Spin-orbit Configuration Interaction Method Research Articles

Environmental considerations in ab initio calculations of electronic states of PtCl4 -2 complexes.

Many quantum chemical methods used for large complexes are based on a limited treatment of electrons due to the computational demand dictated by the number of electrons that must be explicitly considered, especially when considering the chemical environment. Such treatments can fail to correlate accurately with electronic spectra. Ab initio electronic structure theory using the spin-orbit configuration interaction method is applied in a study of spectral transitions in PtCl4 2- including counter-ion environmental effects. In this method, electronic wave functions are eigenfunctions of the total angular momentum operator belonging to one of the symmetry types of the molecular double group. PtCl4 2- is investigated as a charged gas phase complex, a point-charge-neutralized complex, and a pseudopotential-neutralized complex. Results indicate that the use of a whole-atom relativistic effective core potential for the potassium cation provides a more accurate representation of the environment than a point charge and accurately represents electronic states without increasing the complexity of the calculation and, therefore, its computational demand.

Quantum Interference Effects Theoretically Found in the Photodissociation Processes of the Second Absorption Bands of ICl and IBr Molecules.

Some quantum interference effects are exposed directly in experiments, but others are not and remain just hidden and thus require thorough theoretical analysis to be exposed. In this respect, the second absorption bands of IX (X = Cl, Br) molecules show an interesting behavior in the photofragment anisotropy of the lowest I((2)P3/2)+X((2)P3/2) product channel; it changes from strongly parallel distribution on the shorter wavelength side to strongly perpendicular distribution on the longer wavelength side. Because the responsible perpendicular third Ω = 1 (1(III)) excited state correlating adiabatically to this product channel has only a weak absorption, the parallel component flux yielding the same products must be comparatively weak, even though the responsible parallel excitations to the 0(+)(III) and/or 0(+)(IV) excited states have strong absorptions. In the present theoretical study, the branching ratios and the anisotropy parameters have been obtained using the spin-orbit configuration interaction method combined with the quantum mechanical wavepacket and semiclassical approaches. Significant quantum interference effect between the two dissociative de Broglie waves on the 0(+)(III) and 0(+)(IV) potential curves has been found through the avoided crossing, and the weak parallel flux to the ground-state product channel has been explained by their destructive interference character. This interference effect has weak excitation energy dependence due to rather unique behavior of their almost parallel potential curves from the Franck-Condon to avoided crossing regions.

Electric properties of the Cu+, Ag+ and Au+ cations in the ground 1S and excited 3D, 1D electronic states

The lowest-order electric properties of the coinage metal cations Cu+, Ag+ and Au+ are calculated ab initio. For the ground states, accurate coupled cluster estimations are presented for the static and dynamic dipole and quadrupole polarizabilities. Results of the similar quality are obtained for the static dipole polarizabilities and permanent quadrupole moments of the lowest excited triplet 3D states, whereas the first excited singlet 1D states are characterized at the lower level of correlation treatment. Effect of vectorial spin-orbit coupling is assessed using the spin-orbit configuration interaction method.

Theoretical study on the photofragment branching ratios and anisotropy parameters of ICl in the second absorption band

Potential energy curves, transition dipole moments, and non-adiabatic coupling terms of the excited states of ICl molecule have been obtained by the spin–orbit configuration interaction method to examine the branching ratios and the anisotropy parameters of the photodissociation process in the second absorption band. The calculation of the branching ratios with the time-dependent coupled Schrödinger equations, including the quantum interference effect between the 0+(III) and 0+(IV) states, shows good agreement with recent experiments, thus resolves the long standing disagreement. The contribution of the quantum interference effect to the photodissociation process is discussed based on a time-dependent perturbation treatment.

