Calculation Of Transition Dipole Moments Research Articles

SLIMP 2.0: A new version of strong laser interaction model package for atoms and molecules, now with molecular orbital tomography based on high-order harmonic spectra

A new version of strong laser interaction model package for atoms and molecules is presented. Its capacities are enhanced by incorporating modules related to molecular orbital tomography (MOT) in length and velocity forms based on high-order harmonic spectra (HHS). This advanced package enables two-dimensional and three-dimensional MOT of both symmetric and asymmetric molecules using HHS, providing an efficient means for both experimental and theoretical investigations of molecular orbital structures. In addition, it can calculate the precise theoretical orbitals corresponding to those reconstructed by MOT. Furthermore, the package can calculate the transition dipole moment (TDM) in the plane wave approximation and allow for reference MOT based on TDM. It can evaluate the quality of reconstructed orbitals based on HHS and reveal the physical and numerical effects on MOT. This package is suitable for MOT under conditions of driving laser at different intensities and wavelengths, and can be applied to different molecules with various structures. It is designed to facilitate easy expansion for additional capabilities. Program summaryProgram Title: SLIMP, version 2.0CPC Library link to program files:https://doi.org/10.17632/jgcb7m7wwv.1Licensing provisions: GPLv3Programming language: Fortran 90Journal reference of previous version: Comput. Phys. Commun. 192 (2015) 330-341.Does the new version supersede the previous version?: Yes.Reasons for the new version: Molecular orbital tomography (MOT) [1] based on high-order harmonic spectra (HHS) [2] is an important research topic in the field of strong-field physics. It provides an efficient way to probe molecular orbital structures experimentally, which was not considered in the former version of SLIMP [3] and is now included in SLIMP 2.0. The new version package allows performing two-dimensional (2D) and three-dimensional (3D) MOT [4] based on HHS obtained from experiments or simulations, providing reliable detections for many orbitals of interest, either symmetric or asymmetric molecules.Summary of revisions: Extending capacities focus on enabling performing 2D and 3D MOT on symmetric and asymmetric molecules based on HHS, and together the relevantly precise theoretical orbital output, calculation of transition dipole moment (TDM) and reference MOT based on TDM. For 2D MOT, MOT in both length and velocity forms are implemented.Nature of problem: To perform MOT based on HHS, the user needs general reconstruction programs, taking symmetric and asymmetric molecules, 2D and 3D orbitals, and MOT in length and velocity forms into account. In addition, evaluation of imaging quality is required, which can reveal the physical and numerical effects on reconstructions.Solution method: The 2D symmetric and asymmetric, length- and velocity-form, and 3D reconstruction algorithms are implemented based on Fortran 90. Furthermore, this package provides a reference MOT based on directly calculated TDM, served as a comparable result to the reconstructed orbital based on HHS. The comparison between reconstructions based on HHS and TDM can reveal the effects on MOT in physical and numerical aspects.Additional comments including restrictions and unusual features: This package does not include MOT of asymmetric molecules in velocity form. For the 2D MOT based on HHS, the reconstructed 2D projection of gerade, ungerade orbital or the gerade and ungerade components of asymmetric orbital must have the axial symmetry about the x- and z-axis. For the 3D MOT, the reconstructed 3D orbital has to be cylindrically symmetric.

Parameterized Effective Potential for Excited States and Its Application to the Calculation of Transition Dipole Moments

A parameterized effective potential method that was proposed earlier for the ground state has been developed for excited states with symmetry of the ground state. Various approximations for determining exchange-correlation potentials Vxc, have been discussed. In particular, one of the techniques for constructing a new class of Vxc, which is a functional of the external potential (electron–nucleus interaction) in contrast to traditional approaches, in which Vxc explicitly or implicitly depends on the electron density, have been presented on the basis of the Vxc symmetry requirement. The possibilities of the method have been investigated using the example of calculating the electronic dipole moments of the transition of an НеН molecule with a single-determinant wave function. It has been shown that the proposed method for calculating the transition dipole moments can be considered as a compromise between accuracy and computational effort.

On the Choice of a Distributed Basis Set in Calculations of Transition-Dipole Moments in the One-Determinant Approximation

The so-called “asymptotic projection technique” developed in previous papers of the authors is applied to the calculation of electronic transition-dipole moments (TDMs) in the one-determinant approximation between states of the same spin and spatial symmetry. The basic equations of the method and specific features of their application to a TDM calculation are briefly discussed. The attention focusses on the choice of a finite one-particle basis set. For this purpose, two possible algorithms for constructing distributed basis sets are proposed. In the first of them, the construction is based on minimization of the Hartree–Fock energy (EHF) with respect to nonlinear basis set parameters. In the second case, the parameters are determined by minimizing the functional E = EHF + EMP2, which includes the electron correlation through the second order of Moller–Plesset perturbation theory (ЕМР2). On the whole, the results of calculations in both basis sets are in agreement with high-accuracy calculations performed by configuration interaction methods. The basis set adapted for E = EHF + EMP2 significantly improves the accuracy as compared to the basis set of the first type.

