Born-Oppenheimer Potential Energy Surface Research Articles

Imaging a multidimensional multichannel potential energy surface: Photodetachment of H(-)(NH3) and NH4 (.).

Probes of the Born-Oppenheimer potential energy surfaces governing polyatomic molecules often rely on spectroscopy for the bound regions or collision experiments in the continuum. A combined spectroscopic and half-collision approach to image nuclear dynamics in a multidimensional and multichannel system is reported here. The Rydberg radical NH4 and the double Rydberg anion NH4 (-) represent a polyatomic system for benchmarking electronic structure and nine-dimensional quantum dynamics calculations. Photodetachment of the H(-)(NH3) ion-dipole complex and the NH4 (-) DRA probes different regions on the neutral NH4 PES. Photoelectron energy and angular distributions at photon energies of 1.17, 1.60, and 2.33 eV compare well with quantum dynamics. Photoelectron-photofragment coincidence experiments indicate dissociation of the nascent NH4 Rydberg radical occurs to H + NH3 with a peak kinetic energy of 0.13 eV, showing the ground state of NH4 to be unstable, decaying by tunneling-induced dissociation on a time scale beyond the present scope of multidimensional quantum dynamics.

On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods.

The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabaticdynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabaticdynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results show that the inclusion of DBOC can enhance the accuracy of surface hopping simulations when two conditions are simultaneously satisfied: (1) nuclei have kinetic energy lower than DBOC and (2) PESs are not strongly nonadiabatically coupled. The inclusion of DBOC is detrimental in situations where its energy scale becomes very high or even diverges, because in these regions PESs are also very strongly coupled. In this case, the true quantum formalism heavily relies on an interplay between diagonal and off-diagonal nonadiabatic couplings while surface hopping approaches treat diagonal terms as PESs and off-diagonal ones stochastically.

Thermal-light-induced dynamics: Coherence and revivals inV-type and molecular Jaynes-Cummings systems

We examine the interaction of thermal light with matter with emphasis on two aspects that have not been considered before. By employing a fully quantized Jaynes-Cummings--type interaction model on a $V$-type three-level system, we show that multimode thermal light induces coherence in the excited material states. This is in contrast to previous studies that suggest thermal light cannot induce coherence in material systems. We also show that the ratio between the field detuning and the interaction constant has a significant influence on the characteristic time-dependent dynamics. In particular, for some ratio regimes, the thermal light induces dynamics with a ``coherentlike'' collapse and revivals pattern rather than the familiar pattern. We then extend the Jaynes-Cummings model to a two-state Born-Oppenheimer potential energy surface molecular system where the internal vibrational degrees of freedom are fully taken into account. The matter-field bipartite system is represented, and propagated, in the full electronic bond-coordinate Fock product space. We show that single-mode thermal light induces extensive excited-state vibrational coherence in the molecule that, when observed in coordinate space, exhibits wave-packet-like dynamics. The molecular Jaynes-Cummings model we propose is useful for cavity molecular dynamics simulations.

Efficient Computational Research Protocol to Survey Free Energy Surface for Solution Chemical Reaction in the QM/MM Framework: The FEG-ER Methodology and Its Application to Isomerization Reaction of Glycine in Aqueous Solution.

In solution chemical reaction, we often need to consider a multidimensional free energy (FE) surface (FES) which is analogous to a Born-Oppenheimer potential energy surface. To survey the FES, an efficient computational research protocol is proposed within the QM/MM framework; (i) we first obtain some stable states (or transition states) involved by optimizing their structures on the FES, in a stepwise fashion, finally using the free energy gradient (FEG) method, and then (ii) we directly obtain the FE differences among any arbitrary states on the FES, efficiently by employing the QM/MM method with energy representation (ER), i.e., the QM/MM-ER method. To validate the calculation accuracy and efficiency, we applied the above FEG-ER methodology to a typical isomerization reaction of glycine in aqueous solution, and reproduced quite satisfactorily the experimental value of the reaction FE. Further, it was found that the structural relaxation of the solute in the QM/MM force field is not negligible to estimate correctly the FES. We believe that the present research protocol should become prevailing as one computational strategy and will play promising and important roles in solution chemistry toward solution reaction ergodography.