Switching of a coupled spin pair in a single-molecule junction

Single-molecule spintronics investigates electron transport through magnetic molecules that have an internal spin degree of freedom. To understand and control these individual molecules it is important to read their spin state. For unpaired spins, the Kondo effect has been observed as a low-temperature anomaly at small voltages. Here, we show that a coupled spin pair in a single magnetic molecule can be detected and that a bias voltage can be used to switch between two states of the molecule. In particular, we use the mechanically controlled break-junction technique to measure electronic transport through a single-molecule junction containing two coupled spin centres that are confined on two Co(2+) ions. Spin-orbit configuration interaction methods are used to calculate the combined spin system, where the ground state is found to be a pseudo-singlet and the first excitations behave as a pseudo-triplet. Experimentally, these states can be assigned to the absence and occurrence of a Kondo-like zero-bias anomaly in the low-temperature conductance data, respectively. By applying finite bias, we can repeatedly switch between the pseudo-singlet state and the pseudo-triplet state.

An ab initio study on the f-f hypersensitive transition intensities of lanthanide tribromide molecules

The oscillator strengths of the f-f hypersensitive transitions of lanthanide tribromides (LnBr 3; Ln = Pr through Tm except for Gd) were calculated by the multi-reference spin–orbit configuration interaction method. To examine previously proposed mechanisms, the Judd–Ofelt intensity parameters τ 2 based on the dynamic-coupling model were evaluated and compared with those by the CI calculations. The calculated intensity parameters had a similar magnitude, implying that the dynamic-coupling model has a dominant contribution to the intensities. The difference between the two parameters is discussed in terms of the effects of polarization shielding and ligand-to-metal charge transfer.

State-interacting spin-orbit configuration interaction method for J-resolved anisotropic static dipole polarizabilities: Application to Al, Ga, In, and Tl atoms

The state-interacting spin-orbit (SO) configuration interaction (CI) method, which uses the non-relativistic CI wave functions as the basis of the total SO Hamiltonian matrix, is combined with the finite-field approach and applied to J-resolved anisotropic static dipole polarizabilities of the third-group atoms from Al to Tl. Comparison with available data reveals excellent performance of the method for atoms up to the fifth period (In), especially if the scalar relativitic and the high-level correlation corrections are included. The method performs worse for 6s 26p Tl atom, most likely due to growing effect of the second-order SO coupling. Refined values of all the scalar and the tensor ground-state non-relativistic and J-resolved polarizabilities and, whenever possible, excited-state polarizabilities, are recommended based on the calculations performed and thorough analysis of the literature data.

Theoretical Study on the f−f Transition Intensities of Lanthanide Trihalide Systems

The photoabsorption intensities of intra-4f(N) transitions (f-f transitions) in lanthanide systems have been extensively studied with the semiempirical Judd-Ofelt theory. The oscillator strengths of most f-f transitions are insensitive to a change of surrounding environment because 4f electrons are shielded by closed-shell 5s and 5p electrons from outside. However, there are some exceptional transitions, so-called hypersensitive transitions, whose intensities are very sensitive to a change of surrounding environment, and the reason for this hypersensitivity has not been clarified. In this study, we calculated the oscillator strengths of lanthanide trihalides (LnX(3); Ln = Pr, Tm; X = Br, I) with the multireference spin-orbit configuration interaction method and obtained reasonably accurate values. To clarify the cause of hypersensitivity, we examined various possible effects on the oscillator strengths, such as molecular vibration, f-d mixing, ligand to metal charge transfer (LMCT), and intraligand excitation, and concluded that the effect of molecular vibration is very small and that the oscillator strengths of most f-f transitions including hypersensitive transitions arise from both the LMCT and dynamic-coupled intraligand excitations through their configuration mixings with the dominant configurations of 4f(N).

