Christel M. Marian

A mean-field spin-orbit method applicable to correlated wavefunctions

Abstract Starting from the full microscopic Breit-Pauli or no-pair spin-orbit Hamiltonians, we have devised an effective one-electron spin-orbit Hamiltonian in a well defined series of approximations by averaging the two-electron contributions to the spin-orbit matrix element over the valence shell. In addition the two-electron integrals were restricted to comprise only one-centre terms. The validity of these approximations has been tested on several palladium containing compounds. Excellent agreement of the matrix elements of the mean-field operator with corresponding full results is observed; deviations amount to a few cm −1 in absolute value or at most 0.2% on a relative scale. The newly defined mean-field operator can thus safely be employed to evaluate spin-orbit effects in transition metal containing compounds.

Spin–orbit coupling and intersystem crossing in molecules

Many light‐induced molecular processes involve a change in spin state and are formally forbidden in non‐relativistic quantum theory. To make them happen, spin–orbit coupling (SOC) has to be invoked. Intersystem crossing (ISC), the nonradiative transition between two electronic states of different multiplicity, plays a key role in photochemistry and photophysics with a broad range of applications including molecular photonics, biological photosensors, photodynamic therapy, and materials science. Quantum chemistry has become a valuable tool for gaining detailed insight into the mechanisms of ISC. After a short introduction highlighting the importance of ISC and a brief description of the relativistic origins of SOC, this article focusses on approximate SOC operators for practical use in molecular applications and reviews state‐of‐the‐art theoretical methods for evaluating ISC rates. Finally, a few sample applications are discussed that underline the necessity of studying the mechanisms of ISC processes beyond qualitative rules such as the El‐Sayed rules and the energy gap law.

A new pathway for the rapid decay of electronically excited adenine

Combined density functional and multireference configuration interaction methods have been used to calculate the electronic spectrum of 9H-adenine, the most stable tautomer of 6-aminopurine. In addition, constrained minimum energy paths on excited potential energy hypersurfaces have been determined along several relaxation coordinates. The minimum of the first (1)[n-->pi*] state has been located at an energy of 4.54 eV for a nuclear arrangement in which the amino group is pyramidal whereas the ring system remains planar. Close by, another minimum on the S(1) potential energy hypersurface has been detected in which the C(2) center is deflected out of the molecular plane and the electronic character of S(1) corresponds to a nearly equal mixture of (1)[pi-->pi*] and (1)[n-->pi*] configurations. The adiabatic excitation energy of this minimum amounts to 4.47 eV. Vertical and adiabatic excitation energies of the lowest n-->pi* and pi-->pi* transitions as well as transition moments and their directions are in very good agreement with experimental data and lend confidence to the present quantum chemical treatment. On the S(1) potential energy hypersurface, an energetically favorable path from the singlet n-->pi* minimum toward a conical intersection with the electronic ground state has been identified. Close to the conical intersection, the six-membered ring of adenine is strongly puckered and the electronic structure of the S(1) state corresponds to a pi-->pi* excitation. The energetic accessibility of this relaxation path at about 0.1 eV above the singlet n-->pi* minimum is presumably responsible for the ultrafast decay of 9H-adenine after photoexcitation and explains why sharp vibronic peaks can only be observed in a rather narrow wavelength range above the origin. The detected mechanism should be equally applicable to adenosine and 9-methyladenine because it involves primarily geometry changes in the six-membered ring whereas the nuclear arrangement of the five-membered ring (including the N(9) center) is largely preserved.

Performance of the Density Functional Theory/Multireference Configuration Interaction Method on Electronic Excitation of Extended π-Systems

The combined density functional theory/multireference configuration interaction (DFT/MRCI) method [Grimme and Waletzke. J. Chem. Phys. 1999, 111, 5645] has been employed to study the 1La and 1Lb states of linear polyacenes and the low-lying triplet and singlet states of linear polyenes and diphenyl-polyenes. We have systematically investigated the dependence of the electronic state properties on technical parameters of the calculations such as the atomic orbital basis set or the geometry optimization approach. The choice of basis set appears to be of minor importance whereas the excitation energies of the polyenes are quite sensitive to the ground-state geometry parameters. The DFT/MRCI energies at the B3-LYP optimized geometries systematically underestimate the experimental values, but we do not observe a bias toward one or the other type of state. The energy gaps between the electronically excited states are reproduced very well. In particular, this applies also to the first excited singlet 2 1Ag− and t...

Calculation of spin-forbidden radiative transitions using correlated wavefunctions: Lifetimes of b1Σ+, a1Δ states in O2, S2 and SO

