Theoretical study of photodetachment processes of anionic boron clusters. II. Dynamics

Photodetachment bands of anionic boron clusters, B(n) (n = 4,5) are theoretically examined here. The model Hamiltonians developed through extensive ab initio quantum chemistry calculations in Paper I are employed for the required nuclear dynamics study. While the precise location of vibronic lines and progression of vibrational modes within a given electronic band is derived from time-independent quantum mechanical studies, the broadband spectral envelopes and the nonradiative decay rate of electronic states are calculated by propagating wave packets in a time-dependent quantum mechanical framework. The theoretical results are in good accord with the experiment to a large extent. The discrepancies between the two can be partly attributed to the inadequate energy resolution of the experimental results and also to the neglect of dynamic spin-orbit interactions and computational difficulty related with detachment channels involving multi-electron transitions in the theoretical formalism.     

Theoretical study of electronically excited radical cations of naphthalene and anthracene as archetypal models for astrophysical observations. Part I. Static aspects

Motivated by the recent discovery of new diffuse interstellar bands and results from laboratory experiments, ab initio quantum chemistry calculations are carried out for the lowest six electronic states of naphthalene and anthracene radical cations. The calculated adiabatic electronic energies are utilized to construct suitable diabatic electronic Hamiltonians in order to perform nuclear dynamics studies in Part II. Complex entanglement of the electronic states is established for both the radical cations and the coupling surfaces among them are also derived in accordance with the symmetry selection rules. Critical examination of the coupling parameters of the Hamiltonian suggests that 29 (out of 48) and 31 (out of 66) vibrational modes are relevant in the nuclear dynamics in the six lowest electronic states of naphthalene and anthracene radical cations, respectively.     

AB initio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular wavefunctions

The first ab initio procedure for the treatment of spin-orbit coupling in molecules based on the use of relativistic effective potentials derived from Dirac-Fock atomic wavefunctions is presented. A rigorous definition for the spin-orbit operator is given and its use in molecular calculations discussed.     

Spin-orbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation

A new method has been reported recently [H. Ndome, R. Welsch, and W. Eisfeld, J. Chem. Phys. 136, 034103 (2012)] that allows the efficient generation of fully coupled potential energy surfaces (PESs) including derivative and spin-orbit (SO) coupling. The method is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator and therefore is called effective relativistic coupling by asymptotic representation (ERCAR). The resulting diabatic spin-orbit coupling matrix is constant and the geometry dependence of the coupling between the eigenstates is accounted for by the diabatization. This approach allows to generate an analytical model for the fully coupled PESs without performing any ab initio SO calculations (except perhaps for the atoms) and thus is very efficient. In the present work, we study the performance of this new method for the example of hydrogen iodide as a well-established test case. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations. The energies of the adiabatic fine structure states are reproduced in excellent agreement with reference ab initio data. It is shown that the accuracy of the ERCAR approach mainly depends on the quality of the underlying ab initio data. This is also the case for dissociation and vibrational level energies, which are influenced by the SO coupling. A method is presented how one-electron operators and the corresponding properties can be evaluated in the framework of the ERCAR approach. This allows the computation of dipole and transition moments of the fine structure states in good agreement with ab initio data. The new method is shown to be very promising for the construction of fully coupled PESs for more complex polyatomic systems to be used in quantum dynamics studies.     

Theoretical transition probabilities for the OH Meinel system

The authors present a new potential energy curve, electric dipole moment function, and spin-orbit coupling function for OH in the X 2Pi state, based on high-level ab initio calculations. These properties, combined with a spectroscopically parametrized lambda-type doubling Hamiltonian, are used to compute the Einstein A coefficients and photoabsorption cross sections for the OH Meinel transitions. The authors investigate the effect of spin-orbit coupling on the lifetimes of rovibrationally excited states. Comparing their results with earlier ab initio calculations, they conclude that their dipole moment and potential energy curve give the best agreement with experimental data to date. The results are made available via EPAPS Document No. E-JCPSAG-017709.     

The effect of spin-orbit coupling on the surface dynamical properties and electron-phonon interaction of Tl(0001)

We present an ab initio study of the effect of spin-orbit coupling on the dynamical properties of the Tl(0001) surface as well as on the electron-phonon interaction at the surface. The calculations based on density-functional theory were carried out using a linear response approach and a mixed-basis pseudopotential method. It is shown that the spin-orbit effects on the phonon spectrum and the electron-phonon interaction at the Fermi level of the surface are weak but conspire to a reduction in the electron-phonon coupling strength by 16%.     

