Spin-orbit Configuration Research Articles

Spin-forbidden transitions in flavone

The ground and low-lying excited electronic states of flavone were investigated by means of quantum chemical methods including spin–orbit coupling. Minimum structures were determined employing (time-dependent) Kohn–Sham density functional theory. Spectral properties were computed utilizing a combined density functional and multi-reference configuration interaction (DFT/MRCI) method. Intersystem crossing (ISC) rate constants for the S 1 ↝ T 1 transition were computed using a discretized Fermi golden rule approach. For the evaluation of phosphorescence lifetimes a multi-reference spin–orbit configuration interaction procedure (DFT/MRSOCI) was invoked. According to the calculations the phenyl ring is twisted out of the benzopyrone plane by 28 ° in the electronic ground state whereas the nuclear frame is nearly planar in the lowest excited ( n π ∗ ) 1 ( S 1 ) state and is slightly V-shaped in the ( π π ∗ ) 3 ( T 1 ) and ( π π ∗ ) 1 ( S 2 ) states. The calculations clearly show that the T 1 state has mainly π π ∗ character. The large spin–orbit coupling of the S 1 and T 1 states and their small energy gap explain the high S 1 ↝ T 1 ISC rate for which a value of k ISC ≈ 3 × 1 0 11 s is computed, in good agreement with experimental build-up times of the T n ← T 1 absorption. In the absence of collisions and other nonradiative processes, the T 1 state of flavone is prediced to be long-lived with a pure phosphorescence lifetime of τ P ≈ 4 s, in qualitative agreement with low-temperature measurements. The much faster decay of triplet flavone observed in fluid solutions is ascribed to nonradiative processes.

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.

Spin–orbit configuration interaction study of the ultraviolet photofragmentation of XeH+

The multireference spin-orbit CI method is employed to calculate potential energy curves for the ground and low-lying excited states of the XeH+ 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 XeH+. On this basis, the partial and total absorption spectra in this energy range are obtained. It is found that the A-band absorption is dominated by the spin-forbidden b3Pi0+ <-- X1sigma+ parallel transition, while perpendicular transitions to the B(1)Pi and b(3)Pi(1) states are significantly weaker. The Gamma(nu) branching ratio defined as the ratio of the Xe+(2P(1/2)) yield to the total yield of the Xe+ cations from the XeH+ photodissociation is calculated for the (42-80) x 10(3) spectral range. It is shown that Gamma(nu) increases smoothly from <0.2 in the red and blue tails of the band to its maximum of 0.92 in the middle of the band, at E approximately 51.4 x 10(3) cm(-1). The high Gamma(nu) values correspond to the predominant formation of the spin-excited Xe+(2P(1/2)) ions that may be used to obtain IR laser generation at the Xe+(2P(1/2) - 2P(3/2)) transition. The calculated XeH+ data are compared with those for the isovalent ArH+, KrH+, and HI systems.

Excited states of thiophene: ring opening as deactivation mechanism

(Time-dependent) Kohn-Sham density functional theory and a combined density functional/multi-reference configuration interaction method (DFT/MRCI) were employed to explore the ground and low-lying electronically excited states of thiophene. Spin-orbit coupling was taken into account using an efficient, nonempirical mean-field Hamiltonian. Phosphorescence lifetimes were calculated by means of spock.ci, a selecting direct multi-reference spin-orbit configuration interaction program. Throughout this paper, we use the following nomenclature: S1, S2,..., T1, T2,..., denominate electronic structures in their energetic order at the ground state minimum geometry, whereas S1, S2,..., T1, T2,..., refers to the actual order of electronic states at a given nuclear geometry. Multiple minima were found on the first excited singlet (S1) potential energy hypersurface with electronic structures S1 (piHOMO-1-->pi+piHOMO-->pi), S2 (piHOMO-->pi), and S3 (piHOMO-->sigma*) corresponding to the 2 1A1 (S1), 1 1B2 (S2), and 1 1B1 (S3) states in the vertical absorption spectrum, respectively. The S1 and S2 minimum geometries show out-of-plane deformations of the ring. The S3 electronic structure yields the global minimum on the S1 surface with an adiabatic excitation energy of merely 3.81 eV. It exhibits an asymmetric planar nuclear arrangement with one significantly elongated C-S bond. A constrained minimum energy path calculation connecting the S1 and S3 minima suggests that even low-lying vibrational levels of the S1 potential well can access the global minimum of the S1 surface. Nonradiative decay of the electronically excited singlet population to the electronic ground state via a close-by conical intersection will be fast. According to our work, this ring opening mechanism is most likely responsible for the lack of fluorescence in thiophene and the ultrafast decay of the S1 vibrational levels, as observed in time-resolved pump-probe femtosecond multiphoton ionization experiments. An alternative relaxation pathway leads from the S1 minimum via vibronic coupling to the S2 potential well followed by fast inter-system crossing to the T2 state. For an estimate of individual rate constants a quantum dynamical treatment will be required. The global minimum of the T1 surface has a chair-like nuclear conformation and corresponds to the T1 (1 3B2, piHOMO-->pi) electronic structure. Phosphorescence is weak here with a calculated radiative lifetime of 0.59 s. For the second potential well on the T1 surface with T3 (1 3B1, piHOMO-->sigma*) electronic structure, nonradiative processes are predicted to dominate the triplet decay.