Time-independent eigenstate-free calculation of vibronic spectra beyond the harmonic approximation.

The calculation of vibronic spectra and resonance Raman intensities can be performed on the basis of the Raman wavefunction (RWF) formalism. In general, the well-known sum-over-states (SOS) and time-dependent methods can be applied for calculating the RWF. We present an alternative route in which the RWF is determined pointwise in a spectral range on the basis of the inhomogeneous Schrödinger equation using an iterative subspace method, in which explicit state-by-state calculations of vibrational eigenstates are bypassed. We study this approach within the framework of vibrational configuration interaction theory in conjunction with high-level electronic structure calculations for the multidimensional Born-Oppenheimer potential energy surface. The method benefits from an implicit account of interference effects between vibrational states, so that its computational cost correlates with the required resolution in the spectra. The accuracy and efficiency of the method with respect to comparable SOS calculations are tested for the simulation of the photoelectron spectra of ClO2, HS2 (-), ZnOH(-), and Zn(H2O)(+).

Laser-induced dissociation dynamics of triatomic molecule in electronic excited states: A full-dimensional quantum mechanics study.

We present a detailed theoretical approach to investigate the laser-induced dissociation dynamics of a triatomic molecule on its electronic excited state in full dimensional case. In this method, the time evolution of the time-dependent system is propagated via combined the split operator method and the expansion of Chebyshev polynomials (or short-time Chebyshev propagation) and the system wave functions are expanded in terms of molecular rotational bases. As an example of the application of this formalism, the dissociation dynamics of H3(+)→H2(+)+H induced by ultrashort UV laser pulses are investigated on new Born-Oppenheimer potential energy surfaces. Our numerical results show that the signals of dissociation products will be easier to observe as the increasing of field strength. Driving by a 266 nm laser beam, the calculated central value of kinetic-energy-release is 2.04 eV which shows excellent agreement with the experimental estimation of 2.1 eV. When the H3(+) ion is rotationally excited, the spatial distribution of product fragments will become well converged.

A generalized force-modified potential energy surface for mechanochemical simulations.

We describe the modifications that a spatially varying external load produces on a Born-Oppenheimer potential energy surface (PES) by calculating static quantities of interest. The effects of the external loads are exemplified using electronic structure calculations (at the HF/6-31G(∗∗) level) of two different molecules: ethane and hexahydro-1,3,5-trinitro-s-triazine (RDX). The calculated transition states and Hessian matrices of stationary points show that spatially varying external loads shift the stationary points and modify the curvature of the PES, thereby affecting the harmonic transition rates by altering both the energy barrier as well as the prefactor. The harmonic spectra of both molecules are blueshifted with increasing compressive "pressure." Some stationary points on the RDX-PES disappear under application of the external load, indicating the merging of an energy minimum with a saddle point.

Anharmonic Franck-Condon Factors for the X̃(2)B1 ← X̃(1)A1 Photoionization of Ketene.

The X̃(2)B1 ← X̃(1)A1 photoelectron spectra of ketene and its doubly deuterated isotopologue have been computed from correlated vibrational wave functions as determined from vibrational configuration interaction theory relying on multidimensional Born-Oppenheimer potential energy surfaces being obtained from explicitly correlated coupled-cluster calculations. Duschinsky effects were accounted for in all cases. Excellent agreement with available experimental data was achieved.

Semi-quartic force fields retrieved from multi-mode expansions: Accuracy, scaling behavior, and approximations.

Semi-quartic force fields (QFF) rely on a Taylor-expansion of the multi-dimensional Born-Oppenheimer potential energy surface (PES) and are frequently used within the calculation of anharmonic vibrational frequencies based on 2nd order vibrational perturbation theory (VPT2). As such they are usually determined by differentiation of the electronic energy with respect to the nuclear coordinates. Alternatively, potential energy surfaces can be expanded in terms of multi-mode expansions, which typically do not require any derivative techniques. The computational effort to retrieve QFF from size-reduced multi-mode expansions has been studied and has been compared with standard Taylor-expansions. As multi-mode expansions allow for the convenient introduction of subtle approximations, these will be discussed in some detail. In addition, a preliminary study about the applicability of a generalized Duschinsky transformation to QFFs is provided. This transformation allows for the efficient evaluation of VPT2 frequencies of isotopologues from the PES of the parent compound and thus avoids the recalculation of PESs in different axes systems.

