Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

Ground- and excited-state electronic structure of an iron-containing molecular spin photoswitch

The electronic structure of the cation of [Fe(ptz)(6)](BF(4))(2), a prototype of a class of complexes that display light-induced excited-state spin trapping (LIESST), has been investigated by time-independent and time-dependent density-functional theories. The density of states of the singlet ground state reveals that the highest occupied orbitals are metal centered and give rise to a low spin configuration Fe(2+)(3d(xy) ( upward arrow downward arrow)3d(xz) ( upward arrow downward arrow)3d(yz) ( upward arrow downward arrow)) in agreement with experiment. Upon excitation with light in the 2.3-3.3 eV range, metal-centered spin-allowed but parity-forbidden ligand field (LF) antibonding states are populated which, in conjunction with electron-phonon coupling, explain the experimental absorption intensities. The computed excitation energies are in excellent agreement with experiment. Contrary to simpler models we show that the LF absorption bands, which are important for LIESST, do not originate in transitions from the ground to a single excited state but from transitions to manifolds of nearly degenerate excited singlets. Consistent with crystallography, population of the LF states promotes a drastic dilation of the ligand cage surrounding the iron.     

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.     

Quantum chemical study of the electronic structure of NiCH2 + in its ground state and low-lying electronic excited states

The electronic structure of NiCH(2) (+), representative of transition metal carbene ions, is investigated by means of several methods of quantum chemistry. The relative stabilities of the four low-lying doublet electronic states ((2)A(1), (2)A(2), (2)B(1), and (2)B(2)) are determined at the coupled cluster singles and doubles level (CCSD) and triples level [CCSD(T) and CCSDT-3] with both a Hartree-Fock and density functional theory (Kohn-Sham) reference. The equation-of-motion coupled cluster for treatment of excited states in singles and doubles approximation (EOM-CCSD) is used to characterize the transition energies from the (2)A(1) electronic ground state to the low-lying doublet excited states. The (2)A(2) and (2)B(1) states are nearly degenerate, found to be separated by 940 cm(-1) at the EOM-CCSD level, in agreement with the CASSCF energy ordering. The (2)B(2) state is calculated to be higher in energy by more than 1.0 eV. The spin purity of the low-lying doublet and quadruplet states described by CCSD calculations based on the unrestricted open-shell Hartree-Fock reference is discussed.     

Multimode Jahn-Teller and pseudo-Jahn-Teller interactions in the cyclopropane radical cation: complex vibronic spectra and nonradiative decay dynamics

The complex vibronic spectra and the nonradiative decay dynamics of the cyclopropane radical cation (CP+) are simulated theoretically with the aid of a time-dependent wave packet propagation approach using the multireference time-dependent Hartree scheme. The theoretical results are compared with the experimental photoelectron spectrum of cyclopropane. The ground and first excited electronic states of CP+ are of X2E' and A2E' type, respectively. Each of these degenerate electronic states undergoes Jahn-Teller (JT) splitting when the radical cation is distorted along the degenerate vibrational modes of e' symmetry. The JT split components of these two electronic states can also undergo pseudo-Jahn-Teller (PJT)-type crossings via the vibrational modes of e', a1' and a2' symmetries. These lead to the possibility of multiple multidimensional conical intersections and highly nonadiabatic nuclear motions in these coupled manifolds of electronic states. In a previous publication [J. Phys. Chem. A 2004, 108, 2256], we investigated the JT interactions alone in the X2E' ground electronic manifold of CP+. In the present work, the JT interactions in the A2E' electronic manifold are treated, and our previous work is extended by considering the coupling between the X2E' and A2E' electronic states of CP+. The nuclear dynamics in this coupled manifold of two JT split doubly degenerate electronic states is simulated by considering fourteen active and most relevant vibrational degrees of freedom. The vibronic level spectra and the ultrafast nonradiative decay of the excited cationic states are examined and are related to the highly complex entanglement of electronic and nuclear degrees of freedom in this prototypical molecular system.     