Investigating magnetostructural correlations in the pseudooctahedral trans-[Ni(II){(OPPh2)(EPPh2)N}2(sol)2] complexes (E = S, Se; sol = DMF, THF) by magnetometry, HFEPR, and ab initio quantum chemistry

In this work, magnetometry and high-frequency and -field electron paramagnetic resonance spectroscopy (HFEPR) have been employed in order to determine the spin Hamiltonian (SH) parameters of the non-Kramers, S = 1, pseudooctahedral trans-[Ni(II){(OPPh(2))(EPPh(2))N}(2)(sol)(2)] (E = S, Se; sol = DMF, THF) complexes. X-ray crystallographic studies on these compounds revealed a highly anisotropic NiO(4)E(2) coordination environment, as well as subtle structural differences, owing to the nature of the Ni(II)-coordinated solvent molecule or ligand E atoms. The effects of these structural characteristics on the magnetic properties of the complexes were investigated. The accurately HFEPR-determined SH zero-field-splitting (zfs) D and E parameters, along with the structural data, provided the basis for a systematic density functional theory (DFT) and multiconfigurational ab initio computational analysis, aimed at further elucidating the electronic structure of the complexes. DFT methods yielded only qualitatively useful data. However, already entry level ab initio methods yielded good results for the investigated magnetic properties, provided that the property calculations are taken beyond a second-order treatment of the spin-orbit coupling (SOC) interaction. This was achieved by quasi-degenerate perturbation theory, in conjunction with state-averaged complete active space self-consistent-field calculations. The accuracy in the calculated D parameters improves upon recovering dynamic correlation with multiconfigurational ab initio methods, such as the second-order N-electron valence perturbation theory NEVPT2, the difference dedicated configuration interaction, and the spectroscopy-oriented configuration interaction. The calculations showed that the magnitude of D (～3-7 cm(-1)) in these complexes is mainly dominated by multiple SOC contributions, the origin of which was analyzed in detail. In addition, the observed largely rhombic regime (E/D = 0.16-0.33) is attributed to the highly distorted metal coordination sphere. Of special importance is the insight by this work on the zfs effects of Se coordination to Ni(II). Overall, a combined experimental and theoretical methodology is provided, as a means to probe the electronic structure of octahedral Ni(II) complexes.     

Spin-orbit effect in the energy pooling reaction O2(a 1Delta)+O2(a 1Delta)-->O2(b 1Sigma)+O2(X 3Sigma)

Five-dimensional nonadiabatic quantum dynamics studies have been carried out on two new potential energy surfaces of S(2)((1)A(')) and T(7)((3)A(")) states for the title oxygen molecules collision with coplanar configurations, along with the spin-orbit coupling between them. The ab initio calculations are based on complete active state second-order perturbation theory with the 6-31+G(d) basis set. The calculated spin-orbit induced transition probability as a function of collision energy is found to be very small for this energy pooling reaction. The rate constant obtained from a uniform J-shifting approach is compared with the existing theoretical and experimental data, and the spin-orbit effect is also discussed in this electronic energy-transfer process.     

Computing charge-exchange cross sections for Ca+ collisions with Rb at low and ultralow energies

Collisions between Ca cations and Rb atoms are computed within a quantum approach that generates the most relevant potential energy curves from accurate ab initio methods and carries out the low-energy scattering calculations by including nonadiabatic and spin-orbit coupling terms. The cross sections are obtained at relative energies typical for the likely arrangements of Rb atoms in a Magneto-Optical Trap overlapped with a Coulomb Crystal of Ca cations. The dominant nonadiabatic process is clearly identified and the efficiency of the nonadiabatic coupling terms which lead to the charge-exchange process is discussed.     

Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory

A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and pi-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO2 radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.     

Spin-orbit mechanism of predissociation in the Wulf band of ozone

Previously calculated resonance widths of the ground vibrational levels in the electronic states 1 (3)A" ((3)A(2)) and 1 (3)A' ((3)B(2)), which belong to the Wulf band system of ozone, are significantly smaller than observed experimentally. We demonstrate that predissociation is drastically enhanced by spin-orbit coupling between 1 (3)A"/X (1)A' and 1 (3)A'/1 (3)A". Multistate quantum mechanical calculations using ab initio spin-orbit coupling matrix elements give linewidths of optically bright components of the right order of magnitude.     

