Nonadiabatic molecular dynamics with solvent effects: A LR-TDDFT QM/MM study of ruthenium (II) tris (bipyridine) in water

The previously derived trajectory-based nonadiabatic molecular dynamics scheme [E. Tapavicza, I. Tavernelli, U. Rothlisberger, Phys. Rev. Lett. 98 (2007) 023001] is extended to include the coupling of the quantum system with a classically described environment. The dynamics is performed using LR-TDDFT energies and forces computed on-the-fly together with the nonadiabatic coupling vectors needed for the propagation of the nuclear coefficients according to Tully’s fewest-switches surface hopping algorithm. The resulting LR-TDDFT-QM/MM approach is applied to the study of the ultrafast relaxation of the photoexcited singlet metal-to-ligand-charge-transfer state (¹MLCT) of [Ru(bpy)₃]²⁺ (bpy = 2,2′-bipyridine) in water. The observed intersystem crossing dynamics with the triplet MLCT is in good agreement with available experimental results.     

The role of the excited electronic states in the C+ + H2O reaction

The electronic excited states of the [COH2]+ system have been studied in order to establish their role in the dynamics of the C+ + H2O-->[COH]+ +H reaction, which is a prototypical ion-molecule reaction. The most relevant minima and saddle points of the lowest excited state have been determined and energy profiles for the lowest excited doublet and quartet electronic states have been computed along the fragmentation and isomerization coordinates. Also, nonadiabatic coupling strengths between the ground and the first excited state have been computed where they can be large. Our analysis suggests that the first excited state could play an important role in the generation of the formyl isomer, which has been detected in crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], but could not be explained in quasiclassical trajectory computations [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003); J. R. Flores, J. Chem. Phys. 125, 164309 (2006)].     

Nonadiabatic effects in C-Br bond scission in the photodissociation of bromoacetyl chloride

Bromoacetyl chloride photodissociation has been interpreted as a paradigmatic example of a process in which nonadiabatic effects play a major role. In molecular beam experiments by Butler and co-workers [J. Chem. Phys. 95, 3848 (1991); J. Chem. Phys. 97, 355 (1992)], BrCH2C(O)Cl was prepared in its ground electronic state (S0) and excited with a laser at 248 nm to its first excited singlet state (S1). The two main ensuing photoreactions are the ruptures of the C-Cl bond and of the C-Br bond. A nonadiabatic model was proposed in which the C-Br scission is strongly suppressed due to nonadiabatic recrossing at the barrier formed by the avoided crossing between the S1 and S2 states. Recent reduced-dimensional dynamical studies lend support to this model. However, another interpretation that has been given for the experimental results is that the reduced probability of C-Br scission is a consequence of incomplete intramolecular energy redistribution. To provide further insight into this problem, we have studied the energetically lowest six singlet electronic states of bromoacetyl chloride by using an ab initio multiconfigurational perturbative electronic structure method. Stationary points (minima and saddle points) and minimum energy paths have been characterized on the S0 and S1 potential energy surfaces. The fourfold way diabatization method has been applied to transform five adiabatic excited electronic states to a diabatic representation. The diabatic potential energy matrix of the first five excited singlet states has been constructed along several cuts of the potential energy hypersurfaces. The thermochemistry of the photodissociation reactions and a comparison with experimental translational energy distributions strongly suggest that nonadiabatic effects dominate the C-Br scission, but that the reaction proceeds along the energetically allowed diabatic pathway to excited-state products instead of being nonadiabatically suppressed. This conclusion is also supported by the low values of the diabatic couplings on the C-Br scission reaction path. The methodology established in the present study will be used for the construction of global potential energy surfaces suitable for multidimensional dynamics simulations to test these preliminary interpretations.     