On the ultraviolet photofragmentation of CH3Xe+

The multireference spin-orbit configuration interaction method is employed to calculate potential energy surfaces for the ground and low-lying excited states of the CH(3)Xe(+) cation as functions of the Xe-C bond length and the Xe-C-H angle. It is shown that the X (1)A(1) ground state of CH(3)Xe(+) is well bound (D(e)=1.78 eV) and dissociates to the CH(3)(+)(X (1)A(1)(')) + Xe((1)S) limit. In contrast, all lowest excited states of CH(3)Xe(+) are repulsive in the Franck-Condon region and converge to the strongly spin-split CH(3)(X (2)A(")) + Xe(+)((2)P(3/2,1/2)) asymptotes. Transition dipole moments for the low-lying valence states are computed at the X (1)A(1) equilibrium geometry. It is shown that the first absorption continuum (A band) of CH(3)Xe(+) is dominated by the parallel (3)Q(0(+))(A(1)) <-- X (1)A(1) transition, which leads to the CH(3) + Xe(+)((2)P(3/2)) dissociation products. The perpendicular transitions to the (1)Q(E), (3)Q(1)(E), and (3)A(1)(E) states are found to be significantly weaker. The CH(3)Xe(+) photodissociation process in its A band is analyzed on the basis of the computed data and compared with the photodissociation of the isovalent RgH(+) (Rg = Ar,Kr,Xe), HI, and CH(3)I systems.

Ab initio study of the KrH+ photodissociation

The multireference spin-orbit configuration interaction method is employed to calculate potential energy curves for the ground and low-lying excited states of the KrH(+) cation. For the first time, the spin-orbit interaction is taken into account and electric dipole moments are computed for transitions to the states responsible for the first absorption continuum (A band) of KrH(+). On this basis, the partial and total absorption spectra in this energy range are obtained. It is shown that the A-band absorption is dominated by the parallel A (1)Sigma(+)<--X (1)Sigma(+) transition. In the low-energy part of the band (<83x10(3) cm(-1)) the absorption is mainly caused by the spin-forbidden b (3)Pi(0(+) )<--X (1)Sigma(+) excitation, while perpendicular transitions to the B (1)Pi and b (3)Pi(1) states are significantly weaker. The branching ratio Gamma for the photodissociation products is calculated and it is shown to increase smoothly from 0 in the red tail of the band to 1 at E>or=90x10(3) cm(-1). The latter value corresponds to the exclusive formation of the spin-excited Kr(+)((2)P(12)) ions, which may be used to obtain laser generation on the Kr(+)((2)P(12)-(2)P(32)) transition.

Spin-orbit configuration interaction study of the electronic structure of the 5f2 manifold of U4+ and the 5f manifold of U5+

The energy levels of the 5f configuration of U(5+) and 5f(2) configuration of U(4+) have been calculated in a dressed effective Hamiltonian relativistic spin-orbit configuration interaction framework. Electron correlation is treated in the scalar relativistic scheme with either the multistate multireference second-order multiconfigurational perturbation theory (MS-CASPT2) or with the multireference single and double configuration interaction (MRCI) and its size-extensive Davidson corrected variant. The CASPT2 method yields relative energies which are lower than those obtained with the MRCI method, the differences being the largest for the highest state (1)S(0) of the 5f(2) manifold. Both valence correlation effects and spin-orbit polarization of the outer-core orbitals are shown to be important. The satisfactory agreement of the results with experiments and four-component correlated calculations illustrates the relevance of dressed spin-orbit configuration interaction methods for spectroscopy studies of heavy elements.

SPOCK.CI: A multireference spin-orbit configuration interaction method for large molecules

We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.

Theoretical study on the photoabsorption in the Herzberg I band system of the O 2 molecule

