Improved direct diabatization and coupled potential energy surfaces for the photodissociation of ammonia

Diabatic potential energy surfaces are a convenient starting point for dynamics calculations of photochemical processes, and they can be calculated by the fourfold way direct diabatization scheme. Here we present an improved definition of the reference orbital for applying the fourfold way direct diabatization scheme to ammonia. The improved reference orbital is a geometry-dependent hybrid orbital that allows one to define consistent dominant configuration lists at all geometries important for photodissociation. Using diabatic energies calculated with the new reference orbital and consistent dominant configuration lists, we have refitted the analytical representations of the ground and the first electronically excited singlet-state potential energy surfaces and the diabatic coupling surface. Improved functional forms were used to reproduce the experimental dissociation energies and excitation energies, which will be important for subsequent simulations of photochemical dynamics. We find that the lowest-energy conical intersection point is at 5.16 eV, with C _2v symmetry. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. This article is part of the special issue dedicated to the memory of the late Professor Fernando Bernardi.     

A global characterization and similarity analysis of two-dimensional potential energy surfaces

Potential energy surfaces can be classified into combinatiorial equivalence classes, based on their partitioning into catchment regions. Two classification theorems are proven: one for reaction spheres and another for reaction tori. A method for constructing all possible equivalence classes of reaction spheres and reaction tori is presented. As illustration of the general results, it is shown that not all the two-dimensional reaction spheres are combinatorially equivalent to polyhedra in the three-dimensional Euclidean space. As examples, several reaction spheres are calculated by using the RHF method at the 3-21G * level, describing the interactions between a series of polyatomic ions and H⁺. The calculations show that the potential energy surface of the CO …?H⁺ interaction, combinatorially equivalent to that of the NO^?₃ …?H⁺ interaction, is not combinatorially equivalent to any polyhedron in 3-space; however, the combinatorially different potential energy surface of the PO …? H⁺ interaction is equivalent to a polyhedron in 3-space. The topological classification scheme is proposed for the study of similarities between various families of chemical reactions.     

A new method to generate spin-orbit coupled potential energy surfaces: effective relativistic coupling by asymptotic representation

A new method has been developed to generate fully coupled potential energy surfaces including derivative and spin-orbit coupling. The method is based on an asymptotic (atomic) representation of the molecular fine structure states and a corresponding diabatization. The effective relativistic coupling is described by a constant spin-orbit coupling matrix and the geometry dependence of the coupling is accounted for by the diabatization. This approach is very efficient, particularly for certain systems containing a very heavy atom, and yields consistent results throughout nuclear configuration space. A first application to a diatomic system is presented as proof of principle and is compared to accurate ab initio calculations. However, the method is widely applicable to general polyatomic systems in full dimensionality, containing several relativistic atoms and treating higher order relativistic couplings as well.     

Optimizing conical intersections without derivative coupling vectors: application to multistate multireference second-order perturbation theory (MS-CASPT2)

We introduce a new method for optimizing minimal energy conical intersections (MECIs), based on a sequential penalty constrained optimization in conjunction with a smoothing function. The method is applied to optimize MECI geometries using the multistate formulation of second-order multireference perturbation theory (MS-CASPT2). Resulting geometries and energetics for conjugated molecules including ethylene, butadiene, stilbene, and the green fluorescent protein chromophore are compared with state-averaged complete active space self-consistent field (SA-CASSCF) and, where possible, benchmark multireference single- and double-excitation configuration interaction (MRSDCI) optimizations. Finally, we introduce the idea of "minimal distance conical intersections", which are points on the intersection seam that lie closest to some specified geometry such as the Franck-Condon point or a local minimum on the excited state.     

HN2(2A') electronic manifold. II. Ab initio based double-sheeted DMBE potential energy surface via a global diabatization angle

A double-sheeted double many-body expansion potential energy surface is reported for the coupled 12A'/22A' states of HN2 by fitting about 6000 ab initio energies. All crossing seams are described to their full extent on the basis of converged results. The lowest adiabatic sheet is fitted with a rmsd of 0.8 kcal mol-1 with respect to the calculated energies up to 100 kcal mol-1 above the absolute minimum, and the topology of the first excited-state investigated with the aid of the upper adiabatic sheet. A new scheme that overcomes obstacles in previous diabatization methods for modeling global double-sheeted potential energy surfaces is also reported. The novel approach uses a global diabatization angle which allows the diabats to mimic both the crossing seams and atom-diatom dissociation limits.     