A quantum wave-packet study of intersystem crossing effects in the O(3P2,1,0,1D2)+H2 reaction

We present for the first time an exact quantum study of spin-orbit-induced intersystem crossing effects in the title reaction. The time-dependent wave-packet method, combined with an extended split operator scheme, is used to calculate the fine-structure resolved cross section. The calculation involves four electronic potential-energy surfaces of the 1A' state [J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 (1998)], the 3A' and the two degenerate 3A" states [S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A 104, 2308 (2000)], and the spin-orbit couplings between them [B. Maiti, and G. C. Schatz, J. Chem. Phys. 119, 12360 (2003)]. Our quantum dynamics calculations clearly demonstrate that the spin-orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlet-triplet coupling is not an important effect. A branch ratio of the spin state Pi32 to Pi12 of the product OH was calculated to be approximately 2.75, with collision energy higher than 0.6 eV, when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.     

Optical linear response function with linear and diagonal quadratic electron-vibration coupling in mixed quantum-classical systems

Optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed phase systems is derived. The linear response function is derived using Kapral's formalism of statistical mechanics in mixed quantum-classical systems. Our mixed quantum-classical linear dipole moment correlation function J(t) is compared with the full quantum J(t) [Y. J. Yan and S. Mukamel, J. Chem. Phys. 85, 5908 (1986)] in the high temperature limit. Model calculations and discussion of our results are presented. Various formulas of Franck-Condon factors for both linear and quadratic coupling are discussed.     

Ab initio potential energy surfaces and nonadiabatic interactions in the H+ +NO collision system

Ab initio calculations on the H(+)+NO system have been carried out in Jacobi coordinates at the multireference configuration interaction level employing Dunning's correlation-consistent polarized valence triple zeta basis set to analyze the role of low-lying electronic excited states in influencing the collision dynamics relevant to the experimental collision energy range of 9.5-30 eV. The lowest two adiabatic potential energy surfaces, asymptotically correlating to H(+)+NO(X (2)Pi) and H((2)S)+NO(+)(X (1)Sigma(+)), have been obtained. Using ab initio procedures, the (radial) nonadiabatic couplings and the mixing angle between the lowest two electronic states (1 (2)A' and 2 (2)A') have been obtained to yield the corresponding quasidiabatic potential energy matrix. The strengths of the computed vibrational coupling matrix elements reflect a similar trend, as has been observed experimentally in the magnitudes of the state-to-state transition probability for the inelastic vibrational excitations [J. Krutein and F. Linder, J. Chem. Phys. 71, 559 (1979); F. A. Gianturco et al., J. Phys. B 14, 667 (1981)].     

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: applications to Tully's three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully's surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.     

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.     

Ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate excited states in molecules: Population and vibrational coherence transfers

Results of a theoretical study of ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate π-electronic excited states of molecules were presented. Analytical expressions for temporal behaviors of population and vibrational coherence were derived using a simplified model to clarify the quantum mechanical interferences between the two coherently excited electronic states, which appeared in the nuclear wavepacket simulations [M. Kanno, H. Kono, Y. Fujimura, S.H. Lin, Phys. Rev. Lett 104 (2010) 108302]. The photon-polarization direction of the linearly polarized laser, which controls the populations of the two quasi-degenerate electronic states, determines constructive or destructive interference. Features of the vibrational coherence transfer between the two coupled quasi-electronic states through nonadiabatic couplings are also presented. Information on both the transition frequency and nonadiabatic coupling matrix element between the two states can be obtained by analyzing signals of two kinds of quantum beats before and after transfer through nonadiabatic coupling.     

Optical nonlinear response function with linear and diagonal quadratic electron-vibration coupling in mixed quantum-classical systems

While an optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed-phase systems was derived by Toutounji [J. Chem. Phys. 121, 2228 (2004)], the corresponding analytical optical line shape is derived. The respective nonlinear correlation functions are also derived. Model calculations involving photon-echo, pump-probe, and hole-burning signals of model systems with both linear and quadratic coupling are provided. Hole-burning formula of Hayes-Small is compared to that of Mukamel in mixed quantum-classical systems.     