Characterizing metastable states beyond energies and lifetimes: Dyson orbitals and transition dipole moments.

The theoretical description of electronic resonances is extended beyond calculations of energies and lifetimes. We present the formalism for calculating Dyson orbitals and transition dipole moments within the equation-of-motion coupled-cluster singles and doubles method for electron-attached states augmented by a complex absorbing potential (CAP-EOM-EA-CCSD). The capabilities of the new methodology are illustrated by calculations of Dyson orbitals of various transient anions. We also present calculations of transition dipole moments between transient and stable anionic states as well as between different transient states. Dyson orbitals characterize the differences between the initial neutral and final electron-attached states without invoking the mean-field approximation. By extending the molecular-orbital description to correlated many-electron wave functions, they deliver qualitative insights into the character of resonance states. Dyson orbitals and transition moments are also needed for calculating experimental observables such as spectra and cross sections. Physically meaningful results for those quantities are obtained only in the framework of non-Hermitian quantum mechanics, e.g., in the presence of a complex absorbing potential (CAP), when studying resonances. We investigate the dependence of Dyson orbitals and transition moments on the CAP strength and illustrate how Dyson orbitals help understand the properties of metastable species and how they are affected by replacing the usual scalar product by the so-called c-product.

Degree of circular polarization in II–VI diluted magnetic semiconductor quantum dots

Degree of circular polarization (DCP) in II–VI diluted magnetic semiconductor quantum dots (QDs) has been studied analytically. Energy levels have been calculated using Luttinger–Kohn Hamiltonian and effective mass approximation. Effects due to application of externa magnetic field have been investigated, followed by calculation of transition dipole moment and DCP. Numerical estimates made for Mn-doped CdSe/ZnSe QDs show that DCP in undoped QDs is negligible while transition metal ion doping yields substantial polarization rotation (≈−2.20%) even at moderate magnetic fields (≈0.5T).

Calculation of transition dipole moment in fluorescent proteins—towards efficient energy transfer

Förster Resonance Energy Transfer (FRET) between fluorescent proteins (FPs) is widely used to construct fluorescent sensor proteins, to study intracellular protein-protein interactions and to monitor conformational changes in multidomain proteins. Although FRET depends strongly on the orientation of the transition dipole moments (TDMs) of the donor and acceptor fluorophores, this orientation dependence is currently not taken into account in FRET sensor design. Similarly, studies that use FRET to derive structural constrains typically assume a κ(2) of 2/3 or use the TDM of green fluorescent protein, as this is the only FP for which the TDM has been determined experimentally. Here we used time-dependent density functional theory (TD-DFT) methods to calculate the TDM for a comprehensive list of commonly used fluorescent proteins. The method was validated against higher levels of calculation. Validation with model compounds and the experimentally determined TDM of GFP shows that the TDM is mostly determined by the structure of the π-conjugated fluorophore and is insensitive to non-conjugated side chains or the protein surrounding. Our calculations not only provide TDM for most of the currently used FPs, but also suggest an empirical rule that can be used to obtain the TDMs for newly developed fluorescent proteins in the future.

Alignment dependence of high harmonics contributed from HOMO and HOMO-1 orbitals of N2 molecules

Characteristics of high harmonics generated from aligned N2 molecules were investigated by rotating the molecules with respect to the polarization of harmonic generation pulses. The high harmonics in the plateau and the cutoff regions showed distinctive behaviour, which could be explained from the calculation of transition dipole moments between recolliding electron and multi-orbitals of N2 molecule consisting of the highest occupied molecular orbital (HOMO) and the lower-lying orbital below HOMO (HOMO-1). It was also observed that the angular dependence of harmonics from aligned molecules with respect to the polarization of harmonic generation pulses was closely related to the geometrical structure of molecular orbitals, and that the harmonic in the transition region from the plateau to the cutoff was influenced comparably by both HOMO and HOMO-1. These results confirmed that high harmonic generation and molecular structure were closely linked.

Modelling of Kr+ clusters. II. Photoabsorption spectra of small clusters (n=2–5)

Abstract Recently calculated potential energy curves for the krypton dimer cation [R. Kalus et al., Chem. Phys. 294 (2003) 141] are augmented by accurate ab initio calculations of transition dipole moments and used in diatomics-in-molecules modelling of Kr n + ( n =2–5) photoabsorption spectra at both zero and non-zero temperatures. Several models of intra-cluster interactions in Kr n + are used. In addition to a standard diatomics-in-molecules model, the spin–orbit coupling is taken into account through a semi-empirical treatment and the most relevant three-body forces are represented by induced dipole–induced dipole polarization interactions. The transition dipole moments are calculated for n ⩾3 within the point-charge approximation with inclusion of the polarization effects. The results are compared with available experimental data. A reasonable agreement is found.