Flying onto global minima on potential energy surfaces: A swarm intelligence guided route to molecular electronic structure

A novel quantum‐classical recipe for locating the global minimum on the potential energy surface of a large molecule and simultaneously predicting the associated electronic charge distribution is developed by interfacing the classical particle swarm optimization with a near optimal unitary evolution scheme for the trial one electron density matrix. The unitary transformation is generated by an antihermitian matrix linked to the molecular electronic Hamiltonian at the instantaneous nuclear configurations discovered by the swarm as it flies. The algorithm is used to predict the extensive reorganization of electronic charge distribution and bond lengths in polythiophene oligomers on doping at various levels.     

Spin-orbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation

A new method has been reported recently [H. Ndome, R. Welsch, and W. Eisfeld, J. Chem. Phys. 136, 034103 (2012)] that allows the efficient generation of fully coupled potential energy surfaces (PESs) including derivative and spin-orbit (SO) coupling. The method is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator and therefore is called effective relativistic coupling by asymptotic representation (ERCAR). The resulting diabatic spin-orbit coupling matrix is constant and the geometry dependence of the coupling between the eigenstates is accounted for by the diabatization. This approach allows to generate an analytical model for the fully coupled PESs without performing any ab initio SO calculations (except perhaps for the atoms) and thus is very efficient. In the present work, we study the performance of this new method for the example of hydrogen iodide as a well-established test case. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations. The energies of the adiabatic fine structure states are reproduced in excellent agreement with reference ab initio data. It is shown that the accuracy of the ERCAR approach mainly depends on the quality of the underlying ab initio data. This is also the case for dissociation and vibrational level energies, which are influenced by the SO coupling. A method is presented how one-electron operators and the corresponding properties can be evaluated in the framework of the ERCAR approach. This allows the computation of dipole and transition moments of the fine structure states in good agreement with ab initio data. The new method is shown to be very promising for the construction of fully coupled PESs for more complex polyatomic systems to be used in quantum dynamics studies.     

The PyPES library of high quality semi‐global potential energy surfaces

In this article, we present a Python‐based library of high quality semi‐global potential energy surfaces for 50 polyatomic molecules with up to six atoms. We anticipate that these surfaces will find widespread application in the testing of new potential energy surface construction algorithms and nuclear ro‐vibrational structure theories. To this end, we provide the ability to generate the energy derivatives required for Taylor series expansions to sixth order about any point on the potential energy surface in a range of common coordinate systems, including curvilinear internal, Cartesian, and normal mode coordinates. The PyPES package, along with FORTRAN, C, MATLAB and Mathematica wrappers, is available at http://sourceforge.net/projects/pypes-lib . © 2015 Wiley Periodicals, Inc.     

A useful mapping of triatomic potential energy surfaces

We present in this paper a mapping of triatomic three-dimensional Born-Oppenheimer potential energy surfaces V for which all arrangement channels are represented evenhandedly. This representation is very useful for visualizing the geometrical and dynamical properties of such surfaces.     

A useful triangular plot of triatomic potential energy surfaces

A triangular plot of triatomic potential energy surfaces is suggested in which the hidden coordinate - the perimeter of the molecule or the sum of squares of the three bond distances - is allowed to relax in order to give the lowest potential energy. This graphical representation preserves the full permutational symmetry of the problem. Examples are presented for the H₃ and HO₂ systems.     