Quantum wave packet ab initio molecular dynamics: an approach to study quantum dynamics in large systems

A methodology to efficiently conduct simultaneous dynamics of electrons and nuclei is presented. The approach involves quantum wave packet dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator, in conjunction with ab initio molecular dynamics treatment of the electronic and classical nuclear degree of freedom. The latter may be achieved either by using atom-centered density-matrix propagation or by using Born-Oppenheimer dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. The quantum wave packet dynamics is made computationally robust by using adaptive grids to achieve optimized sampling. One notable feature of the approach is that important quantum dynamical effects including zero-point effects, tunneling, as well as over-barrier reflections are treated accurately. The electronic degrees of freedom are simultaneously handled at accurate levels of density functional theory, including hybrid or gradient corrected approximations. Benchmark calculations are provided for proton transfer systems and the dynamics results are compared with exact calculations to determine the accuracy of the approach.     

The effect of spin-orbit coupling on fast neutral chemical reaction O(3P)+CH3-->CH3O

The effect of nonadiabatic transitions through the spin-orbit couplings has been investigated on the fast neutral reaction, O((3)P)+CH(3)-->CH(3)O. Adiabatic potential energies and the spin-orbit coupling terms have been evaluated for the four electronic states of CH(3)O ((2)E, (2)A(2), (4)E, and (4)A(2)) that correlate with the O((3)P)+CH(3) asymptote, as a function of CO distance and OCH angle under the C(3v) symmetry, by ab initio electronic structure calculations using multireference internally contracted single and double excitation configuration interaction method with the 6-311G(2df,2pd) basis sets. Multistate quantum reactive scattering calculations have been carried out with the use of thus obtained potential energies and spin-orbit coupling matrices, based on the generalized R-matrix propagation method. The calculated thermal rate constants show a slight positive dependence on temperature in a range between 50 and 2000 K, supporting the previous experimental results. It is shown that the spin-orbit coupled excited states give rise to reflections over the centrifugal barrier due to the quantum interference. Classical capture calculations yield larger rate constants due to the neglect of quantum reflections. It is concluded that the effect of nonadiabatic transitions is of minor importance on the overall reactivity in this reaction.     

Ab initio treatment of the chemical reaction precursor complex Br(2P)-HCN. 1. Adiabatic and diabatic potential surfaces

The three adiabatic potential surfaces of the Br(2P)-HCN complex that correlate to the 2P ground state of the Br atom were calculated ab initio. With the aid of a geometry-dependent diabatic mixing angle, also calculated ab initio, these adiabatic potential surfaces were transformed into a set of four diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the atom-linear molecule Jacobi angle theta. The dependence of the expansion coefficients on the distance R between Br and the HCN center of mass and on the CH bond length was fit to an analytic form. For HCN in its equilibrium geometry, the global minimum with De = 800.4 cm(-1) and Re = 6.908a0 corresponds to a linear Br-NCH geometry, with an electronic ground state of Sigma symmetry. A local minimum with De = 415.1 cm-1, Re = 8.730a0, and a twofold degenerate Pi ground state is found for the linear Br-HCN geometry. The binding energy, De, depends strongly on the CH bond length for the Br-HCN complex and much less strongly for the Br-NCH complex, with a longer CH bond giving stronger binding for both complexes. Spin-orbit coupling was included and diabatic states were constructed that correlate to the ground 2P3/2 and excited 2P1/2 spin-orbit states of the Br atom. For the ground spin-orbit state with electronic angular momentum j = (3/2) the minimum in the potential for projection quantum number omega = +/-(3/2) coincides with the local minimum for linear Br-HCN of the spin-free case. The minimum in the potential for projection quantum number omega = +/-(1/2) occurs for linear Br-NCH but is considerably less deep than the global minimum of the spin-free case. According to the lowest spin-orbit coupling included adiabatic potential the two linear isomers, Br-NCH and Br-HCN, are about equally stable. In the subsequent paper, we use these potentials in calculations of the rovibronic states of the Br-HCN complex.     

Microwave spectra and molecular structures of (Z)-pent-2-en-4-ynenitrile and maleonitrile.