Dynamical variational approach to non-adiabatic electronic structure

Studying non-adiabatic effects in molecular dynamics simulations and modeling their optical signatures in linear and non-linear spectroscopies calls for electronic structure calculations in a situation when the ground state is degenerate or almost degenerate. Such degeneracy causes serious problems in invoking single Slater determinant Hartree–Fock (HF) and density functional theory (DFT) methods. To resolve this problem, we develop a generalization of time-dependent (dynamical) variational approach which accounts for the degenerate or almost degenerate ground state structure. Specifically, we propose a ground state ansatz for the subspace of generalized electronic configurations spanned on the degenerate grounds state multi-electron wavefunctions. Further employing the invariant form of Hamilton dynamics we arrive with the classical equations of motion describing the time-evolution of this subspace in the vicinity of the stationary point. The developed approach can be used for accurate calculations of molecular excited states and electronic spectra in the degenerate case.     

Alignment, vibronic level splitting, and coherent coupling effects on the pump-probe polarization anisotropy

The pump-probe polarization anisotropy is computed for molecules with a nondegenerate ground state, two degenerate or nearly degenerate excited states with perpendicular transition dipoles, and no resonant excited-state absorption. Including finite pulse effects, the initial polarization anisotropy at zero pump-probe delay is predicted to be r(0) = 3/10 with coherent excitation. During pulse overlap, it is shown that the four-wave mixing classification of signal pathways as ground or excited state is not useful for pump-probe signals. Therefore, a reclassification useful for pump-probe experiments is proposed, and the coherent anisotropy is discussed in terms of a more general transition dipole and molecular axis alignment instead of experiment-dependent ground- versus excited-state pathways. Although coherent excitation enhances alignment of the transition dipole, the molecular axes are less aligned than for a single dipole transition, lowering the initial anisotropy. As the splitting between excited states increases beyond the laser bandwidth and absorption line width, the initial anisotropy increases from 3/10 to 4/10. Asymmetric vibrational coordinates that lift the degeneracy control the electronic energy gap and off-diagonal coupling between electronic states. These vibrations dephase coherence and equilibrate the populations of the (nearly) degenerate states, causing the anisotropy to decay (possibly with oscillations) to 1/10. Small amounts of asymmetric inhomogeneity (2 cm(-1)) cause rapid (130 fs) suppression of both vibrational and electronic anisotropy beats on the excited state, but not vibrational beats on the ground electronic state. Recent measurements of conical intersection dynamics in a silicon napthalocyanine revealed anisotropic quantum beats that had to be assigned to asymmetric vibrations on the ground electronic state only [Farrow, D. A.; J. Chem. Phys. 2008, 128, 144510]. Small environmental asymmetries likely explain the observed absence of excited-state asymmetric vibrations in those experiments.     

Long-range interactions between an atom in its ground S state and an open-shell linear molecule

Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a nonzero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nondiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb((2)S) atom with CO((3)Π), OH((2)Π), NH((1)Δ), and CH((2)Π) and of the ground state Li((2)S) atom with CH((2)Π).     

X-ray illumination induced Fe(II) spin crossover in the Prussian blue analogue cesium iron hexacyanochromate

The effect of X-ray illumination on the structural properties of the mixed valence Prussian blue analogue CsFe(II)[Cr(III)(CN)6] has been studied by time-dependent high-resolution synchrotron X-ray diffraction. Abrupt isosymmetric phase transitions, accompanied by dramatic volume collapse, were found in the temperature range 245-265 K, induced by sudden Fe(II) spin transitions from the high spin (HS) (4t(2g)2e(g), S = 2) to the low spin (LS) (6t(2g)0e(g), S = 0) configuration. Absorption of X-ray photons generates photoexcited Fe(II)(LS) domains whose size rapidly grows with time until the percolation threshold is reached and the structure collapse is triggered. The persistent character of the optically excited spin crossover states derives from the strong electron-phonon coupling, associated with the large lattice relaxations, which accompany the internal spin rearrangements. It is thus possible to use X-ray light in a controllable and efficient way to induce photoswitching between the ground and hidden or inaccessible excited states in suitably selected multistable materials in the bulk.     

