The separation of electronic and nuclear motion in the diatomic molecule

The Schrödinger Coulomb Hamiltonian for electronic and nuclear motion in a diatomic molecule is presented and its effect upon functions which are products of functions of electronic and of nuclear variables is explicitly exhibited. Computational approaches to finding approximate solutions in such a basis are outlined.     

A misconception concerning the electronic density distribution of an atom

It is shown that the electronic charge density of a ground-state atom decreases monotonically as a function of radial distance from the nucleus, contrary to the widespread belief that the shell structure is reflected by relative maxima in the density. Any proposed relationship between chemical bonding and the maxima in the radial density functions of atoms should therefore be regarded with caution. It is proven that the electrostatic potential of an atom must be monotonically decreasing. The changes in charge distribution upon molecule formation are also discussed.     

Electron and nuclear density matrices and the separation of electronic and nuclear motion

The so-called parametric dependency of the electronic wave function in the Born–Oppenheimer approximation is discussed. Considering a function beyond this approximation, a new set of equations is derived with parametric and nonparametric dependency. Nuclear and electron reduced density matrices are introduced in this derivation. They are used in a formulation of the problem of separation of nuclear and electronic motion.     

Determination of the geometry change of the phenol dimer upon electronic excitation.

The change of the phenol dimer (PH2) structure upon electronic excitation is determined by a Franck-Condon analysis of the intensities in the fluorescence emission spectra obtained via excitation of seven different vibronic bands. A total of 547 emission band intensities are fitted, together with the changes of rotational constants upon electronic excitation of fi ve isotopomers. These rotational constants are taken from previously published [Schmitt et al. ChemPhysChem 2006, 7, 1241-1249] high-resolution LIF measurements. The geometry change upon electronic excitation of the pipi* state of the donor moiety can be described by a strong shortening of the hydrogen bond, a shortening of the CO bond in the donor moiety, an overall symmetric expansion of the donor phenol ring, and a nearly unchanged acceptor moiety. The resulting geometry changes are interpreted on the basis of ab initio calculations.     

Changes in molecular properties with changes in molecular geometry: A partitioning into electronic and nuclear components

Most one-electron properties vary with changes in molecular conformation. Although the nuclear component remains constant for some of the one-electron property changes and thus the overall change depends only on the electronic change this result is not general. Often the change in the nuclear component dominates the overall change in a molecular property. An analysis of the changes in a number of one-electron properties with changes in molecular geometry in terms of the changes in the nuclear and the electronic components is presented. The inversion of ammonia and the torsion of ethane were chosen as important examples of conformational changes and the changes in molecular one-electron properties studied.     

Time-dependent density functional study of the electronic potential energy curves and excitation spectrum of the oxygen molecule

Orbital energies, ionization potentials, molecular constants, potential energy curves, and the excitation spectrum of O(2) are calculated using time-dependent density functional theory (TDDFT) with Tamm-Dancoff approximation (TDA). The calculated negative highest occupied molecular orbital energy (-epsilon(HOMO)) is compared with the energy difference ionization potential for five exchange correlation functionals consisting of the local density approximation (LDAxc), gradient corrected Becke exchange plus Perdew correlation (B(88X)+P(86C)), gradient regulated asymptotic correction (GRAC), statistical average of orbital potentials (SAOP), and van Leeuwen and Baerends asymptotically correct potential (LB94). The potential energy curves calculated using TDDFT with the TDA at internuclear distances from 1.0 to 1.8 A are divided into three groups according to the electron configurations. The 1pi(u) (4)1pi(g) (2) electron configuration gives rise to the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) states; the 1pi(u) (3)1pi(g) (3) electron configuration gives rise to the c (1)Sigma(u) (-), C (3)Delta(u), and A (3)Sigma(u) (+) states; and the B (3)Sigma(u) (-), A (1)Delta(u), and f (1)Sigma(u) (+) states are determined by the mixing of two or more electron configurations. The excitation spectrum of the oxygen molecule, calculated with the aforementioned exchange correlation functionals, shows that the results are quite sensitive to the choice of functional. The LDAxc and the B(88X)+P(86C) functionals produce similar spectroscopic patterns with a single strongly absorbing band positioned at 19.82 and 19.72 eV, respectively, while the asymptotically corrected exchange correlation functionals of the SAOP and the LB94 varieties yield similar excitation spectra where the computed strongly absorbing band is located at 16.09 and 16.42 eV, respectively. However, all of the exchange correlation functionals yield only one strongly absorbing band (oscillator strength greater than 0.1) in the energy interval of 0-20 eV, which is assigned to a X (3)Sigma(g) (-) to (3)Sigma(u) (-) transition. Furthermore, the oxygen molecule has a rich spectrum in the energy range of 14-20 eV and no spin allowed absorption bands are predicted to be observed in the range of 0-6 eV.     

A density functional study on the electronic structures of TiN solid

The electronic structures of TiN bulk have been studied by using different theoretical formalisms, and the DFT method, especially the BLYP method can produce reasonable results. The band structure of TiN (001) surface is also investigated and two a type surface states are presented in our results. The state located at 2.9 eV below EF in angle resolved photoemis-sion in (ARPES) is well reproduced in this work, which consists essentially of 2pz orbital of surface N atom. Another surface state is associated with the bands originated from 3d orbital of surface Ti atom. Furthermore, the elastic constants of TiN are also calculated by using BLYP method.     