Abstract The radiative lifetimes of the b 1 Σ + and a 1 Δ states of O 2 , S 2 and SO have been evaluated by perturbation expansions including 3 Σ g − , 1 Δ g , 1 Σ g + , 1 Π g , 3 Π g states for the homonuclear systems and 3 Σ − (2), 1 Δ, 1 Σ + (2), 1 Π (2), 3 Π (2), 3 Σ + states for SO; all wavefunctions are MRD CI expansions up to 5000 terms. The mixing coefficients are obtained from the spin-orbit operator in the Breit-Pauli form evaluating all one- and two-particle terms explicitly. In O 2 and S 2 the radiative lifetime of the b 1 Σ g + state is found to be largely determined by the spin-contributions to the magnetic moment in the magnetic dipole operator. The calculated value of 11.65 s for O 2 is in excellent agreement with the measured value of 12 s; the calculations predict a lifetime of 3.4 s for b 1 Σ g + in S 2 . The calculated lifetime corresponding to the b 1 Σ g + −a 1 Δ g transition is 720 s in good accord with the experimental intensity determination (400 s within a factor of two). The intensity for the a 1 Δ g −X 3 Σ g − transition is dominated by the orbital angular momentum term in the magnetic-dipole operator and arises from 1 Δ g − 1 Π g and X 3 Σ g − − 3 Π g transitions present in the perturbed X 3 Σ − and a 1 Δ g wavefunctions. Calculated values are τ(O 2 ) = 5400 s relative to a measured value of 3900 s, and τ = 350 s for S 2 as a prediction. The absence of the inversion favors electric (rather than magnetic) dipole processes in SO. The b 1 Σ + −X 3 Σ − transition borrows its intensity predominantly from terms connecting b 1 Σ + −2 1 Σ + and X 3 Σ − −2 3 Σ − which occur as perturbers in the pure spin wavefunctions. The calculated b 1 Σ + lifetime is 13.6 ms in fair accord with the recently measured 7 ± 2 ms. For τ (a 1 Δ) the calculations predict intensity borrowing from A 3 Π−X 3 Σ − and C 3 Π−X 3 Σ − as well as 1 Δ− 1 Π and 1 Δ−2 1 Π dipole transitions resulting in a value of 450 ms. The decrease in lifetime from the first- to the second-row molecules is quantitatively demonstrated to arise from increased spin-orbit interaction, while a different mechanism is responsible for the change in b 1 Σ + lifetimes from homonuclear to heteronuclear systems. Finally, all calculations demonstrate that spin-forbidden radiative transition probabilities can be obtained quite effectively by modern-day quantum chemical calculations.

Spin‐orbit coupling of DFT/MRCI wavefunctions: Method, test calculations, and application to thiophene

During the past decade the one‐center mean‐field approximation has proven to be a very appropriate framework for the accurate description of spin‐orbit effects at the correlated all‐electron level. Here, a new efficient code, SPOCK, is introduced that calculates spin‐orbit matrix elements in the one‐center mean‐field approximation for multireference CI wave functions. For the first time, the computation of spin‐dependent interactions within a Kohn‐Sham orbital based CI (DFT/MRCI) scheme 1 is made possible. The latter approach is suitable for large scale systems with up to 100–200 valence electrons. Test calculations are performed on well‐known diatomic molecules and the thiocarbonyl pyranthione. Spin‐orbit matrix elements show good agreement with their Hartree‐Fock orbital based counterparts but are obtained at considerably lower expense, thus demonstrating the power of the method. As an application singlet‐triplet couplings in thiophene are investigated that are important for the photophysics and photochemistry. Spin‐orbit matrix elements between all π → π* excited states are found to be small. Considerably larger spin‐orbit matrix elements are observed only for cases in which π → σ* excited configurations are involved.

Intersystem crossing and characterization of dark states in the pyrimidine nucleobases uracil, thymine, and 1-methylthymine.

The ground and low-lying excited states of the pyrimidine nucleo bases uracil, thymine, and 1-methylthymine have been characterized using ab initio coupled-cluster with approximate doubles (CC2) and a combination of density functional theory (DFT) and semiempirical multireference configuration interaction (MRCI) methods. Intersystem crossing rate constants have been determined perturbationally by employing a nonempirical one-center mean-field approximation to the Breit-Pauli spin-orbit operator for the computation of electronic coupling matrix elements. Our results clearly indicate that the S(2)((1)pi-->pi*)-->T(2)((3)n-->pi*) process cannot compete with the subpicosecond decay of the S(2) population due to spin-allowed nonradiative transitions, whereas the T(1)((3)pi-->pi*) state is populated from the intermediate S(1)((1)n-->pi*) state on a subnanosecond time scale. Hence, it is very unlikely that the S(1)((1)n-->pi*) state corresponds to the long-lived dark state observed in the gas phase.

A new mean-field and ECP-based spin-orbit method. Applications to Pt and PtH

Abstract All-electron spin-orbit mean-field integrals have been modified to be used with effective core potential valence wave-functions. Two different effective core potentials, one of the conventional Huzinaga type and the other an ab initio model potential, have been employed in our investigation. In all cases the full nodal structure of the valence orbitals has been kept. The applicability of the present approach has been tested for the 3D and 1D (d9s1) and the 3F (d8s2) electronic states of atomic platinum, the 2D d9 state of Pt+, and the low-lying 2 Δ , 2 Π , and 2 Σ + states of platinum hydride. Spin-orbit matrix elements evaluated for ab initio model potential wavefunctions are found to agree with all-electron results to within better than 3%, and the corresponding agreement for the spectroscopic constants of PtH is excellent.

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin-orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the , , and spin-orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S1-->T1 population transfer is found to proceed at a rate of approximately 10(7) s(-1) in the isolated molecule.

The generalized active space concept for the relativistic treatment of electron correlation. I. Kramers-restricted two-component configuration interaction

As a prelude to a series of presentations dealing with the treatment of electron correlation and special relativity, we present the theoretical background and the implementation of a new two-component relativistic configuration interaction program. It is based on the method of generalized active spaces which has been extended from a nonrelativistic implementation to make use of two-component Hamiltonians and time reversal and double point group symmetry at both the spinor and Slater determinant level. We demonstrate how the great computational effort arising from such a general approach—the treatment of spin–orbit interaction and electron correlation in a fully variational framework—can be markedly reduced by the use of the aforementioned symmetries. Evidence for the performance of the program is given through a number of calculations on light systems with a significant spin–orbit splitting in low-lying electronic states and the well-known problem case thallium, which often serves as a rigorous test syste...