A hierarchical family of three-dimensional potential energy surfaces for He-CO

A hierarchical family of five three-dimensional potential energy surfaces has been developed for the benchmark He-CO system. Four surfaces were obtained at the coupled cluster singles and doubles level of theory with a perturbational estimate of triple excitations, CCSD(T), and range in quality from the doubly augmented double-zeta basis set to the complete basis set (CBS) limit. The fifth corresponds to an approximate CCSDT/CBS surface (CCSD with iterative triples/CBS, denoted CBS+corr). The CBS limit results were obtained by pointwise basis set extrapolations of the individual counterpoise-corrected interaction energies. For each surface, over 1000 interaction energies were accurately interpolated using a reproducing kernel Hilbert space approach with an R-6+R-7 asymptotic form. In each case, both three-dimensional and effective two-dimensional surfaces were developed. In standard Jacobi coordinates, the final CBS+corr surface has a global minimum at rCO=2.1322a0,R=6.418a0, and gamma=70.84 degrees with a well depth of -22.34 cm-1. The other four surfaces have well depths ranging from -14.83 cm-1 [CCSD(T)/d-aug-cc-pVDZ] to -22.02 cm-1 [CCSD(T)/CBS]. For each of these surfaces the infrared spectrum has been accurately calculated and compared to experiment, as well as to previous theoretical and empirical surfaces. The final CBS+corr surface exhibits root-mean-square and maximum errors compared to experiment (4He) of just 0.03 and 0.04 cm-1, respectively, for all 42 transitions and is the most accurate ab initio surface to date for this system. Other quantities investigated include the interaction second virial coefficient, the integral cross sections, and thermal rate coefficients for rotational relaxation of CO by He, and rate coefficients for CO vibrational relaxation by He. All the observable quantities showed a smooth convergence with respect to the quality of the underlying interaction surface.     

ForceFit: A code to fit classical force fields to quantum mechanical potential energy surfaces

The ForceFit program package has been developed for fitting classical force field parameters based upon a force matching algorithm to quantum mechanical gradients of configurations that span the potential energy surface of the system. The program, which runs under UNIX and is written in C++, is an easy‐to‐use, nonproprietary platform that enables gradient fitting of a wide variety of functional force field forms to quantum mechanical information obtained from an array of common electronic structure codes. All aspects of the fitting process are run from a graphical user interface, from the parsing of quantum mechanical data, assembling of a potential energy surface database, setting the force field, and variables to be optimized, choosing a molecular mechanics code for comparison to the reference data, and finally, the initiation of a least squares minimization algorithm. Furthermore, the code is based on a modular templated code design that enables the facile addition of new functionality to the program. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Exploring artificial neural networks to model interatomic and intermolecular potential energy surfaces

We demonstrate how a back-propagation artificial neural network can be trained to represent a potential energy surface (PES) in a formless manner with limited data points and exploited to predict interaction energies for configurations not included in the training set. A similar exercise is undertaken for predicting the eigenvalues and eigenvectors of a model Hamiltonian matrix that delicately depends on parameters and exhibits crossing of eigen values.     

Using redundant coordinates to represent potential energy surfaces with lower-dimensional functions

We propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction OH+H(2)-->H(2)O+H.     

A topological stochastic approach to the study of multidimensional potential energy surfaces of chemical reactions

In this article we propose a new approach for investigating the properties of multidimensional potential energy surfaces in chemical reactions, based on relations of each multidimensional surface to its one-dimensional image which is the chemical reaction tree. This approach makes it possible to find a common number of independent channels in chemical reactions for complex systems and to construct the probable models.     

A Comparison of radiationless transitions involving single-minimum and double minima potential energy surfaces

The quantum-statistical-mechanical (QSM) approach to molecular relaxation phenomena is employed to compare radiationless transitions originating from an electronic state characterized by a single minimum and double minima potential surface for a vibronically active, non-totally symmetric mode. The vibronic level dependence of the decay rates of these two cases has been investigated for both small and large energy gap transitions. It is shown that the behavior of a molecular system is quite different for an initial state possesing a double minima potential surface as compared to the case in which the initial state possesses a single minimum.     

Model potential energy surfaces for approach of an electrophile to acetylene and fluoroacetylene

Non-empirical LCAO MO SCF calculations have been made on cross sections through prototype potential energy surfaces for the initial approach of an electrophile to acetylene and fluoroacetylene. The electrophile has been simulated by a unit positive charge and this is shown to give a computationally inexpensive means of providing information on such processes.