Correlated electron-nuclear dynamics with conditional wave functions.

The molecular Schrödinger equation is rewritten in terms of nonunitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and nonadiabatic coupling elements. The concept of the potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.

Quantum Dynamics Simulations Reveal Vibronic Effects on the Optical Properties of [n]Cycloparaphenylenes

The size-dependent ultraviolet/visible photophysical property trends of [n]cycloparaphenylenes ([n]CPPs, n = 6, 8, and 10) are theoretically investigated using quantum dynamics simulations. For geometry optimizations on the ground- and excited-state Born-Oppenheimer potential energy surfaces (PESs), we employ density functional theory (DFT) and time-dependent DFT calculations. Harmonic normal-mode analyses are carried out for the electronic ground state at Franck-Condon geometries. A diabatic Hamiltonian, comprising four low-lying singlet excited electronic states and 26 vibrational degrees of freedom of CPP, is constructed within the linear vibronic coupling (VC) model to elucidate the absorption spectral features in the range of 300-500 nm. Quantum nuclear dynamics is simulated within the multiconfiguration time-dependent Hartree approach to calculate the vibronic structure of the excited electronic states. The symmetry-forbidden S0 → S1 transition appears in the longer wavelength region of the spectrum with weak intensity due to VC. It is found that the Jahn-Teller and pseudo-Jahn-Teller effects in the doubly degenerate S2 and S3 electronic states are essential in the quantitative interpretation of the experimental observation of a broad absorption peak around 340 nm. The vibronic mixing of the S1 state with higher electronic states is responsible for the efficient photoluminescence from the S1 state. The fluorescence properties are characterized on the basis of the stationary points of the excited-state PESs. The findings reveal that vibronic effects become important in determining the photophysical properties of CPPs with increased ring size.

A quantum reactive scattering perspective on electronic nonadiabaticity

Based on quantum reactive-scattering theory, we propose a method for studying the electronic nonadiabaticity in collision processes involving electron-ion rearrangements. We investigate the state-to-state transition probability for electron-ion rearrangements with two comparable approaches. In the first approach the information of the electron is only contained in the ground-state Born-Oppenheimer potential-energy surface, which is the starting point of common reactive-scattering calculations. In the second approach, the electron is explicitly taken into account and included in the calculations at the same level as the ions. Hence, the deviation in the results between the two approaches directly reflects the electronic nonadiabaticity during the collision process. To illustrate the method, we apply it to the well-known proton-transfer model of Shin and Metiu (one electron and three ions), generalized by us in order to allow for reactive scattering channels. It is shown that our explicit electron approach is able to capture electronic nonadiabaticity and the renormalization of the reaction barrier near the classical turning points of the potential in nuclear configuration space. In contrast, system properties near the equilibrium geometry of the asymptotic scattering channels are hardly affected by electronic nonadiabatic effects. We also present an analytical expression for the transition amplitude of the asymmetric proton-transfer model based on the direct evaluation of integrals over the involved Airy functions.

Determining factors for the accuracy of DMRG in chemistry.

The Density Matrix Renormalization Group (DMRG) algorithm has been a rising star for the accurate ab initio exploration of Born-Oppenheimer potential energy surfaces in theoretical chemistry. However, owing to its iterative numerical nature, pitfalls that can affect the accuracy of DMRG energies need to be circumvented. Here, after a brief introduction into this quantum chemical method, we discuss criteria that determine the accuracy of DMRG calculations.

Finite-temperature properties of strongly anharmonic and mechanically unstable crystal phases from first principles

We introduce a methodology for constructing anharmonic vibrational Hamiltonians that are parametrized from first-principles electronic-structure calculations and can be used to study high-temperature properties of crystalline materials. Our method provides an accurate description of the Born-Oppenheimer potential energy surface of a crystal that can be systematically refined and is invariant to space-group symmetries of the ideal reference crystal and finite rigid-body rotations and translations. These features make it ideally suited for Monte Carlo or molecular dynamics simulations to predict finite-temperature thermodynamic properties, structural phase transitions, and thermal conductivity. We use this method to construct an anharmonic Hamiltonian for ZrH${}_{2}$, which exhibits a high-temperature cubic phase that undergoes a symmetry-breaking second-order transition to one of three equivalent tetragonal phases upon cooling. Although density functional theory predicts a zero-Kelvin dynamical instability of cubic ZrH${}_{2}$, we find via Monte Carlo simulation that the cubic phase can be anharmonically stabilized at high temperature and predict a cubic-to-tetragonal transition temperature that is in good agreement with extrapolation from experiments. We also calculate finite-temperature free energies for the cubic and tetragonal phases, finding that they are consistent with the phenomenological Landau theory of second-order phase transitions.