Recoil velocities from equal-mass binary black-hole mergers: A systematic investigation of spin-orbit aligned configurations

Binary black-hole systems with spins aligned with the orbital angular momentum are of special interest, as studies indicate that this configuration is preferred in nature due to non-vacuum environmental interactions, as well as post-Newtonian (PN) spin-orbit couplings. If the spins of the two bodies differ, there can be a prominent beaming of the gravitational radiation during the late plunge, causing a recoil of the final merged black hole. In this paper we perform an accurate and systematic study of recoil velocities from a sequence of equal-mass black holes whose spins are aligned with the orbital angular momentum, and whose individual spins range from a=+0.584 to -0.584. In this way we extend and refine the results of a previous study which concentrated on the antialigned portion of this sequence, to arrive at a consistent maximum recoil of 448{+-}5 km/s for antialigned models as well as to a phenomenological expression for the recoil velocity as a function of spin ratio. Quite surprisingly, this relation highlights a nonlinear behavior, not predicted by the PN estimates, and can be readily employed in astrophysical studies on the evolution of binary black holes in massive galaxies. An essential result of our analysis, without which no systematicmore » behavior can be found, is the identification of different stages in the waveform, including a transient due to lack of an initial linear momentum in the initial data. Furthermore, by decomposing the recoil computation into coupled modes, we are able to identify a pair of terms which are largely responsible for the kick, indicating that an accurate computation can be obtained from modes up to l=3. Finally, we provide accurate measures of the radiated energy and angular momentum, finding these to increase linearly with the spin ratio, and derive simple expressions for the final spin and the radiated angular momentum which can be easily implemented in N-body simulations of compact stellar systems. Our code is calibrated with strict convergence tests and we verify the correctness of our measurements by using multiple independent methods whenever possible.« less

An ab initio study of the CH3I photodissociation. I. Potential energy surfaces

The multireference spin-orbit (SO) configuration interaction (CI) method in its Lambda-S contracted SO-CI version is employed to calculate two-dimensional potential energy surfaces for the ground and low-lying excited states of CH3I relevant to the photodissociation process in its A absorption band. The computed equilibrium geometry for the X A1 ground state, as well as vibrational frequencies for the nu2 umbrella and nu3 symmetric stretch modes, are found to be in good agreement with available experimental data. The 3Q0+ state converging to the excited I(2P1/2o) limit is found to possess a shallow minimum of 850 cm(-1) strongly shifted to larger internuclear distances (RC-I approximately 6.5a0) relative to the ground state. This makes a commonly employed single-exponent approximation for analysis of the CH3I fragmentation dynamics unsuitable. The 4E(3A1) state dissociating to the same atomic limit is calculated to lie too high in the Franck-Condon region to have any significant impact on the A-band absorption. The computed vertical excitation energies for the 3Q1, 3Q0+, and 1Q states indicate that the A-band spectrum must lie approximately between 33,000 and 44,300 cm(-1), i.e., between 225 and 300 nm. This result is in very good agreement with the experimental findings. The lowest Rydberg states are computed to lie at >or=49,000 cm(-1) and correspond to the ...a(1)2n3a1(6sI) leading configuration. They are responsible for the vacuum ultraviolet absorption lines found experimentally beyond the A-band spectrum at 201.1 nm (49,722 cm(-1)) and higher.