High resolution vacuum ultraviolet emission spectrum of D(2) from 78 to 103 nm: The D (1)Pi(u)-->X (1)Sigma(g) (+) and D(') (1)Pi(u) (-)-->X (1)Sigma(g) (+) band systems

The emission spectrum of the D(2) molecule has been studied at high resolution in the vacuum ultraviolet region 78.5-102.7 nm. A detailed analysis of the two D (1)Pi(u)-->X (1)Sigma(g) (+) and D(') (1)Pi(u) (-)-->X (1)Sigma(g) (+) electronic band systems is reported. New and improved values of the level energies of the two upper states have been derived with the help of the program IDEN [V. I. Azarov, Phys. Scr. 44, 528 (1991); 48, 656 (1993)], originally developed for atomic spectral analysis. A detailed comparison is made between the observed energy levels and solutions of coupled equations using the newest ab initio potentials by Wolniewicz and co-workers [J. Chem. Phys. 103, 1792 (1995); 99, 1851 (1993); J. Mol. Spectros. 212, 208 (2002); 220, 45 (2003)] taking into account the nonadiabatic coupling terms for the D (1)Pi(u) state with the lowest electronic states B (1)Sigma(u) (+), C (1)Pi(u), and B(') (1)Sigma(u) (+). A satisfactory agreement has been found for most of the level energies belonging to the D and D(') states. The remaining differences between observation and theory are probably due to nonadiabatic couplings with other higher electronic states which were neglected in the calculations.     

Quantum and semiclassical theories for nonadiabatic transitions based on overlap integrals related to fast degrees of freedom

Alternative treatments of quantum and semiclassical theories for nonadiabatic dynamics are presented. These treatments require no derivative couplings and instead are based on overlap integrals between eigenstates corresponding to fast degrees of freedom, such as electronic states. Derived from mathematical transformations of the Schr?dinger equation, the theories describe nonlocal characteristics of nonadiabatic transitions. The idea that overlap integrals can be used for nonadiabatic transitions stems from an article by Johnson and Levine [Chem. Phys. Lett. 13, 168 (1972)]. Furthermore, overlap integrals in path-integral form have been recently made available by Schmidt and Tully [J. Chem. Phys. 127, 094103 (2007)] to analyze nonadiabatic effects in thermal equilibrium systems. The present paper expands this idea to dynamic problems presented in path-integral form that involve nonadiabatic semiclassical propagators. Applications to one-dimensional nonadiabatic transitions have provided excellent results, thereby verifying the procedure. In principle these theories that are presented can be applied to multidimensional systems, although numerical costs could be quite expensive.     

Spectral lineshape simulations of tetracene-argon heteroclusters

Spectral lineshapes of the electronic origin of tetracene·Ar_n (n=1–3,19) clusters have been simulated by the semiclassical spectral density method [L. E. Fried, S. Mukamel, J. Chem. Phys.96, 116 (1992)]. Information is obtained concerning the spectral shifts, the homogeneous linewidths and their temperature dependence.     

Nonadiabatic quantum dynamics in O(3P)+H2→OH+H: a revisited study

To investigate the extent of nonadiabatic effects in the title reaction, quasi-classical trajectory and nonadiabatic quantum scattering as well as the nonadiabatic quantum-classical trajectory calculations were performed on the accurate ab initio benchmark potential energy surfaces of the lowest (3)A' and (3)A" electronic states [Rogers et al., J Phys Chem A 2000, 104, 2308], together with the spin-orbit coupling matrix [Maiti and Schatz, J Chem Phys 2003, 119, 12360] and the lowest singlet (1) A' potential energy surface [Dobby and Knowles, Faraday Discuss 1998, 110, 247]. Comparison of the calculated total cross sections from both adiabatic and nonadiabatic calculations has demonstrated that for adiabatic channels including (3)A'→(3)A' and (3)A"→(3)A", difference does exist between the two kinds of adiabatic and nonadiabatic calculations, showing nonadiabatic effects to some extent. Such nonadiabatic effects tend to become more conspicuous at high collision energies and are found to be more pronounced with trajectories/quantum wave packet initiated on (3)A' than on (3)A". Furthermore, the present study also showed that nonadiabatic effects can bring the component of forward-scattering in the product angular distributions.     