End-substitution effect on the geometry and electronic structure of oligoheterocyclics

The end-substitution effects on the geometric and electronic structures of oligoheterocyclics are systematically studied using the density functional theory. It is found that the influence of the end-substitution does not depend on the heteroatom. End-substitution plays a fine-tune effect on the geometry and the excitation state. While the influences on the conducting type (p-type or n-type) and the inter-chain charge carrier hoping channels are much different between the electron-donating –CH ₃ and electron–accepting –CN substitutions. Both molecular electrostatic potentials and charge carrier injection rates indicate that the –CH ₃/–CH ₃ substitution is beneficial to the p-type doping, while the –CN/–CN substitution is in favor of the n-type doping, which is in agreement with the experimental observations. The –CH ₃ substituted packing dimers exert similar intermolecular interactions to the unsubstituted ones. The –CN substituted packing dimers yield much stronger intermolecular interactions comparing to the –CH ₃ substituted ones. It could be anticipated that the –CN substitution would be helpful to the charge carrier hopings between chains and thereby enhance the conductivity.     

Theoretical electronic structure of the molecule ScBr

The potential energy curves have been investigated for the 23 lowest electronic states in the ^2s+1Λ^± representation of the molecule ScBr via CASSCF and MRCI (single and double excitations with Davidson correction) calculations. Seventeen electronic states have been studied theoretically for the first time. The harmonic frequency ω_e, the internuclear distance r_e, and the electronic energy with respect to the ground state T_e have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points (R_min, R_max) have been calculated for electronic states up to the vibrational level v = 32. The comparison of these values to the theoretical and experimental results available in the literature shows a good agreement. © 2007 Wiley Periodicalsm Inc. Int J Quantum Chem, 2008     

Expanded electronic states of the fluorine molecule

Potential curves of electronically excited states of F₂ with an expanded outer orbital have been calculated using a modified frozen core technique: The ionic core has been described with a two-determinant wave function and for the excited states a mixing of configurations with different cores has been employed. An investigation of the valence shell states of F₂ is presented and potential curves for a singly excited as well as a doubly excited V-state of ¹Σ_u⁺ symmetry have been calculated. Further a low lying two-configuration state resulting from simultaneous excitation to a valence and a Rydberg orbital is predicted.     

Theoretical electronic structure of the molecule ScI

Theoretical investigation of the 18 lowest electronic states of the molecule ScI in the representation ^2S+1Λ^(±) has been performed via CASSCF and MRCI (single and double excitation with Davidson correction) calculations. To the best of our knowledge these calculated electronic states are the first ones from ab initio methods. Thirteen electronic states between 4,500 cm^?1 and 21,000 cm^?1 have been studied for the first time and have not yet been observed experimentally. The harmonic frequency ω_e, the internuclear distance R_e, the electronic transition energy with respect to the ground state T_e, and the rotational constant B_e have been calculated for the considered electronic states. By using the canonical functions approach the eigenvalues E_υ and the rotational constants B_υ have also been calculated for the six lowest‐lying electronic states. The comparison of these results with the theoretical and the experimental data available in the literature shows a good agreement. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

The change in the dressed potential of a polyatomic molecule in intense photon fields: Simple rules based on the nuclear charge-mass ratio

An explicit expression for the dressed potential of a polyatomic molecule, in the adiabatic approximation, is derived. This expression clearly shows the importance of the nuclear charge-mass ratio (NCMR ) for the change of potential due to photon fields. It is found from a simple calculation that the ¹H atom is the only atom having an abnormal NCMR value; all other atoms have similar, or the same, values. This means that only those molecules containing a ¹H atom should be strongly affected by fields. On the basis of this new physical insight, we postulate two rules, which enable us to classify molecules, with respect to their response to intense photon fields, into three classes: high-sensitive, low-sensitive, and insensitive molecules. Qualitative verification is also given by using water isotopes.     

Substitution effect on the geometry and electronic structure of the ferrocene

The substitution effects on the geometry and the electronic structure of the ferrocene are systematically and comparatively studied using the density functional theory. It is found that -NH(2) and -OH substituents exert different influence on the geometry from -CH(3), -SiH(3), -PH(2), and -SH substituents. The topological analysis shows that all the C-C bonds in a-g are typical opened-shell interactions while the Fe-C bonds are typical closed-shell interactions. NBO analysis indicates that the cooperated interaction of d --> pi* and feedback pi --> d + 4s enhances the Fe-ligand interaction. The energy partitioning analysis demonstrates that the substituents with the second row elements lead to stronger iron-ligand interactions than those with the third row elements. The molecular electrostatic potential predicts that the electrophiles are expected to attack preferably the N, O, P, or S atoms in Fer-NH(2), Fer-OH, Fer-PH(2), and Fer-SH, and attack the ring C atoms in Fer-SiH(3) and Fer-CH(3). In turn, the nucleophiles are supposed to interact predominantly by attacking the hydrogen atoms. The simulated theoretical excitation spectra show that the maximum absorption peaks are red-shifted when the substituents going from second row elements to the third row elements.