Generalized Landau-Zener formula for non-adiabatic transitions between degenerate states

Non-adiabatic transitions between degenerate states are considered in a model system of parallel degenerate levels intersected by a single degenerate level. Sublevel populations in the final state are found to be determined by transition matrices between degenerate levels and by phases of ψ-functions of the initial state. Expressions for transition probabilities are obtained, averaged over random phases of the initial state.     

Correlation effects in calculation of electronic states for model molecular systems

Multiply excited configurations have been taken into account in evaluation of singlet, triplet and quinlet state energies and the relevant intensities of electronic transitions for model molecular systems. The results of calculation point out the essential role of interelectron, for (Π,Π^*) triplets and quintets in particular.     

Symmetry effects in the radiation damping of degenerate states

Radiation damping of three atoms in a radiation field is studied for both a linear and closed-chain configuration. One atom of the system is initially excited. Use is made of the Heitler-Ma perturbation procedure up to second order. The discussion is developed in terms of the symmetry of the interactions within the system. The interactions arising from dipole transitions perpendicular to the plane of the closed chain are shown to be similar to the interactions in a two-atom system, and the results are extended to cover larger rings.     

Simultaneous resonance Raman optical activity involving two electronic states

In the present work, the first observation of strong resonance Raman optical activity (RROA) involving more that one resonant electronic state is reported. The chiral transition metal complex bis-(trifluoroacetylcamphorato) copper(II), abbreviated Cu(tfc)(2), exhibits both resonance Raman (RR) and RROA spectra with laser excitation at 532 nm. Vibrational assignments for this complex were carried out by comparing the non-RR spectra of Cu(tfc)(2) excited at 1024 nm to density functional theory (DFT) calculations. The theory of the single-electronic-state (SES) RROA is extended to the next simplest level of theory involving two resonant electronic states (TES) without interstate vibronic coupling as an aide to the interpretation of the observed TES-RROA spectra. Based on measured UV-vis electronic absorbance spectra and corresponding TD-DFT calculations, the most likely two states associated with the RROA spectra are identified.     

Novel electronic transitions within excited doublets of dimers

We consider the electronic transition between the split components of the excited electronic doublet of a dimer species when the monomer species have permanent dipole moments. We show that the transition moment is given in terms of the permanent dipole moments of the ground and excited states of the monomers. Extension to ionic dimers and transitions between exciton bands in molecular crystals are suggested.     

Perturbation theory for degenerate states of atomic and molecular systems

The first few terms of the perturbation expansions for the function and the energy shift of a degenerate state of an arbitrary quantum mechanical system are obtained using the adiabatic formula. It is shown how the expansion for the secular operator may be obtained from the expansion for the function. The results are used to calculate energies of the ground and some excited states and multiplet splittings of some beryllium-like ions.     

Theoretical study of spectroscopic and molecular properties of several low‐lying electronic states of CO molecule

The potential energy curves (PECs) of eight low‐lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ^?, A¹Π, I¹Σ^?, and D¹Δ) of the carbon monoxide molecule have been studied by an ab initio quantum chemical method. The calculations have been performed using the complete active space self‐consistent field method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation‐consistent aug‐cc‐pV5Z basis set. The effects on the PECs by the core‐valence correlation and relativistic corrections are included. The way to consider the relativistic corrections is to use the third‐order Douglas–Kroll Hamiltonian approximation at the level of a cc‐pV5Z basis set. Core‐valence correlation corrections are performed using the cc‐pCVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size‐extensivity errors by means of the Davidson modification (MRCI+Q). The spectroscopic parameters (D_e, T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e, α_e, and γ_e) of these electronic states are calculated using these PECs. The spectroscopic parameters are compared with those reported in the literature. Using the Breit–Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is discussed for the a³Π electronic state. With the PECs obtained by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations, the complete vibrational states of each electronic state have been determined. The vibrational manifolds have been calculated for each vibrational state of each electronic state. The vibrational level G(ν), inertial rotation constant B_ν, and centrifugal distortion constant D_ν of the first 20 vibrational states when the rotational quantum number J equals zero are reported and compared with the experimental data. Comparison with the measurements demonstrates that the present spectroscopic parameters and molecular constants determined by the MRCI+Q/aug‐cc‐pV5Z+CV+DK calculations are both reliable and accurate. © 2012 Wiley Periodicals, Inc.     

