Michael J. Bearpark

A direct method for the location of the lowest energy point on a potential surface crossing

Abstract We present a method, which avoids the use of Lagrange multipliers, for the optimisation of the lowest energy point of the intersection of two potential energy surfaces. The efficiency of this unconstrained algorithm is demonstrated for the n—2 intersection space of a conical intersection and the n—1 intersection space of the crossing of two states of different spin multiplicity.

‘Classical wavepacket’ dynamics through a conical intersection. Application to the S1/S0 photochemistry of benzene

Abstract Excited state dynamics calculations (using semiclassical surface-hopping trajectories first described by Tully and Preston) have been carried out in order to explain the low quantum yield for the photochemical production of benzvalene from benzene. Trajectories are propagated using a series of local quadratic approximations to the potential energy surface. Initial conditions are determined by random sampling of each excited state normal mode within an energy threshold which generates an ensemble of trajectories - a ‘classical wavepacket’. Points on the potential energy surface are computed as required using a parametrised quantum-mechanical/force-field method (molecular mechanics-valence bond, MMVB) which has been designed to simulate the CASSCF potential for ground and covalent excited states. The low benzvalene quantum yield is shown to result from the fact that, after decay via an S 1 /S 0 conical intersection, most trajectories lead back to S 0 benzene and do not reach the region of the prefulvene intermediate.

Mixed state `on the fly' non-adiabatic dynamics: the role of the conical intersection topology

Abstract An algorithm is presented for non-adiabatic `on the fly dynamics simulations using a valence bond wavefunction that arises in the molecular mechanics valence bond method. The electronic wavefunction is propagated using time-dependent quantum mechanics in synchronisation with nuclear propagation using classical mechanics. Some representative computations for the radiationless decay of all-trans-hexa-1,3,5-triene and azulene at a conical intersection channel are presented. In the dynamics studies one observes almost pure diabatic transitions as well as situations where the trajectory propagates in a `mixed state near the conical intersection before decay to the ground state.

Molecular mechanics valence bond methods for large active spaces. Application to conjugated polycyclic hydrocarbons

Abstract The implementation of the Clifford-algebra unitary group approach (first discussed by Paldus) in the context of a Heisenberg Hamiltonian formulation of the VB problem is described. It is demonstrated that this technique leads to an efficient extension of the molecular mechanics valence bond (MM-VB) method to large active space applications, by carrying out full geometry optimisations on the S0 state of coronene (24 active electrons), the S0 and S1 states of naphthalene (10 active electrons) and the S0 and T1 states of triangulene (22 active electrons).

The pseudo-Jahn—Teller effect: a CASSCF diagnostic

A simple test for the pseudo-Jahn-Teller effect is proposed, based on the behaviour of a CASSCF frequency calculation when symmetry is restricted. The test suggests that the pseudo-Jahn-Teller effect operates at the D2h transition structure of S0 pentalene and the D8h transition structure of S0 cyclooctatetraene. The D4h transition structure of S0 cyclooctatetraene is not subject to a pseudo-Jahn-Teller distortion according to this test. Our interpretation of the pseudo-Jahn-Teller effect differs from the conventional one based on a single-transition (CIS-like) approximation.

A simple approach for improving the hybrid MMVB force field: Application to the photoisomerization of s-cis butadiene

MMVB is a QM/MM hybrid method, consisting of a molecular mechanics force field coupled to a valence bond Heisenberg Hamiltonian parametrized from ab initio CASSCF calculations on several prototype molecules. The Heisenberg Hamiltonian matrix elements Qij and Kij, whose expressions are partitioned here into a primary contribution and second‐order correction terms, are calculated analytically in MMVB. When the original MMVB force field fails to produce potential energy surfaces accurate enough for dynamics calculations, we show that significant improvements can be made by refitting the second‐order correction terms for the particular molecule(s) being studied. This “local” reparametrization is based on values of Kij extracted (using effective Hamiltonian techniques) from CASSCF calculations on the same molecule(s). The method is demonstrated for the photoisomerization of s‐cis butadiene, and we explain how the correction terms that enabled a successful MMVB dynamics study [Garavelli, M.; Bernardi, F.; Olivucci, M.; Bearpark, M. J.; Klein, S.; Robb, M. A. J Phys Chem A 2001, 105, 11496] were refitted.