Quantum chemical modeling of photoadsorption properties of the nitrogen-vacancy point defect in diamond

Quantum chemical calculations of geometric and electronic structure and vertical transition energies for several low-lying excited states of the neutral and negatively charged nitrogen-vacancy point defect in diamond (NV(0) and NV(-)) have been performed employing various theoretical methods and basis sets and using finite model NC(n)H(m) clusters. Unpaired electrons in the ground doublet state of NV(0) and triplet state of NV(-) are found to be localized mainly on three carbon atoms around the vacancy and the electronic density on the nitrogen and rest of C atoms is only weakly disturbed. The lowest excited states involve different electronic distributions on molecular orbitals localized close to the vacancy and their wave functions exhibit a strong multireference character with significant contributions from diffuse functions. CASSCF calculations underestimate excitation energies for the anionic defect and overestimate those for the neutral system. The inclusion of dynamic electronic correlation at the CASPT2 level leads to a reasonable agreement (within 0.25 eV) of the calculated transition energy to the lowest excited state with experiment for both systems. Several excited states for NV(-) are found in the energy range of 2-3 eV, but only for the 1(3)E and 5(3)E states the excitation probabilities from the ground state are significant, with the first absorption band calculated at approximately 1.9 eV and the second lying 0.8-1 eV higher in energy than the first one. For NV(0), we predict the following order of electronic states: 1(2)E (0.0), 1(2)A(2) (approximately 2.4 eV), 2(2)E (2.7-2.8 eV), 1(2)A(1), 3(2)E (approximately 3.2 eV and higher).     

Towards experimental determination of conical intersection properties: a twin state based comparison with bound excited states

The energy and approximate structure of certain S(0)/S(1) conical intersections (CI) are shown computationally to be deducible from those of two bound states: the first triplet (T(1)), which is iso-energetic with the CI, and the second excited singlet state (S(2)). This is demonstrated for acepentalene (I) and its perfluoro derivative (II) using the twin state concept for three states systems and based on the fact that the triplet T(1) is almost degenerate with the CI. The stable S(2) (C(3v) configuration) state exhibits unusual exaltation of Jahn-Teller active degenerate mode-ν(JT) = 2058 cm(-1) (～500 cm(-1) higher than analogous e-mode of the symmetric (C(3v)) T(1) and the dianion I(-2) or any C-C vibration of the Jahn-Teller distorted (C(s)) ground state minimum). The acepentalene molecule, whose rigid structure and possibility to attain the relatively high symmetry C(3v) configuration, is a particularly suitable candidate for this purpose.     

Ab initio rovibronic states of the thioketenyl radical in its X2Π electronic ground state

We present an ab initio study of the thioketenyl (HCCS) radical in its degenerate X(2)Π electronic ground state. All rotational and vibrational degrees of freedom are taken into account including the electronic orbital and spin angular momenta. The structure of the rovibronic levels and the nature of the corresponding wave functions show resonances even at very low energies due to strong couplings between the bending, rotation, and spin terms in the Hamiltonian. Assignments from the dominant contributions of the eigenvectors are discussed in parallel with previously published data. The rotational structures for the first excited vibronic states are computed as well as transition intensities for the fundamental one.     

Spin-state tuning at pseudotetrahedral d(7) ions: examining the structural and magnetic phenomena of four-coordinate [BP3]CoII-X systems