Accurate equilibrium structures have been determined for (Z)-pent-2-en-4-ynenitrile (8) and maleonitrile (9) by combining microwave spectroscopy data and ab initio quantum chemistry calculations. The microwave spectra of 10 isotopomers of 8 and 5 isotopomers of 9 were obtained using a pulsed nozzle Fourier transform microwave spectrometer. The ground-state rotational constants were adjusted for vibration-rotation interaction effects calculated from force fields obtained from ab initio calculations. The resultant equilibrium rotational constants were used to determine structures that are in very good agreement with those obtained from high-level ab initio calculations (CCSD(T)/cc-pVTZ). The geometric parameters in 8 and 9 are very similar; they also do not differ significantly from the all-carbon analogue, (Z)-hex-3-ene-1,5-diyne (7), the parent molecule for the Bergman cyclization. A small deviation from linearity about the alkyne and cyano linkages is observed for 7-9 and several related species where accurate equilibrium parameters are available. The data on 7-9 should be of interest to radioastronomy and may provide insights on the formation and interstellar chemistry of unsaturated species such as the cyanopolyynes.     

Ab initio dynamics with wave-packets and density matrices

Efficient methodologies to conduct simultaneous dynamics of electrons and nuclei are discussed. Particularly, attention is directed to a recent development that combines quantum dynamics with ab initio molecular dynamics. The two components of the methodology, namely, quantum dynamics and ab initio molecular dynamics, are harnessed together using a time-dependent self-consistent field-like coupling procedure. An approach to conduct quantum dynamics using an accurate banded, sparse and Toeplitz representation for the discrete free propagator is highlighted with suitable review of other related approaches. One notable feature of the method is that all important quantum dynamical effects including zero-point effects, tunneling as well as over-barrier reflections are accurately treated. Computational methodologies for improved efficiency of the quantum dynamics are also discussed. There exists a number of ways to carry out simultaneous ab initio molecular dynamics (such as Born–Oppenheimer dynamics and extended Lagrangian dynamics, Car–Parrinello dynamics being a prime example of the latter); our prime focus remains on atom-centered density-matrix propagation and Born–Oppenheimer dynamics. The electronic degrees of freedom are handled at accurate levels of density functional theory, using hybrid or gradient corrected approximations. Benchmark calculations are provided for a prototypical proton transfer system. Future generalizations and goals are discussed.     

Treatment of collinear and noncollinear electron spin within an approximate density functional based method

We report benchmark calculations of the density functional based tight-binding method concerning the magnetic properties of small iron clusters (Fe2 to Fe5) and the Fe13 icosahedron. Energetics and stability with respect to changes of cluster geometry of collinear and noncollinear spin configurations are in good agreement with ab initio results. The inclusion of spin-orbit coupling has been tested for the iron dimer.     

Ab initio potential energy surface and spectrum of the B(3Pi) state of the HeI2 complex

The three-dimensional interaction potential for I2(B 3Pi0u+)+He is computed using accurate ab initio methods and a large basis set. Scalar relativistic effects are accounted for by large-core relativistic pseudopotentials for the iodine atoms. Using multireference configuration interaction calculations with subsequent treatment of spin-orbit coupling, it is shown for linear and perpendicular structures of the complex that the interaction potential for I2(B 3Pi0u+)+He is very well approximated by the average of the 3A' and 3A" interaction potentials obtained without spin-orbit coupling. The three-dimensional 3A' and 3A" interaction potentials are computed at the unrestricted open-shell coupled-cluster level of theory using large basis sets. Bound state calculations based on the averaged surface are carried out and binding energies, vibrationally averaged structures, and frequencies are determined. These results are found to be in excellent accord with recent experimental measurements from laser-induced fluorescence and action spectra of HeI2. Furthermore, in combination with a recent X-state potential, the spectral blueshift is obtained and compared with available experimental values.     

High resolution probe of spin-orbit coupling and the singlet-triplet gap in chlorocarbene

Among the most important of chemical intermediates are the carbenes, characterized by a divalent carbon that generates low-lying biradical (triplet) and spin-paired (singlet) configurations with unique chemical reactivities. The "holy grail" of carbene chemistry has been determining the singlet-triplet gap and intersystem crossing rates. We report here the first high resolution spectra of singlet-triplet transitions in a prototypical singlet carbene, CHCl, which probe in detail the triplet state structure and spin-orbit coupling with the ground singlet state. Our spectra reveal a pronounced vibrational state dependence of the triplet state spin-spin splitting parameter, which we show is a sensitive probe of spin-orbit coupling with nearby singlet states. The parameters derived from our spectra, including a precise determination of the singlet-triplet energy gap, are in excellent agreement with recent ab initio calculations.