POTLIB2Math: A Mathematica interface to the potential energy surface library for chemical systems

The theoretical description of molecular dynamics proceeds from the specification of an appropriate Born–Oppenheimer potential energy surface (PES) or surfaces. For many chemical systems, such surfaces are incorporated within a repository of standardized FORTRAN codes known as POTLIB. The present work describes a Mathematica package that uses a MathLink interface to interactively call POTLIB subroutines from within a Mathematica session. This allows for rapid prototyping and deployment of new algorithms and is useful for both pedagogical and research applications in chemical physics. We present basic usage of the package functions and several simple applications for illustration. Program summaryProgram title: POTLIB2MathCatalogue identifier: AEQJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEQJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 63859No. of bytes in distributed program, including test data, etc.: 1481706Distribution format: tar.gzProgramming language: C, FORTRAN, and Mathematica.Computer: Developed and tested on GNU/Linux PC, Macintosh, and Windows PC platforms running Mathematica version 8 or higher.Operating system: Tested on MacOSX, SUSE Linux, and WindowsXP/7/8.RAM: Varies depending on user-defined applications.Classification: 16.8.External routines: GNU make, gcc, gfortran, Mathematica, and MathLink DeveloperKitSubprograms used:Cat IdTitleReferenceADPJ_v1_0POTLIB 2001CPC 144(2002)169Nature of problem:POTLIB [1, 2] is a collection of FORTRAN subprograms that calculate potential energy surfaces and gradients for various chemical systems as a function of molecular geometry. The objective of this work is to develop an interface that allows users to interactively execute POTLIB subprograms from within a Mathematica session.Solution method:POTLIB2Math is a fully-documented Mathematica package that uses a MathLink interface for passing data between Mathematica and POTLIB subprograms. GNU make and C/FORTRAN compilers are used to automate building the executables on various platforms.Running time:The examples included in the distribution file take just a few minutes to run.

Interpolation of multi-sheeted multi-dimensional potential-energy surfaces via a linear optimization procedure

Significant progress has been achieved in recent years with the development of high-dimensional permutationally invariant analytic Born-Oppenheimer potential-energy surfaces, making use of polynomial invariant theory. In this work, we have developed a generalization of this approach which is suitable for the construction of multi-sheeted multi-dimensional potential-energy surfaces exhibiting seams of conical intersections. The method avoids the nonlinear optimization problem which is encountered in the construction of multi-sheeted diabatic potential-energy surfaces from ab initio electronic-structure data. The key of the method is the expansion of the coefficients of the characteristic polynomial in polynomials which are invariant with respect to the point group of the molecule or the permutation group of like atoms. The multi-sheeted adiabatic potential-energy surface is obtained from the Frobenius companion matrix which contains the fitted coefficients. A three-sheeted nine-dimensional adiabatic potential-energy surface of the (2)T2 electronic ground state of the methane cation has been constructed as an example of the application of this method.

Calculation of Rotation–Vibration Energy Levels of the Water Molecule with Near-Experimental Accuracy Based on an ab Initio Potential Energy Surface

A recently computed, high-accuracy ab initio Born-Oppenheimer (BO) potential energy surface (PES) for the water molecule is combined with relativistic, adiabatic, quantum electrodynamics, and, crucially, nonadiabatic corrections. Calculations of ro-vibrational levels are presented for several water isotopologues and shown to have unprecedented accuracy. A purely ab initio calculation reproduces some 200 known band origins associated with seven isotopologues of water with a standard deviation (σ) of about 0.35 cm(-1). Introducing three semiempirical scaling parameters, two affecting the BO PES and one controlling nonadiabatic effects, reduces σ below 0.1 cm(-1). Introducing one further rotational nonadiabatic parameter gives σ better than 0.1 cm(-1) for all observed ro-vibrational energy levels up to J = 25. We conjecture that the energy levels of closed-shell molecules with roughly the same number of electrons as water, such as NH3, CH4, and H3O(+), could be calculated to this accuracy using an analogous procedure. This means that near-ab initio calculations are capable of predicting transition frequencies with an accuracy only about a factor of 5 worse than high resolution experiments.