The Herzberg I band system of the oxygen molecule is electric-dipole forbidden and its absorption strength has been explained by intensity borrowing models which include the spin–orbit (SO) and L-uncoupling (RO) interactions as perturbations. We employed three different levels of theoretical models to evaluate these two interactions, and obtained the rotational and vibronic absorption strengths using the ab initio method. The first model calculates the transition moments induced by the SO interaction variationally with the SO configuration interaction method (SOCI), and uses the first-order perturbation theory for the RO interaction, and is called SOCI. The second is based on the first-order perturbation theory for both the SO and RO interactions, and is called Pert(Full). The last is a limited version of Pert(Full), in that the first-order perturbation wavefunction for the initial and final state is represented by only one dominant basis, namely the 1 3Π g and B 3 Σ u - state, respectively, as originally used by England et al. [Can. J. Phys. 74 (1996) 185], and is called Pert(England). The vibronic oscillator strengths calculated by these three models were in good agreement with the experimental values. As for the integrated rotational linestrengths, the SOCI and Pert(Full) models reproduced the experimental results very well, however the Pert(England) model did not give satisfactory results. Since the Pert(England) model takes only the 1 3Π g and B 3 Σ u - states into consideration, it cannot contain the complicated configuration interactions with highly excited states induced by the SO and RO interaction, which plays an important role for calculating the delicate integrated rotational linestrength. This result suggests that the configuration interaction with highly excited states due to some perturbations cannot be neglected in the case of very weak absorption band systems.

Theoretical study of nonadiabatic transitions in the photodissociation of Cl 2 and Br 2

Lower-lying potential curves of Br 2 are calculated by the spin–orbit configuration interaction method, and the spin–orbit branching mechanisms in the photodissociation processes are examined. The second absorption band at 227 nm is assigned unambiguously to the transition from the X 1 Σ + g to the 3 Σ + 1 u ( σ g→ σ u *) state. The calculated potential curves and the radial derivative coupling elements of Cl 2 and Br 2 are used to evaluate the nonadiabatic transition probabilities by solving the time-dependent coupled Schrödinger equations semiclassically. The different nonadiabatic behavior in Cl 2 and Br 2 is analyzed in terms of the differences in the electronic factors and the reduced mass.

The convergence of spin–orbit configuration interaction calculations for TlH and (113)H

To test the convergence of spin–orbit effects for molecules, the ground states of TlH and (113)H are calculated by configuration interaction(CI) calculations using relativistic effective core potentials with one-electron spin–orbit operators. The employed CI methods are the Kramers’ restricted CI (KRCI) and the spin–orbit CI (SOCI) methods. The KRCI method includes the spin–orbit interactions in the generation of one-electron basis space through the use of the two-component molecular spinors obtained by the Kramers’ restricted Hartree–Fock (KRHF) method, whereas the SOCI adds the spin–orbit term only at the CI level. For systems with heavy atoms, orbital relaxations due to the spin–orbit interaction could become sizable, resulting in slow convergences for the SOCI method. Spin–orbit effects on bond lengths and energies using single- and multireference CI calculations at the SOCI level of theory are evaluated and compared with KRCI results for TlH and (113)H. The spin–orbit effects on energies converge easily for TlH but slowly for (113)H. Especially, bond lengths do not converge for the seventh-row (113)H in our calculations. The present results imply that large-scale multireference SOCI calculations are necessary for some molecules to recover orbital relaxation effects due to large spin–orbit interactions in the SOCI scheme. In those cases, the KRCI scheme based upon two-component spinors will have advantages over SOCI and other one-component orbital based methods.

A two-step uncontracted determinantal effective Hamiltonian-based SO–CI method

We present a new two-step uncontracted spin-orbit configuration interaction (CI) method which automatically accounts for spin-orbit polarization effects on multiconfigurational wave functions by selecting the single excitations having a significant spin-orbit interaction with a chosen determinantal reference space. This approach is in the line of a conventional two-step method, as a sophisticated correlation treatment in a scalar relativistic approximation is carried out in the first step. In the second step, we define a model space which includes a set of reference configurations able to represent all the wanted states along with singly excited configurations selected with the spin-orbit (SO) operator. We then exploit the first-step calculation in order to include correlation effects via an effective Hamiltonian technique and diagonalize the full matrix on the determinantal basis. The method combines the advantages of both one-step and conventional two-step SO–CI methods; it intends to treat efficiently the cases where both relativity and extended CI treatments are needed. The new code EPCISO is tested on the spin-orbit splitting of the P2 electronic ground state of the thallium atom which, in spite of its very simple electronic structure is a well-known difficult case study for SO–CI methods. The EPCISO code yields results in excellent agreement with the experimental splitting value; they are compared to those obtained using the conventional two-step CIPSO code.

