in a terpyridine-molybdenum complex hosting a nonreactive substrate—dinitrogen. Ultrafast coherence spectroscopies revealed a Fermi-resonance coupling mechanism connecting in-plane breathing motion of the light-harvesting terpyridines with the stretching motion of the spatially disparate dinitrogen bridge. Notably, the coupling is significantly enhanced in the photoexcited state. This Fermi resonance indicates an energy conduit that drives the two motions in sync and thereby amplifies vibrational energy exchange. Achieving selective bond activation by bridging vibrations could present a quantum-inspired design principle in synthetic chemistry.

Locating Exceptional Points on Multidimensional Complex-Valued Potential Energy Surfaces.

We present a method for locating non-Hermitian degeneracies, called exceptional points (EPs), and minimum-energy EPs between molecular resonances using the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) method. EPs are the complex-valued analogue of conical intersections (CIs) and have a similar impact on nonadiabatic processes between resonances as CIs have on nonradiative transitions between bound states. We demonstrate that the CAP-EOM-CC method in the singles and doubles approximation (CAP-EOM-CCSD) yields crossings of the correct dimensionality. The use of analytic gradients enables applications to multidimensional problems. Results are presented for hydrogen cyanide and chloroethylene, for which the location of the crossings of anionic resonances is crucial for understanding the dissociative electron attachment process.

Rigorous use of symmetry within the construction of multidimensional potential energy surfaces.

A method is presented, which allows for the rigorous use of symmetry within the construction of multidimensional potential energy surfaces (PESs). This approach is based on a crude but very fast energy estimate, which retains the symmetry of a molecule. This enables the efficient use of coordinate systems, which mix molecular and permutational symmetry, as, for example, in the case of normal coordinates with subsets of localized normal coordinates. The impact of symmetry within the individual terms of an expansion of the PES is studied together with a symmetry consideration within the individual electronic structure calculations. A trade between symmetry within the surface and the electronic structure calculations has been observed and has been investigated in dependence on different coordinate systems. Differences occur between molecules belonging to Abelian point groups in contrast to non-Abelian groups, in which further benefits can be achieved by rotating normal coordinates belonging to degenerate vibrational frequencies. In general, the exploitation of surface symmetry was found to be very important within the construction of PESs of small and medium-sized molecules-irrespective of the coordinate system. Benchmark calculations are provided for formaldehyde, ethene, chloromethane, and cubane.

Ultrafast relaxation dynamics in a polymer: fullerene blend for organic photovoltaics probed by two-dimensional electronic spectroscopy

Ultrafast charge transfer from a photoexcited donor to an acceptor moiety is at the heart of the energy conversion in organic photovoltaics (OPVs). Efficient charge transfer on ultrafast, sub-100-fs timescales has been reported in many OPV materials. Yet at present, the elementary mechanisms underlying this process in OPV materials, in particular the role of coupled electronic and nuclear motion for the transfer dynamics and yield, are still unclear. Here, we use ultrafast two-dimensional electronic spectroscopy (2DES) to investigate vibronic couplings in the initial, light-induced charge separation dynamics in a blend of poly-3-hexyl-thiophene (P3HT) and [6,6]-phenyl-C61 butyric acid methyl ester (PCBM), a prototypical OPV system. At early times, we observe a distinct breakup of the unstructured linear spectrum into a series of well-resolved vibronic resonances. A comparison to 2DES spectra of pure P3HT suggests that these resonances arise from the vibronic coupling between donor states of the polymer and charge-separated states involving the PCBM acceptors. We identify new, short-lived diagonal peaks, decaying substantially within only about 20–30 fs and lacking a well-resolved cross-peak structure. We argue that these unexpected dynamics likely arise from strong anharmonic couplings to several vibrational modes. One possibility to explain the rapid decay of the blend peaks would be passing of the photoexcited wavepacket through a conical intersection. Our results suggest that nonadiabatic dynamics on multidimensional potential energy surfaces (PESs) might be highly relevant for the initial steps of light-induced charge separation in organic materials. Since theoretical investigations of vibronically-assisted dynamics in such complex organic systems are just emerging, we hope that our results will stimulate further experimental and theoretical work on the role of such dynamics in artificial energy conversion materials. To this end, coherent multidimensional spectroscopy might be a key experimental tool.

Non-equilibrium x-ray spectroscopy using direct quantum dynamics.