An ab initio study of the CH3I photodissociation. II. Transition moments and vibrational state control of the I* quantum yields

Multireference spin-orbit configuration interaction calculations of transition moments from the X A1 ground state to the 3Q0+, 3Q1, and 1Q excited states responsible for the A absorption band of CH3I are reported and employed for an analysis of the photofragmentation in this system. Contrary to what is usually assumed, the 3Q0+(A1), 3Q1(E), and 1Q(E)<--X A1 transition moments are found to be strongly dependent on the C-I fragmentation coordinate. The sign of this dependence is opposite for the parallel and perpendicular transitions, which opens an opportunity for vibrational state control of the photodissociation product yields. The computed absorption intensity distribution and the I* quantum yield as a function of excitation energy are analyzed in comparison with existing experimental data, and good agreement between theory and experiment is found. It is predicted that significantly higher I* quantum yield values (>0.9) may be achieved when vibrationally hot CH3I molecules are excited in the appropriate spectral range. It is shown that vibrational state control of the I*/I branching ratio in the alkyl (hydrogen) iodide photodissociation has an electronic rather than a dynamic nature: Due to a different electron density distribution at various molecular geometries, one achieves a more efficient excitation of a particular fragmentation channel rather than influences the dynamics of the decay process.

Photodissociation of gas-phase I3−: Comprehensive understanding of nonadiabatic dissociation dynamics

Photodissociation of the gas-phase tri-iodide anion, I3-, was investigated using photofragment time of flight (TOF) mass spectrometry combined with the core extraction method. An analysis of the TOF profiles provided the kinetic energy and angular distributions of photofragment ions and photoneutrals, from which the photoproduct branching fractions were determined in the excitation energy range of 3.26-4.27 eV. The measurement has revealed that (1) in the entire energy range investigated, three-body dissociation occurs preferentially as the "charge-asymmetric" process I-(1S)+I(2P3/2)+I(2P3/2) with the yield of approximately 30%-40%, where the excess charge is localized on the end atoms of the dissociating I3-, and that (2) two-body dissociation via the 3Piu(0u+)<--1Sigmag+(0g+) excitation proceeds as I-(1S)+I2(X 1Sigmag+)/I2(A 3Pi1u) or I(2P3/2)+I2-(X 2Sigmau+) with the yield of approximately 60%, while that via the 1Sigmau+(0u+)<--1Sigmag+(0g+) excitation alternatively as I*(2P1/2)+I2-(X 2Sigmau+) or I-(1S)+I2(B 3Piu) with the yield of approximately 60%. Ab initio calculations including spin-orbit configuration interactions were also performed to gain precise information on the potential energy surfaces relevant to the I3- photodissociation. The calculations have shown the presence of conical intersections and avoided crossings located along the symmetric stretch coordinate near the ground-state equilibrium geometry of I3-, which play key roles for the two-body and the three-body product branching. The nonadiabatic nature of the I3- photodissociation dynamics is discussed by combining the experimental findings and the ab initio results.

Calculated spectroscopic properties of HgH2

Ab initio calculations of the coupled cluster and spin–orbit configuration type, in conjunction with a small-core pseudopotential for the mercury atom, have been employed to construct near-equilibrium potential energy and electric dipole moment functions for HgH2. On that basis, rovibrational term energies and wavefunctions as well as transition dipole moments, absolute IR intensities and Einstein coefficients of spontaneous emission have been calculated variationally. Throughout, excellent agreement is obtained with recent experimental data from Fourier transform infrared emission spectroscopy. The gas-phase wavenumbers of the symmetric stretching and the bending vibrations of 202HgH2 and 202HgD2 (in parentheses) are predicted to be 2012.3 (1442.8) cm−1 and 784.3 (564.1) cm−1, respectively. Various predictions are made for 202HgHD, for which no high-resolution spectra have yet been published.

Theoretical study of the ArH+ photodissociation

The multireference Spin-Orbit (SO) Configuration Interaction (CI) method in its Lambda-S Contracted SO-CI (LSC-SO-CI) version is employed to calculate potential energy curves for the ground and low-lying excited states of the ArH(+) cation. For the first time, electric dipole moments are also computed in the approach, including SO coupling for transitions to the states responsible for the first absorption continuum (A-band) of ArH(+). On this basis, the partial and total absorption spectra in this energy range are obtained. It is shown that absorption in the A-band is dominated by the parallel A(1)Sigma(+)<--X(1)Sigma(+) transition. In the low-energy part of the band (<95 x 10(3) cm(-1)) the absorption is caused by the perpendicular B(1)Pi<--X(1)Sigma(+) excitation, but transitions to the b(3)Pi(0(+),1) states are also not negligible. The branching ratio Gamma for the final 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= 10(5) cm(-1). The latter value corresponds to the exclusive formation of the spin-excited Ar(+)((2)P(1/2)) ions, and thus leads to the inverse population of the Ar(+)((2)P(1/2)-(2)P(3/2)) ion states.