Side-chain effects in molecular electronic devices

We discuss the effect of an abundant structural element of molecules on the transmission probabilities of molecular electronic devices. We show that an attachment of side chains to a molecular conductor may lead to zero transmission probabilities. The gaps in the transmission-probability appear approximately at the eigenvalues of the isolated side chains, provided that the corresponding eigenstates are not localized away from the molecular conductor. Simple Hückel-type calculations serve to illustrate the described effect. Furthermore, we show that complex transmission-probability curves, obtained with Kohn-Sham density-functional theory, also exhibit the described side-chain effect.     

Exchange effects on electronic states in jellium clusters

Hartree-Fock calculations are done for finite number of valence electrons (8, 20, 40, and 58) in a positively charged uniform background (jellium) with the density of bulk sodium. Differences and similarities with the results of Kohn-Sham local-density calculations are discussed. State-dependence and suppression of the wave functions are the two important effects coming from the nonlocality of the Hartree-Fock potential. These two effects, however, cancel in the density profile of electrons. The Kohn-Sham calculations consequently produce similar density profiles as in the Hartree-Fock calculations. The dipole polarizability is also calculated for 8-mers. The calculated value is still smaller than the measured one and is not an improvement of the insufficient Kohn-Sham result.deceased     

Vibrational spectroscopic study on polymorphism and molecular aggregation states in polyoxymethylene

Polarized Raman spectra of the moth-shaped single-crystal of orthorhombic polyoxymethylene (metastable phase) have been investigated by means of the Raman microprobe technique in the frequency range covering both molecular and lattice vibrations. The observed polarizations of the Raman bands are found to be strongly influenced by the optical alignment in the microscope, mainly by the polarization scrambling effect. By taking the optical effect into account, the orientation of the crystal axes in the single-crystal is investigated. Normal mode analysis of the orthorhombic crystal is performed based on the newly obtained polarization data. Raman spectra of two crystalline samples of trigonal polyoxymethylene (stable phase) differing in their morphology and in their structural orderliness are compared. In the spectrum of the needle-like crystal consisting of the fully extended molecules, measured at low temperature, eight Raman bands due to the E₂ symmetry species are newly detected     

Relativistic effects in low-lying electronic states of iron

Excited electronic states of Fe I have been calculated using the MRCI Douglas?CKroll?CHess method. Average spin-free excitation energies of the eight lowest even electronic terms ( $\hbox{a}^5\hbox{D}, \hbox{a}^5\hbox{F}, \hbox{a}^3\hbox{F}, \hbox{a}^5\hbox{P}, \hbox{a}^3\hbox{P2}, \hbox{a}^3\hbox{H}, \hbox{b}^3\hbox{F2}, \hbox{and a}^3\hbox{G}$ ) are reported. The RASSI method was employed for calculation of individual J levels of the four lowest terms. All reported values are in good agreement with experiment. Our study pointed out significant relativistic effects even in relatively light element like iron.     

Note on the role of vibrational modes in molecular electronic transitions

A simple application of a readily available quantum chemistry program (AMPAC) permits an illuminating presentation of the role of vibrational modes in electronic transitions. A direct comparison of modal surfaces for different electronic states of the same molecule can be made by using a perspective plot of the Duschinsky matrix for the transition with mode indices or eigenvalue sequence, as the planar axes. The sum of squares of the off-diagonal elements of the Duschinsky matrix can be used to give a measure of the difference between vibrational modes of the initial and final states. Calculations indicate that, in biacetyl, the triplet state is closer vibrationally to the anion ground state than either the singlet or the neutral ground state, while in glyoxal the ground state neutral has greater vibrational similarity to the anion ground state. The measure also indicates little change in vibrational modes upon intersystem crossing in formaldehyde.     

