Calculation Of Excited State Energies Research Articles

Guanine-adenine interactions in DNA tetranucleotide cation radicals revealed by UV/vis photodissociation action spectroscopy and theory.

Hydrogen-rich cation radicals (GATT + 2H)+˙ and (AGTT + 2H)+˙ represent oligonucleotide models of charged hydrogen atom adducts to DNA. These tetranucleotide cation radicals were generated in the gas phase by one-electron reduction of the respective (GATT + 2H)2+ and (AGTT + 2H)2+ dications in which the charging protons were placed on the guanine and adenine nucleobases. We used wavelength-dependent UV/Vis photodissociation in the valence-electron excitation region of 210-700 nm to produce action spectra of (GATT + 2H)+˙ and (AGTT + 2H)+˙ that showed radical-associated absorption bands in the near-UV (330 nm) and visible (400-440 nm) regions. Born-Oppenheimer molecular dynamics and density-functional theory calculations were used to obtain and rank by energy multiple (GATT + 2H) dication and cation-radical structures. Time-dependent density functional theory (TD-DFT) calculations of excited-state energies and electronic transitions in (GATT + 2H)+˙ were augmented by vibronic spectra calculations at 310 K for selected low-energy cation radicals to provide a match with the action spectrum. The stable product of one-electron reduction was identified as having a 7,8-dihydroguanine cation radical moiety, formed by intramolecular hydrogen atom migration from adenine N-1-H. The hydrogen migration was calculated to have a transition state with a low activation energy, Ea = 96.5 kJ mol-1, and positive activation entropy, ΔS‡ = 75 J mol-1 K-1. This allowed for a fast isomerization of the primary reduction products on the ion-trap time scale of 150 ms that was substantially accelerated by highly exothermic electron transfer.

Variational Quantum Computation of Excited States

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.

Electronic transition dipole moments from orthogonality constrained Hartree–Fock wavefunctions

In our recent paper (Glushkov V N and Assfeld X 2016 Theor. Chem. Acc. 135), we have presented some applications of the so-called orthogonality constrained Hartree–Fock (OCHF) theory to calculations of excited state energies of the same symmetry, including highly and core excited states. In this paper we report an attempt to apply this methodology to practical calculations of electronic dipole transition moments focusing on transitions between states having the same spatial symmetry as the ground state. Basic tenets of this method are briefly reviewed and its specific features for ab initio calculations of electronic transitions are discussed. The effect of non-orthogonal HF wave functions on transition dipole moments is studied and analyzed. OCHF electronic transition moments calculated for the HeH molecule are presented as a function of the internuclear separation for five 2Σ+ states (X 2Σ+, A2Σ+, C2Σ+, D2Σ+and F 2Σ+). The results of the calculations are, in general, in good agreement with those obtained by multi-reference configuration interaction methods which take correlation effects into account and show a favorable balance between accuracy and computational efficiency.

A deterministic alternative to the full configuration interaction quantum Monte Carlo method.

Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such technique, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. However, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method that can achieve chemical accuracy for a wide range of systems, including the difficult Cr2 molecule. We demonstrate for systems like Cr2 that such calculations can be performed in just a few cpu hours which makes it one of the most efficient and accurate methods that can attain chemical accuracy for strongly correlated systems. In addition our method also allows efficient calculation of excited state energies, which we illustrate with benchmark results for the excited states of C2.

Towards a pair natural orbital coupled cluster method for excited states.

The use of back-transformed pair natural orbitals in the calculation of excited state energies, ionization potentials, and electron affinities is investigated within the framework of equation of motion coupled cluster theory and its similarity transformed variant. Possible approaches to a more optimal use of pair natural orbitals in these methods are indicated.

Optimized effective potential method for individual low-lying excited states

This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.

Excited states by quantum Monte Carlo method

We present applications of a new Monte Carlo algorithm for the calculation of excited state energies of multi-dimensional quantum systems. The method relies on computation of imaginary time correlation functions of appropriately chosen projection operators, followed by a numerical inverse Laplace transformation performed with the maximum entropy method.

Quantum Monte Carlo methods for rovibrational states of molecular systems

We present applications to molecular problems of a recently developed quantum Monte Carlo algorithm [Phys. Rev. E 55, 3664 (1997)] for the calculation of excited state energies of multi-dimensional quantum systems, employing a projection operator imaginary time spectral evolution (POITSE). The extraction of vibrational energies is demonstrated on a double well potential and on two coupled harmonic oscillators, and on excited rotational states of a rotating harmonic oscillator. All energies extracted by the quantum Monte Carlo algorithm are in good agreement with exact results, showing that the new method is very promising for the calculation of tunneling splittings, and of vibrational and rotational excitations in real multi-dimensional molecular systems.

Excited states by quantum Monte Carlo methods: Imaginary time evolution with projection operators

We present a Monte Carlo algorithm suitable for the calculation of excited state energies of multidimensional quantum systems. Energies are extracted from a maximum entropy analysis of the imaginary time evolution of a state prepared by application of a projection operator on an initial wave function. The imaginary time evolution is computed with a pure diffusion Monte Carlo algorithm. The method is demonstrated on a harmonic oscillator and several Morse oscillator test problems.