Ab initio study of a Bi3+ impurity in Cs2NaYCl6 and Y2O3: Comparison of perturbative and variational electron correlation methods

Ab initio study of excitation energies and oscillator strengths for absorption towards the (3)P(1) and (1)P(1) states of the Bi(3+) ion has been performed for the Bi(3+) ion in gas phase and as a dopant of the cubic elpasolite Cs(2)NaYCl(6) and the yttria Y(2)O(3) crystal using the ab initio embedded-cluster method. The ground and excited states were computed with a relativistic spin-orbit configuration interaction approach suited for heavy elements. Electron correlation was treated in the scalar relativistic scheme with perturbative, variational, and coupled-cluster methods. Intermediate coupling is included via an effective-Hamiltonian based spin-orbit configuration interaction approach. Small-core (60 electrons) and large-core (78 electrons) relativistic effective core potentials (ECPs) have been used to describe the bismuth ion. The best match with experiment was obtained with the small-core ECP. The accuracy of excitation energies strongly depends on the electron correlation method used. The agreement between experimental data and the results obtained using second-order multiconfigurational perturbation theory is greatly improved with the shifted zeroth-order Hamiltonian proposed by Ghido et al. [Chem. Phys. Lett. 396, 142 (2004)]. Although quite time consuming, coupled-cluster and variational methods yield good agreement with experimental data. The first absorption band recorded for the doped elpasolite crystal is positioned with an excellent accuracy while the computed energy of the second absorbing manifold is in poorer agreement with experimental data. This suggests that interactions with neglected close-lying excited states with a ligand-to-metal charge transfer character may be significant. Calculations of the spectrum of Bi(3+) doping yttria in both the S(6) and C(2) site symmetries indicate that the absorbing manifold arises from electronic excitations localized on the Bi(3+) doping ion with main triplet 6s6p character. Our results predict the first absorbing peak to lie about 0.5 eV lower for the S(6) sites than for the C(2) site, thus attributing the violet and the green emission wavelengths to the S(6) and C(2) sites, respectively. A subsequent study of Stokes shift and emission wavelength should hopefully lead to a final assignment of the measured excitation spectra.

Chaos in Compact Binaries with Frequency Map Analysis

The dynamics of compact binaries is very complicated because of spin-orbit cou- pling and spin-spin coupling. With Laskar's frequency map analysis (FMA) and frequency diffusion as an indicator, we found that misalignment of the spins and orbital angular mo- mentum has a great effect on the dynamics, and for systems with different mass ratios β ≡ m2/m1 chaos occurs at different spin-orbit configurations. For equal-mass binaries (β =1 ), chaos occurs when the spins nearly cancel each other out. For some other systems (for example β ∼ 1/2), the binaries are irregular,even chaotic, when the spins are perpendic- ular to the orbital angular momentum. For the case where gravitational radiation is taken into account, we give an analytic estimation for the frequency diffusion based on the decay of the orbit, which is roughly consistent with our simulations. This means the FMA is not suitable as a chaos indicator for weak chaotic cases with dissipative terms.

Electronic spectra of heteroatom-containing isoelectronic carbon chains C2nS and C2nCl+ (n=1–5)

Structures and stabilities of carbon chains C(2n)S and C2(n)Cl+ (n=1-5) in their ground states have been investigated by the density functional theory and the coupled cluster approach using single and double substitutions. The complete active space self-consistent-field method has been used for geometry optimization of selected excited states in both series. Calculations show that both C(2n)S (n=1-5) and C2(n)Cl+ (n=3-5) have linear structures in the triplet ground state 3Sigma-, while C2Cl+ and C4Cl+ have nonlinear structures in the ground state 3A". The vertical transition energies and emission energies by the multiconfigurational second-order perturbation theory in linear clusters C(2n)S and C2(n)Cl+ exhibit similar size dependences. In comparison with the available experimental observations, the predicted excitation energies for the allowed 2 3Sigma- <--X 3Sigma- transitions have an accuracy of no more than 0.24 eV. Spin-orbit coupling configuration interaction calculations indicate that the spin-forbidden 2 1Sigma+<--X 3Sigma- transition in these species has an oscillator strength with the magnitude of 10(-4)-10(-5), and they may be observable experimentally.

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.