Photodissociation of CCH: classical trajectory calculations involving seven electronic states

The photodissociation dynamics of ethynyl radical, C(2)H, involving seven electronic states is studied by classical trajectory calculations. Initial values of the trajectories are selected based on relative absorption intensities calculated by Mebel et al. The energies and the derivatives are interpolated by three-dimensional cubic spline interpolator using an extended data pool. Mean square errors and standard deviations in interpolation of energies for 450 data points are found to be in the range 3.1 x 10(-6)-1.4 x 10(-5) and 1.7 x 10(-3)-3.8 x 10(-3) hartrees, respectively. The photofragments of C(2) and H are produced mainly in the X (1)Sigma(g) (+), a (3)Pi(u), b (3)Sigma(g) (-), c (3)Sigma(u) (+), A (1)Pi(u), B (1)Delta(g) electronic states of C(2) as product. The avoided crossings do not appear to be in the main dissociation pathways. The internal distributions are in good accord with the experimental results where comparison is possible, suggesting that the fragmentation mechanism of C(2)H(2) into C(2) and H is a two step process involving C(2)H radical as an intermediate with a life time long enough to allow complete collection of the phase space in the experiments.     

Optical transitions,XPS, electronic states in NiPS3

We have measured the optical absorption below the fundamental threshold, the normal-incidence reflectivity between 1.5 and 30 eV and the X-ray photoemission spectra of NiPS₃. Shake-up satellites present at the Ni 2p and 3p core levels are strong evidence for the ionicity of the NiS bonds. We have also derived a qualitative molecular orbital model of NiPS₃ in which the trigonal crystal field splits the P and S 3p_xp_y-3p_a states, and strong covalent hybridization between P and S p_xp_y orbitals leads to covalent electronic bonding. Ni is envisaged as a divalent ion which plays little role in the electronic bonding and its 3d levels are localized, lying near the top both of the valence states. This model accounts well for both the valence band XPS data and the low energy optical transitions. Our model should represent, at the center of the Brillouin zone but not at the boundaries, the energy level sequence in NiPS₃ and other related MPX₃ layer-type compounds where M Co²⁺, Mn²⁺, Fe²⁺, Zn²⁺ and X is sulfur or selenium.The XPS spectra and optical properties of NiPS₃ have been obtained and interpreted on a qualitative molecular orbital model in which the Ni is a divalent positive ion which plays little role in the bonding. Evidence for such ionicity appears in the optical properties and XPS satellite structures, as well as in the magnetic properties. The model should represent qualitatively the band structure at the center of the Brillouin zone, but not at the boundaries. It should also be valid for other compounds similar to NiPS₃, i.e. those with other metals in place of Ni and those with Se in place of S.     

Characteristics of calculation of electronic states of orbitally degenerate systems for some macrocyclic ligands

Taking into account electron correlation in the -electron approximation, we have calculated the splitting of the quasidegenerate states in the dianions of porphyrin and TAAB metal complexes. The position of the phosphorescent terms for the metalloporphyrin in this approach comes closer to the experimental result than when only singly degenerate configurations are taken into account.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 3, pp. 332–334, May–June, 1990.     

Vibrational dynamics of excited electronic states of molecular iodine

Femtosecond degenerate four-wave-mixing spectroscopy following an initial pump laser pulse was used to observe the wave packet dynamics in excited electronic states of gas phase iodine. The focus of the investigation was on the ion pair states belonging to the first tier dissociating into the two ions I-(1S) + I+(3P2). By a proper choice of the wavelengths of the initial pump and degenerate four-wave-mixing pulses, we were able to observe the vibrational dynamics of the B (3)Pi(u) (+) state of molecular iodine as well as the ion pair states accessible from there by a one-photon transition. The method proves to be a valuable tool for exploring higher lying states that cannot be directly accessed from the ground state due to selection rule exclusion or unfavorable Franck-Condon overlap.     

Vibronic dressed electronic states and nonadiabatic effects in polyacetylene

Conditions for low and high T_c superconductors following from the nonadiabatic electron-vibrational theory at ab initio level have been obtained. According to the presented results, the supercurrent is realized by the motion of the ground-state electronic-charge distribution of the fully occupied band. The motion of the electronic-charge distribution is conditioned by the newly arisen, nondissipative degrees of freedom of nuclear, Jahn–Teller-like, microflows. The Meissner effect is also interpreted.