Nuclear motion on the orbitally degenerate electronic ground state of fully deuterated triatomic hydrogen

Nuclear motion in the vicinity of conical intersections of the degenerate electronic ground state of fully deuterated triatomic hydrogen, D(3), is investigated with the aid of a time-dependent wavepacket approach in hyperspherical coordinates. Vibronic energy level spectra and the eigenfunctions are examined by including, for example, (1) geometric phase (GP) correction, (2) diagonal Born-Huang (BH) correction, and (3) both GP and BH corrections to the Born-Oppenheimer adiabatic Hamiltonian and finally by considering the nonadiabatic coupling between the two electronic surfaces explicitly. It emerges from this study that inclusion of both the GP and BH corrections is insufficient to explain the spectral features observed in the experiment. The latter are recovered by considering the complete two-states coupled Hamiltonian only. This study shows that both the GP and BH corrections constitute a minor part of the surface coupling effects, in particular, on the dynamics of the upper adiabatic sheet. Most importantly, we add that the experimental signature of the GP effect appears only in the observed shift of the eigenlevels of the electronic state when compared to those obtained from a completely Born-Oppenheimer Hamiltonian. The detail fine structure of the observed band of the electronic state is shaped by the off-diagonal derivative coupling elements of the nonadiabatic coupling operator.     

On the calculation of vibronic coupling matrix elements

The non-diagonal matrix elements in the adiabatic Born-Oppenheimer approximation are considered. The effect of the Q-dependence of the electronic energy denominator is calculated explicitly for an arbitrary initial and final state. It is shown that the inclusion of this effect does not change the relative values of the coupling matrix elements for different initial vibronic states.     

A quantum wave packet dynamical study of the electronic and spin-orbit coupling effects on the resonances in Cl(2P) + H2 scattering

Dynamical resonances in Cl(2P) + H2 scattering are investigated with the aid of a time-dependent wave packet approach using the Capecchi-Werner coupled ab initio potential energy surfaces [Phys. Chem. Chem. Phys. 2004, 6, 4975]. The resonances arising from the prereactive van der Waals well (approximately 0.5 kcal/mol) and the transition-state (TS) region of the 2Sigma(1/2) ground spin-orbit (SO) state of the Cl(2P) + H2 system are calculated and assigned by computing their eigenfunctions and lifetimes. The excitation of even quanta along the bending coordinate of the resonances is observed. The resonances exhibit an extended van der Waals progression, which can be attributed to the dissociative states of ClH2. Excitation of H2 vibration is also identified in the high-energy resonances. The effect of the excited 2P(1/2) SO state of Cl on these resonances is examined by considering the electronic and SO coupling in the dynamical simulations. While the electronic coupling has only a minor impact on the resonance structures, the SO coupling has significant effect on them. The nonadiabatic effect due to the SO coupling is stronger, and as a result, the spectrum becomes broad and diffuse particularly at high energies. We also report the photodetachment spectrum of ClD2- and compare the theoretical findings with the available experimental results.     

Energy Stabilities,Magnetic Properties,and Electronic Structures of Diluted Magnetic Semiconductor Zn1-xMnxS(001) Thin Films

We investigate the electronic and magnetic properties of the diluted magnetic semiconductors Zn_1-xMn_xS(001) thin films with different Mn doping concentrations using the total energy density functional theory. The energy stability and density of states of a single Mn atom and two Mn atoms at various doped configurations and different magnetic coupling state were calculated. Different doping configurations have different degrees of p-d hybridization, and because Mn atoms are located in different crystal-field environment, the 3d projected densities of states peak splitting of different Mn doping configurations are quite different. In the two Mn atoms doped, the calculated ground states of three kinds of stable configurations are anti-ferromagnetic state. We analyzed the 3d density of states diagram of three kinds of energy stability configurations with the two Mn atoms in different magnetic coupling state. When the two Mn atoms are ferromagnetic coupling, due to d-d electron interactions, density of states of anti-bonding state have significant broadening peaks. As the concentration of Mn atoms increases, there is a tendency for Mn atoms to form nearest neighbors and cluster around S. For such these configurations, the antiferromagnetic coupling between Mn atoms is energetically more favorable.     