Advances in experimental methodology aligned with technological developments, such as 3rd generation light sources, X-ray Free Electron Lasers, and High Harmonic Generation, have led to a paradigm shift in the capability of X-ray spectroscopy to deliver high temporal and spectral resolution on an extremely broad range of samples in a wide array of different environments. Importantly, the complex nature and high information content of this class of techniques mean that detailed theoretical studies are often essential to provide a firm link between the spectroscopic observables and the underlying molecular structure and dynamics. In this paper, we present approaches for simulating dynamical processes in X-ray spectroscopy based upon on-the-fly quantum dynamics with a Gaussian basis set. We show that it is possible to provide a fully quantum description of X-ray spectra without the need of precomputing highly multidimensional potential energy surfaces. It is applied to study two different dynamical situations, namely, the core-hole lifetime dynamics of the water monomer and the dissociation of recently studied using pump-probe X-ray spectroscopy. Our results compare favourably to previous experiments, while reducing the computational effort, providing the scope to apply them to larger systems.

Communication: Mode-dependent excited-state lifetime of phenol under the S1/S2 conical intersection.

Phenol can serve as a model for examining the deactivation of the aromatic amino acid tyrosine following UV excitation, which mainly occurs through a repulsive πσ* state along the O-H bond. The reaction barrier formed by the conical intersection between the optically bright S1 (ππ*) state and the dissociative S2 (πσ*) state does not inhibit O-H bond rupture even though the excitation energy is below the barrier height. To examine the O-H bond-rupture dynamics in association with the initial excited vibrational modes, we used a picosecond laser to investigate the vibrational-mode-dependent excited-state lifetime of phenol under the S1/S2 conical intersection. Unexpectedly short lifetimes were observed in the S1 state for a″ symmetric vibrational modes (including v4, v16a, τOH, and v5). These results clarify recent theoretical calculations showing that the relaxation from S1 to S2 either occurs via symmetry-allowed non-adiabatic transitions or is topographically linked to a lower energy minimum on the multidimensional potential energy surface.

One-dimensional cuts through multidimensional potential-energy surfaces by tunable x rays

The concept of the potential-energy surface (PES) and directional reaction coordinates is the backbone of ourdescription of chemical reaction mechanisms. Although the eigenenergies of the nuclear H ...

Exploring potential energy surfaces with gentlest ascent dynamics in combination with the shrinking dimer method and Newtonian dynamics

We revisit the so-called gentlest ascent dynamics reaction path model for finding saddle points of any index in multidimensional potential energy surfaces. The variational nature of the method is analyzed in detail, and an algorithm for the integration of its equations of motion is proposed based on the optimization-based shrinking dimer method. By means of three different two-dimensional model potential energy surfaces, we argue that the combination of the proposed method with Newtonian (dissipative) dynamics could lead to a practical scheme for the exhaustive exploration of potential energy landscapes.

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier**Supported by National Natural Science Foundation of China (11675148, 11505157), the Project of Youth Backbone Teachers of Colleges and Universities of Henan Province (2017GGJS008), the Foundation and Advanced Technology Research Program of Henan Province (162300410222), the Outstanding Young Talent Research Fund

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94–118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional (β2, γ, β4) deformation space. Taking the heavier 252Cf nucleus (with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β2 values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei (e.g., the Z=112–118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications (e.g., the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.

Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions.

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.

Extension of the effective relativistic coupling by asymptotic representation (ERCAR) approach to multi-dimensional potential energy surfaces: 3D model for CH3I

The Effective Relativistic Coupling by Asymptotic Representation (ERCAR) approach is a new method developed by us over the past few years that allows for the accurate diabatic representation of a molecular Coulomb and spin-orbit Hamiltonian and yields an analytic potential energy surface (PES) model for use in quantum dynamics simulations. So far, we focused on the single one dissociation coordinate defining the asymptote for diabatic representation and corresponding to removing a single, strongly relativistic atom from the remaining fragment. In the present study, we extend this approach to multiple dimensions for the first time. To this end, a 3D PES model is developed for the methyl iodide (CH3I) system accounting for all totally symmetric coordinates (C–I stretch, CH3 umbrella, and CH3 breathing modes). The model parameters are fitted with respect to high-level ab initio reference data for the spin space (“spin-free”) states which are reproduced with very good accuracy. The ERCAR method also yields the fine structure states and energies which are not computed ab initio. This is particularly important for the 1Q1 and 3Q0 fine structure states of CH3I which form an intersection that is considered key for the photodissociation dynamics of the system. Our new model shows that this intersection is considerably curved in the 2D subspace of the C–I stretch and CH3 umbrella coordinate. This will certainly affect the complicated nonadiabatic photodissociation dynamics of CH3I. The construction of a full 9D diabatic PES model is currently in progress.