Potential energy surfaces of pseudoaromatic molecules: An MMVB and CASSCF study of pentalene

The S0 and S1 potential energy surfaces of pentalene were studied using MMVB—a hybrid force-field/parametrized valence bond (VB) method designed to simulate CASSCF calculations for ground and covalent excited states. The results were calibrated against full CASSCF calculations. Four distinct critical points were optimized: on S0, a C2h minimum (with alternating single and double bonds) and a D2h transition structure; and on S1, a D2h minimum and an adjacent S1/S0 conical intersection. A VB exchange density matrix (which is independent of the choice of the spin-coupled basis) was used to rationalize the S0 and S1 surface topologies. Craig defined pseudoaromatic molecules to be those with nontotally symmetric electronic ground states. For pentalene, this is true for both CASSCF and MMVB calculations: the CASSCF S0 transition structure is an open-shell B1x singlet, and the VB ground state is dominated by a spin-coupling which transforms as B1g. A C2v minimum and a D2h transition structure were located on the CASSCF S2 potential energy surface. This state cannot be represented by MMVB because of the importance of ionic configurations. The characters of the S1S2 states of pentalene are shown to be reverse of the S1 and S2 states of benzene.

Spin-orbit interactions from self consistent field wavefunctions

Effects of the spin-orbit Hamiltonian HLS , including both the spin-same orbit and spin-other orbit terms, are studied at the self consistent field (SCF) level of theory. Separate calculations are carried out for each state considered, and biorthogonal orbitals are constructed for the evaluation of matrix elements. Doublet-doublet and singlet-triplet interactions are discussed. The evaluation of the Gaussian basis function integrals is described in a Cartesian component representation, these integrals being directly related to one and two electron second derivative integrals. This new SCF spin-orbit code is used to (i) determine the spatial dependence of the spin-orbit parameters for the Renner-Teller 2B1, 2A1 states of H2O+, (ii) determine the spin-orbit splitting of the 2Π states of OH as a function of bond-length and (iii) calculate the radiative lifetime of the a 3Σ+ state of NO+. In each case these calculations are compared with more sophisticated configuration interaction studies, but it is found th...

Characterization of the indacene S0/S1 conical intersection: An MMVB and CASSCF study

A conical intersection between the S0 and S1 states of s-indacene has been located with the molecular mechanics with valence bond (MMVB) and complete active space SCF (CASSCF) methods. In both cases the intersection minimum is close in energy and geometry to the overall minimum on the S1 surface, and can be reached directly along the coordinate which leads from the Franck—Condon geometry to the minimum on S1. The existence of such an accessible S1/S0 surface crossing leading to efficient non-radiative decay can explain the short S1 excited state lifetime and lack of fluorescence for s-indacene. Based on a comparison with X-ray structures for a derivative of s-indacene, we argue that the CASSCF ordering of S0 and S1 states is the correct one, whereas MMVB inverts the two states. However, because the energy differences involved are a few kcal mol-1, a definitive prediction will probably require a multi-reference correlated level of theory with gradient optimization.

A hybrid MC-SCF method: generalised valence bond (GVB) with complete active space SCF (CASSCF)

Abstract A hybrid GVB and CASSCF method is proposed, GVBCAS, in which a full CAS CI is performed amongst the active orbitals (the CAS part), and GVB type excitations are allowed amongst a set of GVB orbitals. We demonstrate that the computational effort required for the energy and gradients is little more than that for a CASSCF calculation with the strongly occupied GVB orbitals allocated to the inactive space, and substantially less than that for a full CASSCF in the space of active + GVB orbitals. The efficacy of the method is illustrated with an example.