Curl condition for a four-state Born-Oppenheimer system employing the Mathieu equation

When a group of four states forms a subspace of the Hilbert space, i.e., appears to be strongly coupled with each other but very weakly interacts with all other states of the entire space, it is possible to express the nonadiabatic coupling (NAC) elements either in terms of s or in terms of electronic basis function angles, namely, mixing angles presumably representing the same sub-Hilbert space. We demonstrate that those explicit forms of the NAC terms satisfy the curl conditions--the necessary requirements to ensure the adiabatic-diabatic transformation in order to remove the NAC terms (could be often singular also at specific point(s) or along a seam in the configuration space) in the adiabatic representation of nuclear SE and to obtain the diabatic one with smooth functional form of coupling terms among the electronic states. In order to formulate extended Born-Oppenheimer (EBO) equations [J. Chem. Phys. 2006, 124, 074101] for a group of four states, we show that there should exist a coordinate independent ratio of the gradients for each pair of ADT/mixing angles leading to zero curls and, thereafter, provide a brief discussion on its analytical validity. As a numerical justification, we consider the first four eigenfunctions of the Mathieu equation to demonstrate the interesting features of nonadiabatic coupling (NAC) elements, namely, the validity of curl conditions and the nature of curl equations around CIs.     

Electronic spectrum of UO2(2+) and [UO2Cl4]2- calculated with time-dependent density functional theory

The electronic spectra of UO(2) (2+) and [UO(2)Cl(4)](2-) are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding sigma(u) (+) orbital into the nonbonding delta(u) or phi(u) orbitals for UO(2) (2+) and the corresponding excitations for [UO(2)Cl(4)](2-) are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U-O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.     

An ab initio study of the hyperfine structure in the X2 Pi electronic state of CCCH

The results of an ab initio study of the magnetic hyperfine structure in the X (2)Pi electronic state of CCCH are reported. The potential surfaces for two components of the X (2)Pi electronic state were computed by means of an extensive configuration interaction approach. The electronically averaged hyperfine coupling constants of H and (13)C for (12)C (12)C (12)CH, (13)C (12)C (12)CH, (12)C (13)C (12)CH, and (12)C (12)C (13)CH are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with the help of a variational approach which takes into account the Renner-Teller effect and spin-orbit coupling. The model Hamiltonian is expressed in terms of the normal bending coordinates. It is found that, due to the generally strong geometry dependence of the hyperfine coupling constants, it is necessary to carry out the vibronic averaging of the corresponding functions in order to obtain the values which can be compared to the results of the measurements. The results of the present study help to reliably interpret the experimental data previously published. They also predict the yet unobserved hyperfine structure in excited vibronic states.     

Ab initio calculations on the excited states of Na3 cluster to explore beyond Born-Oppenheimer theories: adiabatic to diabatic potential energy surfaces and nuclear dynamics

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na(3) cluster and present the adiabatic PESs for the electronic states 2(2)E' and 1(2)A(1)', and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 2(2)E' and 1(2)A(1)' demonstrate the numerical validity of so called "Curl Condition," such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the "adiabatic-diabatic transformation (ADT)" equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na(3) cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation.     

An Anderson impurity model for efficient sampling of adiabatic potential energy surfaces of transition metal complexes

We present a model intended for rapid sampling of ground and excited state potential energy surfaces for first-row transition metal active sites. The method is computationally inexpensive and is suited for dynamics simulations where (1) adiabatic states are required "on-the-fly" and (2) the primary source of the electronic coupling between the diabatic states is the perturbative spin-orbit interaction among the 3d electrons. The model Hamiltonian we develop is a variant of the Anderson impurity model and achieves efficiency through a physically motivated basis set reduction based on the large value of the d-d Coulomb interaction U(d) and a Lanczos matrix diagonalization routine to solve for eigenvalues. The model parameters are constrained by fits to the partial density of states obtained from ab initio density functional theory calculations. For a particular application of our model we focus on electron transfer occurring between cobalt ions solvated by ammonium, incorporating configuration interaction between multiplet states for both metal ions. We demonstrate the capability of the method to efficiently calculate adiabatic potential energy surfaces and the electronic coupling factor we have calculated compares well to previous calculations and experiment. (     

Accurate, two-state ab initio study of the ground and first-excited states of He2+, including exact treatment of all Born-Oppenheimer correction terms