Electronic structure, spin-state, and geometrical relationships for a series of pseudotetrahedral Co(II) aryloxide, siloxide, arylthiolate, and silylthiolate complexes supported by the tris(phosphino)borate [BP(3)] ligands [PhBP(3)] and [PhBP(i)()(Pr)(3)] ([PhB(CH(2)PPh(2))(3)](-) and [PhB(CH(2)P(i)()Pr(2))(3)](-), respectively) are described. Standard (1)H NMR, optical, electrochemical, and solution magnetic data, in addition to low-temperature EPR and variable temperature SQUID magnetization data, are presented for the new cobalt(II) complexes [PhBP(3)]CoOSiPh(3) (2), [PhBP(3)]CoO(4-(t)()Bu-Ph) (3), [PhBP(3)]CoO(C(6)F(5)) (4), [PhBP(3)]CoSPh (5), [PhBP(3)]CoS(2,6-Me(2)-Ph) (6), [PhBP(3)]CoS(2,4,6-(i)()Pr(3)-Ph) (7), [PhBP(3)]CoS(2,4,6-(t)()Bu(3)-Ph) (8), [PhBP(3)]CoSSiPh(3) (9), [PhBP(3)]CoOSi(4-NMe(2)-Ph)(3) (10), [PhBP(3)]CoOSi(4-CF(3)-Ph)(3) (11), [PhBP(3)]CoOCPh(3) (12), [PhBP(i)()(Pr)(3)]CoOSiPh(3) (14), and [PhBP(i)()(Pr)(3)]CoSSiPh(3) (15). The low-temperature solid-state crystal structures of 2, 3, 5-10, 12, and 15 are also described. These pseudotetrahedral cobalt(II) complexes are classified as featuring one of two limiting distortions, either umbrella or off-axis. Magnetic and spectroscopic data demonstrate that both S = (1)/(2) and S = (3)/(2) ground-state electronic configurations are accessible for the umbrella distorted structure type, depending on the nature of the X-type ligand, its denticity (eta(1) versus eta(3)), and the tripodal phosphine ligand employed. Off-axis distorted complexes populate an S = (1)/(2) ground-state exclusively. For those four-coordinate complexes that populate S = (1)/(2) ground states, X-ray data show two Co-P bond distances that are invariably shorter than a third Co-P bond. The pseudotetrahedral siloxides 2, 10, and 11 are exceptional in that they display gradual spin crossover in the solid state. The diamagnetic cobalt(III) complex {[PhBP(3)]CoOSiPh(3)}{BAr(4)} ({16}{BAr(4)}) (Ar = Ph or 3,5-(CF(3))(2)-C(6)H(3)) has also been prepared and structurally characterized. Accompanying electronic structure calculations (DFT) for complexes 2, 6, and {16}(+) support the notion of a close electronic structure relationship between these four-coordinate systems and octahedral, sandwich, and half-sandwich coordination complexes.     

Structural and spectroscopic study of the excited electronic states of silver dihalides by quantum chemical methods

The structural and electronic properties of the excited electronic states of AgX(2) (X = F, Cl, Br, and I), have been calculated, taking electron correlation and spin-orbit coupling into account and employing improved relativistic-effective-core potentials for silver and the halogen atoms. The relative ordering of the excited states of these molecules has been discussed via molecular-orbital arguments. The spin-orbit splittings of three degenerate electronic states ((2)Pi(g), (2)Pi(u), and (2)Delta(g)) have been calculated and the spin-orbit induced inter-state (Sigma - Pi) coupling has been discussed. The composition of the spin-orbit eigenstates is analyzed in terms of scalar-relativistic electronic states. Finally, a theoretical prediction of the photodetachment bands of the title molecules has been accomplished.     

Pi topology and spin alignment in unique photoexcited triplet and quintet states arising from four unpaired electrons of an organic spin system

Syntheses, electronic structures in the ground state, unique photoexcited states, and spin alignment are reported for novel biradical 1, which was designed as an ideal model compound to investigate photoinduced spin alignment in the excited state. Electron spin resonance (ESR), time-resolved ESR (TRESR), and laser-excitation pulsed ESR experiments were carried out. The magnetic properties were examined with a SQUID magnetometer. In the electronic ground state, two radical moieties interact very weakly (almost no interaction) with each other through the closed-shell diphenylanthracene spin coupler. On photoirradiation, a novel lowest photoexcited state with the intermediate spin (S = 1) arising from four unpaired electrons with low-lying quintet (S = 2) photoexcited state was detected. The unique triplet state has an interesting electronic structure, the D value of which is reduced by antiferromagnetic spin alignment between two radical spins through the excited triplet spin coupler. The general theoretical predictions of the spin alignment and the reduction of the fine-structure splitting of the triplet bis(radical) systems are presented. The fine-structure splitting of the unique photoexcited triplet state of 1, as well as the existence of the low-lying quintet state, is interpreted well on the basis of theoretical predictions. Details of the spin alignment in the photoexcited states are discussed.     