Quantum Chemical Methods for the Design of Molecular Non-Linear Optical Materials

AbstractThe quantum chemical design of new molecular materials for non-linear applications requires a fundamental understanding of electronic structure and properties. Targeted synthesis of candidates greatly reduces the costs and timescales of an empirical search and this is aided by prior calculation of excited state energies, energy relaxation and transfer rates, molecule-environment interactions and excited state chemistry.Essentially, the problems encountered in the routine application of standard quantum chemical methods are caused by the large size of the molecules of interest. This necessitates either the design of ultra-fast computers or numerical methods which facilitate the application of ‘exact’ techniques or the development of less resource intensive approximate methods with proven accuracy.We shall outline the theories used in the calculation of optical properties and review their computational implementation. Calculations on annellated tetraazaporphyrazines will be presented in illustration.

Ensemble-Density functional theory for excited states

Fundamental aspects of the ensemble-density functional approach to the calculation of excited state energies are reviewed. Attention is given to the quasilocal density approximation for the equiensemble exchange-correlation energy functional. In particular, compared with experimental data, numerical results for the excitation spectrum of the helium atom produce an estimate of the deviations introduced by that approximation.

Computer program for optimization of a molecular basis in the calculation of excited state energies in the single-determinant approximation

An important step in variational calculations of excited state (ES) energies is the choice of a test function orthogonal to wave functions which describe the lower-lying states of the same symmetry. We describe an attempt to calculate the ES energy in the single-determinant approximation, but with the Roothaan basis tuned to the corresponding ES. The problem reduces to minimization of the energy functional with respect to nonlinear parameters of the basis set,with an additional condition that the states be orthogonal.

Density-functional theory for excited states in a quasi-local-density approximation.

The starting point of this paper is a recent extension by Theophilou of the Hohenberg-Kohn-Sham (HKS) density-functional theory to ensembles of systems consisting of the M lowest eigenstates, equally weighted. As in the HKS theory the key quantities are the exchange-correlation energy, ${E}_{\mathrm{xc}{}^{M}[\mathrm{n}(\mathrm{r})]}$, and potential, ${v}_{\mathrm{xc}{}^{M}(\mathit{r};[\mathit{n}(\mathit{r}\mathcal{'})])}$. The present paper provides expressions for these quantities, valid for systems of slowly varying density. Even for such systems, however, there are essential nonlocal effects. Nevertheless both ${E}_{\mathrm{xc}{}^{M}}$ and ${v}_{\mathrm{xc}{}^{M}}$ can be calculated in terms of quantities characteristic of appropriate uniform thermal ensembles. This theory is the analog of the ground-state local-density approximation and allows calculation of excited-state energies and densities.

Excited-state energies from many-body perturbation theory with the excitation-adapted one-particle potential

Calculation of excited-state energies by many-body perturbation theory is discussed. A Hartree-Fock-type potential suitable for a given excited-state configuration is introduced. Advantages which follow from the excitation-adapted one-particle potential are examined. The theory resembles that for external perturbation effects and amounts to removing or minimizing the contribution of non-diagonal one-particle terms.

Calculations of the electronic structures of cage molecules using free-electron orbitals as a basis

A non-empirical molecular orbital method, particularly suitable for calculations on cage-like molecules, is described. The method uses as basis functions the set of free-electron functions which are the solutions of Schrodinger's equation for an electron confined between two concentric, spherical potential energy barriers. Application of the theory to the SCF calculation of the energies of the delocalized electrons in benzene and tetrasulphur tetranitride shows that the model is capable of interpreting the properties of such systems. However, it does highlight a difficulty in the calculation of excited state energies with one-centre models which appears to be largely unrecognized.

The lowest electronic states of the benzoyl ion. A molecular orbital study with configuration interaction

AbstractA configuration interaction method of molecular orbital theory shown to be accurate for the calculation of excited state energies in several aromatic systems was applied to the problem of excited states of the benzoyl ion. The excited singlet and triplet states of the benzoyl ion lie at least 3.8 eV and 2.6 eV, respectively, above the ground state. These results are not in agreement with a postulated state 20 kcal above the ground state. On the other hand, the charge distribution in excited states does agree with that postulated for the 20 kcal state. The p‐hydroxy and p‐cyano substituents do not greatly influence the charge distribution between the ring and the carbonyl group in either the ground or lowest excited states.

A comparative study of SCFMO calculations on alternant and nonalternant hydrocarbons

A form of the semiempirical self-consistent-field LCAO-π-MO method in which allowance is made for bond length-bond order correlation is presented. The results of calculations of excited state energies calculated according to this method are compared with those calculated by several other methods. The comparison indicates that the method here described can successfully predict the spectra of various classes of conjugated hydrocarbons with a consistent set of parameters. It is shown that the success of the Huckel LCAO procedure in predicting the p-band transition energy is principally due to three factors: the relative unimportance of configuration interaction, the invariance of the SCF electron-interaction terms for various hydrocarbons, and the proportionality of the Huckel energy number to the corresponding term in the SCF theory.