Born-Oppenheimer (BO) potentials for the ground and first-excited electronic states of He2+ are determined using high level ab initio techniques for internuclear separations R of 1.2-100 bohrs and accurately fit to analytical functions. In the present formulation, the BO potentials are nuclear mass independent, and the corresponding BO approximation is obtained by ignoring four terms of the full rovibronic Hamiltonian. These four Born-Oppenheimer correction (BOC) terms are as follows: (1) mass polarization, (2) electronic orbital angular momentum, (3) first derivative with respect to R, and (4) second derivative with respect to R. In order to enable an exact rovibronic calculation, each of the four BOC terms are computed as a function of R, for the two electronic states and for their coupling, without any approximation or use of empirical parameters. Each of the BOC terms is found to make a contribution to the total energy over at least some portion of the range of R investigated. Interestingly, the most significant coupling contribution arises from the electronic orbital angular momentum term, which is evidently computed for the first time in this work. Although several BOC curves exhibit a nontrivial dependence on R, all are accurately fit to analytical functions. The resulting functions, together with the BO potentials, are used to compute exact rovibronic energy levels for 3He 3He+,3He 4He+) and 4He 4He+. Comparison to available high quality experimental data indicates that the present BOC potentials provide the most accurate representation currently available of both the low- and high-lying levels of the ground electronic state and the bound levels of the excited state.     

Ab initio vibration and ro-vibrational spectrum of the 1A1 state of He2Si2+

The low-lying ro-vibrational states for the ground electronic state (1A1) of HeSi2+ have been calculated using an ab initio variational solution of the nuclear Schr?dinger equation. A 96 point CCSD(T)/cc-pCVQZ potential energy surface (PES) has been calculated and a Ogilvie-Padé (3,6) potential energy function has been generated. This force field was embedded in the Eckart-Watson Hamiltonian from which the vibrational and ro-vibrational eigenfunctions and eigenenergies have been variationally calculated. A 70 point QCISD/aug-cc-pCVTZ discrete dipole moment surface (DMS) was calculated and a 5th order power series expansion (in terms of the two bond lengths and the included bond angle) has been generated. Absolute line intensities have been calculated and are presented for some of the most intense transitions between the vibrational ground state and the low-lying ro-vibrational states of this ion.     

Influence of ion pairing on the UV-spectral behavior of KI dissolved in supercritical NH3: from vapor phase to condensed liquid

The UV-spectroscopic behavior of KI dissolved in supercritical ammonia enabled us to identify two species that contribute to the optical absorption depending on the fluid density rho1 and the temperature T. At low rho1 and high T, contact ion pairs (CIPs) prevail, while at high density of ammonia, solvent separated ion pairs (SSIPs) and free iodide ions dominate the optical absorption of the solute. The features of the electron excitation process depend on the state of the K+ I- species present. Starting with isolated KI in the vapor, where the process is an interionic charge transfer, when the CIP becomes solvated the UV absorption shifts strongly to the blue. As rho1 increases, the amounts of SSIP and of free iodide increase progressively and their electronic excited states become those characteristic of the charge-transfer-to-solvent process. This study suggests there is a strong influence of the cation on the electronic transition of dissolved iodide when it is forming CIPs. Moreover, the fact that K+-NH3 interaction is much larger than that of I(-)-NH3 suggests that the electronic photoinduced excited state of CIPs is similar to the ground state observed for alkali metals in NH3 clusters.     

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.     

A combined computational and experimental study on DNA-photocleavage of Ru(II) polypyridyl complexes [Ru(bpy)2(L)]2+ (L = pip, o-mopip and p-mopip)

A combined computational and experimental study on DNA-photocleavage by Ru(II) polypyridyl complexes [Ru(bpy)2(L)]2+ 1-3 (bpy = 2,2-bipyridine; L: pip = 2-phenylimidazo[4,5-f]1,10-phenanthroline, o-mopip = 2-(2-methoxyphenyl)imidazo[4,5-f]1,10-phenanthroline and p-mopip = 2-(4-methoxyphenyl)imidazo[4,5-f]1,10-phenanthroline) has been carried out. The DNA-photocleavage behavior of these complexes was comparably measured by the gel electrophoresis experiments. The experimental results show that they can induce considerable DNA-photocleavage, and have different DNA-photocleavage efficiencies (phi) following the order phi (1) < phi (2) < phi (3). In order to understand their DNA-photocleavage mechanism and trend, the theoretical studies on the geometric and electronic structures of these complexes in the ground state (S0), the first singlet excited state (S1) and triplet excited states (T1), have been carried out using the density functional theory (DFT/TD-DFT), Hartree-Fock (HF) and configuration interaction singles (CIS) methods. In particular, the reduction potentials (E*red) of the excited complexes in aqueous solution, which seem to be closely responsible for the DNA-photocleavage behavior, were calculated to be 0.966 V (vs. SCE) for complex , 1.024 V (vs. SCE) for complex and 1.030 V (vs. SCE) for complex , respectively. Such computational results show that the reduction potentials of the excited complexes reach the theoretical range for oxidizing some DNA-bases, and follow the order E*red (1) < E*red (2) < E*red (3). Therefore, here, in addition to the general theoretical explanation of their DNA-photocleavage mechanism according to our recent report, a further explanation on the trend of their DNA-photocleavage efficiencies, i.e., phi (1) < phi (2) < phi (3), was reasonably carried out, on the basis of the calculated electrochemical properties in the excited states as well as general photochemical insights.     