Simulation of X-ray absorption near edge spectra of organometallic compounds in the ground and optically excited states

The Mg K-edge and Zn K- and L3-edge X-ray absorption near edge spectra of Mg and Zn porphyrins in the ground state and low-lying optically excited states are calculated. Also computed are X-ray absorption near edge spectra of Fe(II) spin crossover compound in its ground and low-lying optically excited states, motivated by a recent experiment (J. Phys. Chem. A 2006, 110, 38). The calculated absorption spectra of optically excited states can be used to simulate ultrafast optical pump/X-ray probe experiments.     

Photodissociation studies of the electronic and vibrational spectroscopy of Ni(+)(H2O)

The electronic spectrum of Ni?(H?O) has been measured from 16200 to 18000 cm?1 using photofragment spectroscopy. Transitions to two excited electronic states are observed; they are sufficiently long-lived that the spectrum is vibrationally and partially rotationally resolved. An extended progression in the metal-ligand stretch is observed, and the absolute vibrational quantum numbering is assigned by comparing isotopic shifts between ??Ni?(H?O) and ??Ni?(H?O). Time-dependent density functional calculations aid in assigning the spectrum. Two electronic transitions are observed, from the 2A? ground state (which correlates to the 2D, 3d? ground state of Ni?) to the 32A? and 22A? excited states. These states are nearly degenerate and correlate to the 2F, 3d?4s excited state of Ni?. Both transitions are quite weak, but surprisingly, the transition to the 2A? state is stronger, although it is symmetry-forbidden. The 3d?4s states of Ni? interact less strongly with water than does the ground state; therefore, the excited states observed are less tightly bound and have a longer metal-ligand bond than the ground state. Calculations at the CCSD(T)/aug-cc-pVTZ level predict that binding to Ni? increases the H-O-H angle in water from 104.2 to 107.5° as the metal removes electron density from the oxygen lone pairs. The photodissociation spectrum shows well-resolved rotational structure due to rotation about the Ni-O axis. This permits determination of the spin rotation constants ε(αα)' = -12 cm?1 and ε(αα)' = -3 cm?1 and the excited state rotational constant A' = 14.5 cm?1. This implies a H-O-H angle of 104 ± 1° in the 22A? excited state. The O-H stretching frequencies of the ground state of Ni?(H?O) were measured by combining IR excitation with visible photodissociation in a double resonance experiment. The O-H symmetric stretch is ν?' = 3616.5 cm?1; the antisymmetric stretch is ν?' = 3688 cm?1. These values are 40 and 68 cm?1 lower, respectively, than those in bare H?O.     

On the triplet ground state of tetrahedral X4 clusters (X = Li, Na, K, Cu)

The lowest electronic state of distorted tetrahedral X(4) clusters (with X = Li, Na, K, Cu) is studied at coupled-cluster level using high-quality atomic basis sets. The ground state is found to have a triplet spin symmetry for this kind of geometry and for all the considered atomic species. The equilibrium geometries correspond to Jahn-Teller-distorted oblate tetrahedra having D(2d) symmetry, and tetrahedric structures are local minima on the potential-energy surfaces for the triplet states. Their energies lie between 0.2 eV (for the K(4) cluster) and 0.9 eV (for Cu(4)) above the absolute minimum of the corresponding systems, which is a spin singlet having a rhombus geometry.     

Electronic states and radiative transitions in LiAr

Ab initio MRD-CI calculations have been carried out on the ground and the eight lowest excited electronic states of LiAr, correlating with excited Li atom states up to 3d ²D. The ground (X²∑⁺ (2s)) and 2 ²Σ⁺ (2p) electronic states are repulsive while the higher excited states show shallow Rydberg minima. Rates of radiative bound-bound and bound-free transitions have been also calculated.