Nonlinear optical properties of confined excitons in clusters

Size effects in femtosecond photon echo spectroscopy of neat clusters are calculated using a quasiparticle representation of the nonlinear response. We extend our previous study of cooperative effects on the nonlinear response of assemblies of two level molecules [J. A. Leegwater and S. Mukamel, Phys. Rev. A46, 452 (1992)] to allow for nuclear motion and to have an s-p model of polarizable atoms. Photon echos in Benzene/Argon clusters are calculated using a semiclassical phase averaging procedure [L. E. Fried and S. Mukamel, Adv. Chem. Phys. (in Press)].     

Communication: Linear-expansion shooting techniques for accelerating self-consistent field convergence

Based on the corrected Hohenberg-Kohn-Sham total energy density functional [Y. A. Zhang and Y. A. Wang, J. Chem. Phys. 130, 144116 (2009)], we have developed two linear-expansion shooting techniques (LIST)- direct LIST (LISTd) and indirect LIST (LISTi), to accelerate the convergence of self-consistent field (SCF) calculations. Case studies show that overall LISTi is the most robust and efficient algorithm for accelerating SCF convergence, whereas LISTd is advantageous in the early stage of an SCF process. More importantly, LISTi outperforms Pulay's direct inversion in the iterative subspace (DIIS) [P. Pulay, J. Comput. Chem. 3, 556 (1982)] and its two recent improvements, energy-DIIS [K. N. Kudin, G. E. Scuseria, and E. Cance?s, J. Chem. Phys. 116, 8255 (2002)] and augmented Roothaan-Hall energy-DIIS [X. Hu and W. Yang, J. Chem. Phys. 132, 054109 (2010)].     

Assigning signs to the electronic nonadiabatic coupling terms: the H2,O system as a case study

This paper is devoted to a specific difficulty related to the electronic nonadiabatic coupling terms (NACT), namely, how to determine correctly their signs. It is well known that correct NACTs, including their signs, are crucial for any numerical treatment of the nuclear Schrodinger equation [see, i.e., A. Kuppermaan and R. Abrol, Adv. Chem. Phys. 124, 283 (2003)]. In most cases the derivation of the correct sign of the nonadiabatic coupling matrix (NACM) is done employing various continuity procedures. However, there are cases where these procedures do not suffice and for these cases we suggest to apply an additional procedure based on a mathematical lemma which asserts that the exponentiated line integral which yields the D matrix is invariant with respect to the initial point of the integration [M. Baer, J. Phys. Chem. A 104, 3181 (2000)]. In the numerical study we apply this lemma to determine the signs of the 3x3 NACM elements for the three excited states of the {H(2),O} system (some of these NACTs are presented here for the first time). It turns out that the ab initio treatment yields results from which one can form eight different 3x3 NACMs. However the application of this lemma (which does not require any significant additional numerical effort) reduces this number to two. The final selection is done by an enhanced numerical study which requires more accurate calculations.     

Vibrational-exciton couplings for the amide I, II, III, and A modes of peptides

The couplings between all amide fundamentals and their overtones and combination vibrational states are calculated. Combined with the level energies reported previously (Hayashi, T.; Zhuang, W.; Mukamel, S. J. Phys. Chem. A 2005, 109, 9747), we obtain a complete effective vibrational Hamiltonian for the entire amide system. Couplings between neighboring peptide units are obtained using the anharmonic vibrational Hamiltonian of glycine dipeptide (GLDP) at the BPW91/6-31G(d,p) level. Electrostatic couplings between non-neighboring units are calculated by the fourth rank transition multipole coupling (TMC) expansion, including 1/R3 (dipole-dipole), 1/R4 (quadrupole-dipole), and 1/R5 (quadrupole-quadrupole and octapole-dipole) interactions. Exciton delocalization length and its variation with frequency in the various amide bands are calculated. The simulated infrared amide I and II absorptions and CD spectra of 24 residue alpha-helical motifs (SPE3) are in good agreement with experiment.