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (13Πg ← B3Σu−, 13Πg ← A3Σu+, 13Πg ← A′ 3Δu, B3Σ u− ← X3Σg−, 23Πu ← 13Π g, 23Σg− ← B3Σu−, 13Πu ← X3Σg−, 23Πu ← X3Σg−, 23Π g ← A′3Δu, 33Πg ← A′ 3Δ u, 23Δu ← 23Πg, 33Πg ← B3Σ u−, and 23Πg ← A3Σ u+) and singlet-singlet (21Σg+ ← 21Πu, 21Πu ← 11Π g, 1Πu ← 21Δg, 11Πg ← c1Σ u−, 1Πu ← b1Σg+, 11Δ u ← a1Δg, 21Πu ← a1Δg, 21Δg ← 11Δu, 1Π u ← a1Δ g, 11Πu ← b1Σg+, 21Πg ← 11Πu, 21Π g ← c1Σu−, 11Δ u ← 11Π g, f′Σ u+ ← b1Σg+, 21Σg+ ← f ′1Σ u+, 31Πg ← 11Δu) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.

Recommendations from the raden data base for the electronic transition moments on diatomic molecules of astrophysical interest. I: C2, CH, and CN molecules

Abstract Within the scope of the data base RADEN an analysis of the radiative parameters has been carried out for a number of astrophysically significant molecular systems. Result of the experimental studies and the ab initio calculations of transition dipole moments D(R), electronic fe and band fv′v″ oscillator strengths, and radiative lifetimes τnv1 have been analysed. Finally, the electronic transition moments D(R) are recommended for the Swan and Phillips systems of C2, the A2 Δ-X2II system of CH, and the red and violet systems of CN. The recommended functions provide the most reliable data at present and they should be used in preparing lists of molecular line parameters (to calculate gf-values).

On quantum Monte Carlo for the electronic structure of molecules

We present recent advances in the quantum Monte Carlo (QMC) method for the electronic structure of atoms and molecules. The QMC method used here is a procedure for solving the Schrödinger equation stochastically based on the formal similarity between the Schrödinger equation and the classical diffusion equation. Quantum mechanical expectation values are obtained as Monte Carlo averages over an ensemble of random walkers undergoing diffusion, drift (from importance sampling), and branching. The power of the QMC method is that it is inherently an N-body method which can capture all of the dynamic correlation of the electrons. The approach yields highly accurate energies and has been used to determine other properties, including dipole moments and molecular geometry energy gradients. Here we present a description of the QMC method that we employ and give representative results. In addition we discuss recent progress on the calculation of transition dipole moments and developments with the “damped-core” QMC method which enables studies of molecular systems containing heavy atoms without reliance on Pseudopotentials.

The Role of “Rotational Freezing” in the Polarisation‐Dependent Two‐Photon Excitation of Triply Degenerate Vibrations in Spherical‐Top‐Molecules

AbstractUnder certain circumstances at low rotational temperatures the multiphoton excitation probabilities of vibrational‐rotational levels in high‐symmetric molecules do not depend on the rotational quantum numbers J and M of the initially populated levels. Then the rotation of the molecule as a whole is “frozen”. This has the consequence that during the absorption process the photon spin is not transferred to the molecular rotation but to the molecular vibration. In more detail the two‐photon A1g(v = 0) → A1g(v = 2) transition in SF6 at 944.5 cm−1 is theoretically studied: If the “average lifetime” in the intermediate (v = 1)‐level is small compared with the effective molecular rotation period the considered transition is forbidden for circularly polarised light. Further the excitation process of the Eg(v = 2) and F2g(v = 2) vibrational levels is investigated; it is discussed under which conditions it is not necessary to consider the rotational degrees of freedom for a calculation of transition dipole moments.

A reinterpretation of the infrared linear dichroism of oriented nucleic acid films and a calculation of some effective partial changes on the ribose phosphate backbone

In this paper we show, based on symmetry considerations, that structural information cannot be obtained from the linear infrared dichroism of the dioxy vibrations of the phosphate group of nucleic acids. Consequently, the discrepancies between the results of x-ray structure measurements and linear dichroism measurements are not meaningful. The linear dichroism measurements are instead important for a calculation of transition dipole moments that involve both the vibrations of all the atoms of the nucleotide and their charges. Independent information on either the atomic displacements contributing to a given vibration or the atomic charges permits a refinement of the unknown quantities. Based on the molecular dynamics calculations of Prohofsky et al., atomic charges of DNA are calculated to reproduce the observed linear dichroism results. Some of the resulting charges are unexpected and may reflect the inadequacy of the molecular dynamic calculation.