Ab initio non-adiabatic molecular dynamics

Adiabatic nuclear potential energy surfaces (PESs) defined via the Born-Oppenheimer (BO) approximation are a fundamental concept underlying chemical reactivity theory. For a wide range of excited-state phenomena such as radiationless decay, energy and charge transfer, and photochemical reactions, the BO approximation breaks down due to strong couplings between two or more BO PESs. Non-adiabatic molecular dynamics (NAMD) is the method of choice to model these processes. We review new developments in quantum-classical dynamics, analytical derivative methods, and time-dependent density functional theory (TDDFT) which have lead to a dramatic expansion of the scope of ab initio NAMD simulations for molecular systems in recent years. We focus on atom-centered Gaussian basis sets allowing highly efficient simulations for molecules and clusters, especially in conjunction with hybrid density functionals. Using analytical derivative techniques, forces and derivative couplings can be obtained with machine precision in a given basis set, which is crucial for accurate and stable dynamics. We illustrate the performance of surface-hopping TDDFT for photochemical reactions of the lowest singlet excited states of cyclohexadiene, several vitamin D derivatives, and a bicyclic cyclobutene. With few exceptions, the calculated quantum yields and excited state lifetimes agree qualitatively with experiment. For systems with ∼50 atoms, the present Turbomole implementation allows NAMD simulations with 0.2-0.4 ns total simulation time using hybrid density functionals and polarized double zeta valence basis sets on medium-size compute clusters. We close by discussing open problems and future directions.

An adaptive potential energy surface generation method using curvilinear valence coordinates

An automatic Born-Oppenheimer potential energy surface (PES) generation method AGAPES is presented designed for the calculation of vibrational spectra of large rigid and semi-rigid polyatomic molecules within the mid-infrared energy range. An adaptive approach guided by information from intermediate vibrational calculations in connection with a multi-mode expansion of the PES in internal valence coordinates is used and its versatility is tested for a selection of molecules: HNO, HClCO, and formaldoxime. Significant computational savings are reported. The possibility of linear scaling of the sampling grid size with the molecular size due to decrease of correlation of remote coordinates in large molecules is examined and finally, possible improvements are suggested.

Nonadiabatic investigations of ro-vibrational frequencies within the systems , H2, and prospects for : use of distance-dependent effective masses

For small hydrogenic systems the discrepancy between theoretical and experimental studies of ro-vibrational spectra is mostly related to the neglect of adiabatic and non-adiabatic effects on the ro-vibrational eigenvalues. In the case of and its isotopomers, detailed investigations of low lying ro-vibrational excitations have been performed. Using gaussian geminals an absolute accuracy of the Born–Oppenheimer potential energy surface (PES) by ∼0.02 cm−1 was reached. Of similar quality are calculations of relativistic effects and diagonal adiabatic contributions. Non-adiabaticity can be simulated by using atomic masses for vibrational motion and nuclear masses for rotational motion, so that the deviation to experiment can be reduced to a few hundredths of a wavenumber. Recently, a rigorous non-adiabatic theory in terms of a single potential energy surface had been developed and was tested numerically for and H2. Within this new non-adiabatic theory distance-dependent effective nuclear masses have to be used. Our main interest is to use these new ideas for taking into account the effects of non-adiabaticity on the ro-vibrational spectrum of and its isotopomers. Within a perturbative approach we investigate the influence of the operator of nuclear kinetic energy of a triatomic molecule on the electronic wave function. For the asymptotic arrangement of a nearly separated atom–diatomic system we can calculate numerically with high accuracy the distance-dependent effective nuclear masses for and H2. The kinetic energy operator for a triatomic molecule describing ro-vibrational motion has many different terms, where different effective masses have to be taken into account. Within the present work for , the distance-dependent effective mass for the diatomic motion part, using Jacobi coordinates, will be presented.