Multiconfigurational nuclear-electronic orbital approach: Incorporation of nuclear quantum effects in electronic structure calculations (original) (raw)
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Vibrational analysis for the nuclear–electronic orbital method
The Journal of Chemical Physics, 2003
The methodology for a vibrational analysis within the nuclear-electronic orbital ͑NEO͒ framework is presented. In the NEO approach, specified nuclei are treated quantum mechanically on the same level as the electrons, and mixed nuclear-electronic wave functions are calculated variationally with molecular orbital methods. Both electronic and nuclear molecular orbitals are expressed as linear combinations of Gaussian basis functions. The NEO potential energy surface depends on only the classical nuclei, and each point on this surface is optimized variationally with respect to all molecular orbitals as well as the centers of the nuclear basis functions. The NEO vibrational analysis involves the calculation, projection, and diagonalization of a numerical Hessian to obtain the harmonic vibrational frequencies corresponding to the classical nuclei. This analysis allows the characterization of stationary points on the NEO potential energy surface. It also enables the calculation of zero point energy corrections and thermodynamic properties such as enthalpy, entropy, and free energy for chemical reactions on the NEO potential energy surface. Illustrative applications of this vibrational analysis to a series of molecules and to a nucleophilic substitution reaction are presented.
The Journal of Chemical Physics, 2013
An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 implements the model where electrons and light nuclei are treated simultaneously at Hartree-Fock or second-order Möller-Plesset levels of theory. The APMO-MOLPRO interface allows to include highlevel electronic correlation as implemented in the MOLPRO package and to describe nuclear quantum effects at Hartree-Fock level of theory with the APMO code. Different model systems illustrate the implementation: 4 He 2 dimer as a protype of a weakly bound van der Waals system; isotopomers of [He-H-He] + molecule as an example of a hydrogen bonded system; and molecular hydrogen to compare with very accurate non-Born-Oppenheimer calculations. The possible improvements and future developments are outlined. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4803546\] 2
Chemical Physics Letters, 2007
The translation-and rotation-free nuclear orbital plus molecular orbital (TRF-NOMO) theory was developed in order to accurately determine the nonadiabatic nuclear and electronic wave functions without Born-Oppenheimer approximation. This study presents a hybrid method combining the TRF-NOMO theory with the generator coordinate method (GCM). The TRF-NOMO/GCM treatment is capable of giving the vibrational excited states with high accuracy, as well as improving the ground-state description by inclusion of the many-body effect. Numerical applications of the TRF-NOMO/GCM calculations to an HF molecule confirm its reliability and usefulness.
Recent Progress in the Variational Orbital Approach to Atomic and Molecular Electronic Structure
Advances in Quantum Chemistry, 2016
Abstract Recent progress in selected configuration interaction (CI) with truncation energy error (SCI-TEE) is discussed together with applications. In molecular CI, we take up (i) preselection of huge numbers of configurations and sensitivity analyses, (ii) highlights of SCI-TEE applied to H 2 O ground state, and (iii) symmetric dissociation of H 2 O ground state. We describe automatic optimization of atomic orbital bases to within a prescribed complete basis set energy error and an application of it to Ne ground state. New perspectives on the use of optimized orbital bases are briefly outlined. We discuss opportunities for new theory and new predictions in connection with a genuine variational theorem for the Breit–Dirac Hamiltonian. We explain the meaning of positive- and negative-energy orbitals in contrast with positive-energy and unphysical N-electron states. We conclude with an overview of current and planned work.
Highly accurate calculations of molecular electronic structure
1999
The highly accurate calculation of molecular electronic structure requires the expansion of the molecular electronic wavefunction to be as nearly complete as possible both in one-and nelectron space. In this review, we consider the convergence behaviour of computed electronic energies, in particular electronic enthalpies of reaction, as a function of the one-electron space. Based on the convergence behaviour, extrapolations to the limit of a complete one-electron basis are possible and such extrapolations are compared with the direct computation of electronic energies near the basis-set limit by means of explicitly correlated methods. The most elaborate and accurate computations are put into perspective with respect to standard and-from a computational point of view-inexpensive density functional, complete basis set (CBS) and Gaussian-2 calculations. Using the explicitly correlated coupled-cluster method including singles, doubles and non-iterative triples replacements, it is possible to compute (the electronic part of) enthalpies of reaction accurate to within 1 kJ mol −1 . To achieve this level of accuracy with standard coupled-cluster methods, large basis sets or extrapolations to the basis-set limit are necessary to exploit fully the intrinsic accuracy of the coupled-cluster methods.