Structural sensitivity of C[sbnd]H vibrational band in methyl benzoate

The CH vibrational bands of methyl benzoate are studied to understand its coupling pattern with other vibrational bands of the biological molecule. This will facilitate to understand the biological structure and dynamics in spectroscopic as well as in microscopic study. Due to the congested spectroscopic pattern, near degeneracy, and strong anharmonicity of the CH stretch vibrations, assignment of the CH vibrational frequencies are often misleading. Anharmonic vibrational frequency calculation with multidimensional potential energy surface interprets the CH vibrational spectra more accurately. In this article we have presented the importance of multidimensional potential energy surface in anharmonic vibrational frequency calculation and discuss the unexpected red shift of asymmetric CH stretch vibration of methyl group. The CD stretch vibrational band which is splitted to double peaks due to the Fermi resonance is also discussed here.

Refined analysis of the X̃ 2A2←X̃ 1A1 photoelectron spectrum of furan.

The X̃ 2A2←X̃ 1A1 photoelectron spectrum of furan has been studied by a time-independent eigenstate-free Raman wave function approach based on multi-dimensional potential energy surfaces obtained from explicitly correlated distinguishable clusters calculations. Individual vibronic transitions with the most significant Franck-Condon factors were determined by our recently developed residual-based algorithm for the calculation of eigenpairs in conjunction with the formalism of contracted invariant Krylov subspaces. The account of anharmonic and temperature effects allowed us to explain most bands in an experimental high-resolution zero kinetic energy photoelectron spectrum. This led to the reassignment of many spectral features, as well as a refined interpretation of the intensity mechanism for the corresponding transitions.

Comparison of Degrees of Potential-Energy-Surface Anharmonicity for Complexes and Clusters with Hydrogen Bonds

Previously calculated multidimensional potential-energy surfaces of the MeOH monomer and dimer, water dimer, malonaldehyde, formic acid dimer, free pyridine-N-oxide/trichloroacetic acid complex, and protonated water dimer were analyzed. The corresponding harmonic potential-energy surfaces near the global minima were constructed for series of clusters and complexes with hydrogen bonds of different strengths based on the behavior of the calculated multidimensional potential-energy surfaces. This enabled the introduction of an obvious anharmonicity parameter for the calculated potential-energy surfaces. The anharmonicity parameter was analyzed as functions of the size of the analyzed area near the energy minimum, the number of points over which energies were compared, and the dimensionality of the solved vibrational problem. Anharmonicity parameters for potential-energy surfaces in complexes with strong, medium, and weak H-bonds were calculated under identical conditions. The obtained anharmonicity parameters were compared with the corresponding diagonal anharmonicity constants for stretching vibrations of the bridging protons and the lengths of the hydrogen bridges.

Construction of reactive potential energy surfaces with Gaussian process regression: active data selection

ABSTRACTGaussian process regression (GPR) is an efficient non-parametric method for constructing multi-dimensional potential energy surfaces (PESs) for polyatomic molecules. Since not only the posterior mean but also the posterior variance can be easily calculated, GPR provides a well-established model for active learning, through which PESs can be constructed more efficiently and accurately. We propose a strategy of active data selection for the construction of PESs with emphasis on low energy regions. Through three-dimensional (3D) example of H3, the validity of this strategy is verified. The PESs for two prototypically reactive systems, namely, H + H2O ↔ H2 + OH reaction and H + CH4 ↔ H2 + CH3 reaction are reconstructed. Only 920 and 4000 points are assembled to reconstruct these two PESs respectively. The accuracy of the GP PESs is not only tested by energy errors but also validated by quantum scattering calculations.

Sub-500 fs electronically nonadiabatic chemical dynamics of energetic molecules from the S1 excited state: Ab initio multiple spawning study.