Electronic and quantum dynamical insight into the ultrafast proton transfer of 1-hydroxy-2-acetonaphthone

The ultrafast proton-transfer dynamics of 1-hydroxy-2-acetonaphthone has been theoretically analyzed in the ground and first singlet excited electronic states by density functional theory calculations and quantum dynamics. The potential energies obtained in the ground electronic state reveal that the proton-transfer process does not lead to a stable keto tautomer unless the transfer of the hydrogen from the enol form is accompanied by an internal rotation of the newly formed O-H bond. Calculations in the first singlet excited electronic state point to a very low barrier for the formation of the keto tautomer. The analysis of the calculated frequencies of the two tautomers in the excited state unveils a coupling of the skeletal motions (low frequency modes) with the proton-transfer process, as it has been stated from time-resolved experiments. The electronic energies obtained by the time-dependent density functional theory formalism have been fitted to a monodimensional potential energy surface in order to perform an exact quantum dynamics study of the process. Our results show that the proton-transfer process is completed within 25.5 fs, in remarkable good agreement with experiments.     

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Spin-inversion dynamics in O₂ binding to a model heme complex, which consisted of Fe(II)-porphyrin and imidazole, were studied using nonadiabatic wave packet dynamics calculations. We considered three active nuclear degrees of freedom in the dynamics, including the motions along the Fe–O distance, Fe–O–O angle, and Fe out-of-plane distance. Spin-free potential energy surfaces for the singlet, triplet, quintet, and septet states were developed using density functional theory calculations, and spin–orbit coupling elements were obtained from CASSCF-level electronic structure calculations. The spin-inversion mainly occurred between the singlet state and one of the triplet states due to large spin–orbit couplings and the contributions of other states were extremely small. The present quantum dynamics calculations suggested that the narrow crossing region model plays a dominant role in the O₂ binding dynamics. In addition, the one-dimensional Landau–Zener model underestimated the nonadiabatic transition probability.     

The influence of vibronic interactions on the chiroptical spectra of dissymmetric pseudo tetragonal metal complexes

The influence of vibronic interactions on the chiroptical spectra associated with a threesome of nearly degenerate electronic excited states in a dissymmetric molecular system is examined on a formal theoretical model. The model considers two vibrational modes to be effective in promoting pseudo Jahn-Teller (PJT) type interactions between the three closely spaced electronic excited states. Formal expressions are developed for the rotatory strengths of individual vibronic levels derived from the coupled electronic states. Two mode (vibrational)-three state (electronic) vibronic Hamiltonians are constructed (basis set size, 63–108, depending upon interaction parameters used) and diagonalized for a large number of different parameter sets representative of various vibronic coupling strengths, electronic energy level spacings, oscillator (vibrational mode) frequencies, and electronic rotatory strengths. Diagonalization of these vibronic Hamiltonians yields vibronic wave functions and energies which are then used to calculate rotatory strength spectra for the model system. The calculated results demonstrate the profound influence which vibronic interactions of the PJT type may have on the sign patterns and intensity distributions within the rotatory strength spectrum associated with a set of nearly degenerate electronic states. The implication of these results for the interpretation of circular dichroism spectra of chiral transition metal complexes with pseudo tetragonal symmetry are discussed.     

Computed lifetimes of metastable states of the NO2+ dication

Based on the ab initio potential energy, spin-orbit coupling, electronic transition dipole moment, and radial nonadiabatic coupling functions, the energy level positions, lifetimes, and radiative transition probabilities (Einstein A coefficients) have been determined for the lowest electronic states of NO2+ using the log-amplitude-phase, stabilization, and complex-scaling methods. The calculated characteristics are in reasonable agreement to the available experimental data, thus, evidencing the reliability of the theoretical predictions for the characteristics unobserved to date. With the exception of the v相似文献   

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.