Evolution of Mercury's obliquity

Mercury has a near-zero obliquity, i.e. its spin axis is nearly perpendicular to its orbital plane. The value of the obliquity must be known precisely in order to constrain the size of the planet's core within the framework suggested by Peale [Peale, S.J., 1976. Nature 262, 765–766]. Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381–393] have suggested that Mercury's obliquity varies on thousand-year timescales due to planetary perturbations, potentially ruining the feasibility of Peale's experiment. We use a Hamiltonian approach (free of energy dissipation) to study the spin–orbit evolution of Mercury subject to secular planetary perturbations. We can reproduce an obliquity evolution similar to that of Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381–393] if we integrate the system with a set of initial conditions that differs from the Cassini state. However the thousand-year oscillations in the obliquity disappear if we use initial conditions corresponding to the equilibrium position of the Cassini state. This result indicates that planetary perturbations do not force short-period, large amplitude oscillations in the obliquity of Mercury. In the absence of excitation processes on short timescales, Mercury's obliquity will remain quasi-constant, suggesting that one of the important conditions for the success of Peale's experiment is realized. We show that interpretation of data obtained in support of this experiment will require a precise knowledge of the spin–orbit configuration, and we provide estimates for two of the critical parameters, the instantaneous Laplace plane orientation and the orbital precession rate from numerical fits to ephemeris data. Finally we provide geometrical relationships and a scheme for identifying the correct initial conditions required in numerical integrations involving a Cassini state configuration subject to planetary perturbations.

Vibronic absorption, fluorescence, and phosphorescence spectra of psoralen: a quantum chemical investigation

Excited state potential energy hypersurfaces of 7H-furo[3,2-g][1]benzopyran-7-one (psoralen) have been explored employing (time-dependent) Kohn-Sham density functional theory. At selected points, we have determined electronic excitation energies and electric dipole (transition) moments utilizing a combined density functional/multireference configuration interaction method. Spin-orbit coupling has been taken into account employing an efficient, non-empirical spin-orbit mean-field Hamiltonian. Franck-Condon factors have been computed for vibrational modes with large displacements in the respective Dushinsky transformations. The simulated band spectra closely resemble experimental band shapes and thus validate the theoretically determined nuclear structures at the S(0), S(1), and T(1) minima. In the S(1) (pi(HOMO)-->pi*(LUMO)) state, the lactone bond of the pyrone ring is significantly elongated. From excited vibrational levels of the S(1) state a conical intersection between a (pi-->sigma*) excited state and the electronic ground state may be energetically accessible. Fast non-radiative decay via this relaxation pathway could explain the low fluorescence quantum yield of psoralen. The T(1) (pi(HOMO-1)-->pi*(LUMO)) exhibits a diradicaloid electronic structure with a broken C(5)-C(6) double bond in the pyrone ring. A variational multireference spin-orbit configuration interaction procedure yields a phosphorescence lifetime of 3 s, in excellent agreement with experimental estimates.

On the accuracy of one-component pseudopotential spin-orbit calculations

Improvements on current one-component extraction procedures of spin-orbit pseudopotentials are investigated for high accuracy computation of spin-orbit coupling energies. By means of the perturbation-theory formalism we first show that spin-orbit pseudopotentials, extracted at the one-component self-consistent-field level from a reference all-electron Dirac-Coulomb or Dirac-Coulomb-Breit calculation, include valence spin-orbit polarization and relaxation effects. As a consequence the use of these pseudopotentials in uncontracted spin-orbit configuration interaction (CI) with singles from the reference ground-state configuration gives rise to double counting of these spin-orbit effects. Two new methods that avoid such double counting have been investigated. The first, so-called "explicit" method, calculates explicitly, by means of a four-component spin-orbit CI, the double-counted spin-orbit effects and removes them from the pseudopotentials. Due to the nonadditivity of the core and valence spin-orbit effects as well as the so-called "pseudovariational collapse," this method is shown to be cumbersome. In the second "implicit" method the spin-orbit pseudopotential is extracted at the spin-orbit polarized and relaxed level by means of a single-excitation spin-orbit CI calculation. Atomic tests on iodine demonstrate the ability of the latter method to solve the double-counting problem.

In Search of the Electron Electric Dipole Moment: Relativistic Correlation Calculations of theP,T-Violating Effect in the Ground State ofHI+

We report the first results of ab initio relativistic correlation calculation of the effective electric field on the electron, E(eff), in the ground state of the HI+ cation. This value is required for interpretation of the suggested experiment on the search for the electron electric dipole moment. The generalized relativistic effective core potential, Fock-space relativistic coupled cluster with single and double cluster amplitudes (RCC-SD), and spin-orbit direct configuration interaction (SODCI) methods are used, followed by nonvariational one-center restoration of the four-component wave function in the iodine core. The RCC-SD value is E(eff) = 0.345 x 10(24) Hz/e cm and SODCI study gives E(eff) = 0.336 x 10(24) Hz/e cm (our final value). The structure of chemical bonding in HI+ is clarified, and a significant deviation of our value from that of Ravaine et al. [Phys. Rev. Lett. 94, 013001 (2005)] is explained.