Physical Review A, 2011
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method is formulated for treating the coupled electronic and nuclear dynamics of diatomic molecules without the Born- Oppenheimer approximation. The method treats the full dimensionality of the electronic motion, uses no model interactions, and is in principle capable of an exact nonrelativistic description of diatomics in electromagnetic fields. An expansion of the wave function in terms of configurations of orbitals whose dependence on internuclear distance is only that provided by the underlying prolate spheroidal coordinate system is demonstrated to provide the key simplifications of the working equations that allow their practical solution. Photoionization cross sections are also computed from the MCTDHF wave function in calculations using short pulses.
Computing electronic structures: A new multiconfiguration approach for excited states
Journal of Computational Physics, 2006
We present a new method for the computation of electronic excited states of molecular systems. This method is based upon a recent theoretical definition of multiconfiguration excited states (due to one of us, see M. Lewin, Solutions of the Multiconfiguration Equations in Quantum Chemistry, Arch. Rat. Mech. Anal. 171 (2004) 83-114). Contrarily to previously used methods, our algorithm always converges to a stationary state of the multiconfiguration model, which can be interpreted as an approximate excited state of the molecule.
An efficient algorithm for energy gradients and orbital optimization in valence bond theory
Journal of Computational Chemistry, 2009
An efficient algorithm for energy gradients in valence bond theory with nonorthogonal orbitals is presented. A general Hartree‐Fock‐like expression for the Hamiltonian matrix element between valence bond (VB) determinants is derived by introducing a transition density matrix. Analytical expressions for the energy gradients with respect to the orbital coefficients are obtained explicitly, whose scaling for computational cost is m4, where m is the number of basis functions, and is thus approximately the same as in HF method. Compared with other existing approaches, the present algorithm has lower scaling, and thus is much more efficient. Furthermore, the expression for the energy gradient with respect to the nuclear coordinates is also presented, and it provides an effective algorithm for the geometry optimization and the evaluation of various molecular properties in VB theory. Test applications show that our new algorithm runs faster than other methods. © 2008 Wiley Periodicals, Inc....
Molecular Modeling and Electronic Structure Calculations
2017
This laboratory is designed to use the program GAMESS (General Atomic Molecular Electronic Structure System, developed in Gordon research group at Iowa State) through a website called nanoHUB (www.nanoHUB.org) to determine the geometric and electronic properties of numerous small molecules. GAMESS uses ab initio and semi-empirical calculations to determine these properties. Ab initio (“from first principles”) calculations solve the Schrödinger equation using the exact computational expression for the energy of the electrons. The particular ab initio method that we will use for this lab is called HartreeFock (HF). HF uses an approximate wavefunction to solve Schrödinger, so the resulting molecular properties are approximate, but for many applications the accuracy is adequate for interpreting experiments. Semi-empirical calculations use an approximate energy expression for the electrons, but solve for the exact wavefunction associated with this expression. Usually the energy expressio...
Advanced multiconfiguration methods for complex atoms: I. Energies and wave functions
Journal of Physics B: Atomic, Molecular and Optical Physics, 2016
Multiconfiguration wave function expansions combined with configuration interaction methods are a method of choice for complex atoms where atomic state functions are expanded in a basis of configuration state functions. Combined with a variational method such as the multiconfiguration Hartree-Fock (MCHF) or multiconfiguration Dirac-Hartree-Fock (MCDHF), the associated set of radial functions can be optimized for the levels of interest. The present review updates the variational MCHF theory to include MCDHF, describes the multireference single and double (MRSD) process for generating expansions and the systematic procedure of a computational scheme for monitoring convergence. It focuses on the calculations of energies and wave functions from which other atomic properties can be predicted such as transition rates, hyperfine structures and isotope shifts, for example.