Low-lying states of Tl2 calculated by the configuration interaction methods based upon relativistic effective core potentials and two-component spinors

We have modified a Dirac–Fock program package, MOLFDIR [L. Visscher et al., Comput. Phys. Commun. 81, 120 (1994)], to perform two-component molecular spinor calculations based upon the relativistic effective core potentials (REPs) incorporating effective spin–orbit operators. The modified MOLFDIR can be used to perform two-component REP calculations instead of four-component all-electron calculations at various levels of theory including the configuration interaction (CI) level. As a test case for the multireference CI methods, the low-lying states of Tl2 are calculated with the two-component CI method and the more conventional spin–orbit CI method. Results indicate that the two-component method has some advantages in describing the ground state of Tl2 while excited states are similarly described by both methods.

Comparison of spin-orbit configuration interaction methods employing relativistic effective core potentials for the calculation of zero-field splittings of heavy atoms with a 2P o ground state

Computational strategies for the treatment of relativistic effects including spin-orbit coupling at a highly correlated level are compared for a number of heavy atoms: indium, iodine, thallium, and astatine. Initial tests with perturbation theory emphasize the importance of high-energy singly excited configurations which possess large spin-orbit matrix elements with the ground state. A contracted basis consisting of L–S CI eigenfunctions (LSC–SO–CI) is found to give an accurate representation of both spin-perturbed 2Po components as long as key np→pi* singly excited configurations are included. Comparison is made with a more extensive treatment in which all selected configurations of various L–S symmetries form the basis for the multireference–spin-orbit–configuration interaction (MR–SO–CI). Good agreement is obtained with experimental SO splittings for the In, I, and At atoms at a variety of levels of treatment, indicating that the L–S contracted SO–CI approach can be implemented quite effectively with relativistic effective core potentials (RECPs) for both very electronegative atoms and also for lighter electropositive elements up through the fifth row of the periodic table. The thallium atom SO splitting is more difficult to obtain accurately because of greater differences between its valence p1/2 and p3/2 spinors than in the other cases studied, but good results are also possible with the contracted SO–CI approach in this instance, provided proper care is given to the inclusion of key singly excited L–S states. The relationship between all-electron two-component SO–CI treatments and those employing RECPs is also analyzed, and it is concluded that triply excited configurations relative to the 2Po ground state are far less important than previously reported.

Full nine-dimensional ab initio potential energy surfaces and trajectory studies of A-band photodissociation dynamics: CH3I*→CH3+I, CH3+I*, and CD3I*→CD3+I, CD3+I*

The full nine-dimensional potential energy surfaces (PESs) of the 3Q0 and 1Q1 states of CH3I have been calculated with the ab initio contracted spin–orbit configuration interaction method. The results are fitted to three diabatic potential terms and their couplings as functions of all the internal degrees of freedom. The transition dipole at the Franck–Condon region has also been calculated. Surface hopping quasiclassical trajectory calculations on these potential energy surfaces have been performed to examine the photodissociation dynamics of both CH3I and CD3I in the A-continuum. The results are in general good agreement with the recent experimental findings. The reasonable I*/(I*+I) branching ratio can be obtained with these PESs when the contribution of direct transition to the 1Q1 state is considered. The rotational distribution of the CH3 and CD3 fragments and its I*/(I*+I)-channel selectivity are determined by the shape of the PESs with respect to the bending angle outside the conical intersection region. The vibrational distribution of umbrella mode is closely related to the shape of PESs for the umbrella angle; the sudden switch of reaction coordinate from 3Q0 to 1Q1 at the conical intersection is the origin of vibrational excitation in the I* channel. The larger umbrella excitation of the CD3 fragment in both I and I* channels, in comparison with the CH3 fragment, is related to the larger separation of the reaction coordinate from the Franck–Condon geometry. The symmetric stretching energy increases during the dissociation, which is related to the shape of PESs with respect to this coordinate, and the excitation of symmetric stretching mode seems to be possible.