Energetic materials store a large amount of chemical energy. Different ignition processes, including laser ignition and shock or compression wave, initiate the energy release process by first promoting energetic molecules to the electronically excited states. This is why a full understanding of initial steps of the chemical dynamics of energetic molecules from the excited electronic states is highly desirable. In general, conical intersection (CI), which is the crossing point of multidimensional electronic potential energy surfaces, is well established as a controlling factor in the initial steps of chemical dynamics of energetic molecules following their electronic excitations. In this article, we have presented different aspects of the ultrafast unimolecular relaxation dynamics of energetic molecules through CIs. For this task, we have employed ab initio multiple spawning (AIMS) simulation using the complete active space self-consistent field (CASSCF) electronic wavefunction and frozen Gaussian-based nuclear wavefunction. The AIMS simulation results collectively reveal that the ultrafast relaxation step of the best energetic molecules (which are known to exhibit very good detonation properties) is completed in less than 500 fs. Many, however, exhibit sub-50 fs dynamics. For example, nitro-containing molecules (including C-NO2, N-NO2, and O-NO2 active moieties) relax back to the ground state in approximately 40 fs through similar (S1/S0)CI conical intersections. The N3-based energetic molecule undergoes the N2 elimination process in 40 fs through the (S1/S0)CI conical intersection. Nitramine-Fe complexes exhibit sub-50 fs Fe-O and N-O bond dissociation through the respective (S1/S0)CI conical intersection. On the other hand, tetrazine-N-oxides, which are known to exhibit better detonation properties than tetrazines, undergo internal conversion in a 400-fs time scale, while the relaxation time of tetrazine is very long (about 100 ns). Many other characteristics of sub-500 fs nonadiabatic decay of energetic molecules are discussed. In the end, many unresolved issues associated with the ultrafast nonadiabatic chemical dynamics of energetic molecules are presented.

The Topology of the Energy Landscapes of Macromolecules in the Torsion Angle Space and the Principle of the Minimum Energy Dissipation Rate in Conformational Relaxation

This article discusses some basic problems of structural biology and molecular dynamics simulation methods that need to be taken into account when considering, the protein folding problem, and prediction of 3D-structures for biopolymers. A multidimensional Fourier series expansions were formulated for the energy landscapes of the systems with conformational mobility, These energy landscape representations are correct from the viewpoint of the topology of the macromolecule configuration spaces. The problem of the single global minimum on the energy landscape for proteins is discussed and is formulated in tems of phase rules for the component of Fourier expansions. This rule is formally similar to the problem of diffraction on a multidimensional cubic lattice. The calibration of biopolymer force fields and their correspondence to topologically correct energy landscapes are discussed. Equations of motion were obtained in a matrix form for the relaxation of a representative point position on a multidimensional potential energy surface. The solutions of the equations for conformational relaxation were shown to obey the principle of the minimum energy dissipation rate at a given relaxation rate of potential energy (or folding rate).

Toolkit for the Construction of Reproducing Kernel-Based Representations of Data: Application to Multidimensional Potential Energy Surfaces.

In the early days of computation, slow processor speeds limited the amount of data that could be generated and used for scientific purposes. In the age of big data, the limiting factor usually is the method with which large amounts of data are analyzed and useful information is extracted. A typical example from chemistry are high-level ab initio calculations for small systems, which have nowadays become feasible even if energies at many different geometries are required. Molecular dynamics simulations often require several thousand distinct trajectories to be run. Under such circumstances suitable analytical representations of potential energy surfaces (PESs) based on ab initio calculations are required to propagate the dynamics at an acceptable cost. In this work we introduce a toolkit which allows the automatic construction of multidimensional PESs from gridded ab initio data based on reproducing kernel Hilbert space (RKHS) theory. The resulting representations require no tuning of parameters and allow energy and force evaluations at ab initio quality at the same cost as empirical force fields. Although the toolkit is primarily intended for constructing multidimensional potential energy surfaces for molecular systems, it can also be used for general machine learning purposes. The software is published under the MIT license and can be downloaded, modified, and used in other projects for free.

Modeling Coronene Nanostructures: Analytical Potential, Stable Configurations and Ab Initio Energies

Coronene is one of the basic polycyclic aromatic hydrocarbons (PAHs) used to test the reliabilty of a multidimensional potential energy surface (PES) and to assess its influence on the formation dynamics of PAH clusters with defined physical and chemical properties. We report an analytical potential energy surface for modeling the coronene–coronene interaction, whose parameters were fine-tuned on dispersion-corrected DFT estimations performed within the generalized gradient PBE approximation, that is suitable for describing molecular aggregates involving aromatic species. This model was used to build a potential function for coronene clusters (Corn) that was then applied in a detailed global geometry optimization study with an evolutionary algorithm. A large variety of low-energy structures were obtained for the Corn (n = 2–15) clusters ranging from columnar-type to two-stacked in a handshake association motifs. Moreover, it was found that a transition from a single-stack columnar regime to other more com...