Non-adiabatic direct quantum dynamics using force fields: Toward solvation.

Quantum dynamics simulations are becoming a powerful tool for understanding photo-excited molecules. Their poor scaling, however, means that it is hard to study molecules with more than a few atoms accurately, and a major challenge at the moment is the inclusion of the molecular environment. Here, we present a proof of principle for a way to break the two bottlenecks preventing large but accurate simulations. First, the problem of providing the potential energy surfaces for a general system is addressed by parameterizing a standard force field to reproduce the potential surfaces of the molecule's excited-states, including the all-important vibronic coupling. While not shown here, this would trivially enable the use of an explicit solvent. Second, to help the scaling of the nuclear dynamics propagation, a hierarchy of approximations is introduced to the variational multi-configurational Gaussian method that retains the variational quantum wavepacket description of the key quantum degrees of freedom and uses classical trajectories for the remaining in a quantum mechanics/molecular mechanics like approach. The method is referred to as force field quantum dynamics (FF-QD), and a two-state ππ*/nπ* model of uracil, excited to its lowest bright ππ* state, is used as a test case.

Mixed-quantum-classical or fully-quantized dynamics? A unified code to compare methods.

Three methods for non-adiabatic dynamics are compared to highlight their capabilities. Multi-configurational time-dependent Hartree is a full grid-based solution to the time-dependent Schrödinger equation, variational multi-configurational Gaussian (vMCG) uses a less flexible but unrestricted Gaussian wavepacket basis, and trajectory surface hopping (TSH) replaces the nuclear wavepacket with a swarm of classical trajectories. Calculations with all methods using a model Hamiltonian were performed. The vMCG and TSH were also then run in a direct dynamics mode, with the potential energy surfaces calculated on-the-fly using quantum chemistry calculations. All dynamics calculations used the Quantics package, with the TSH calculations using a new interface to a surface hopping code. A novel approach to calculate adiabatic populations from grid-based quantum dynamics using a time-dependent discrete variable representation is presented, allowing a proper comparison of methods. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Conformer-resolved quantum dynamics study of the photodissociation of 3-pyrroline.

A model Hamiltonian based on the vibronic coupling model is developed to describe the excited state dynamics of 3-pyrroline. With the use of the method of improved relaxation in conjunction with the MCTDH wavepacket propagation algorithm, vibrational eigenstates corresponding to both the axial and equatorial conformers of 3-pyrroline are calculated and subsequently used in a conformer-resolved study of the photodissociation of 3-pyrroline following excitation to its S1(3s/πσ*) and S2(3px) states. In analogy with ammonia, the excited state dynamics of both conformers of 3-pyrroline are found to be dominated by the (quasi-) planarization of the molecule in its electronically excited states and predominantly diabatic behavior of dissociation mediated by a conical intersection between the S1 and S0 states.

A reinterpretation of the electronic spectrum of pyrrole: a quantum dynamics study.

The first band in the electronic spectrum of pyrrole is calculated from wavepacket propagations performed using the MCTDH method. To do so, two model Hamiltonians are constructed to describe seven low-lying excited electronic states of pyrrole. These Hamiltonians are based on the vibronic coupling model, and are parameterised via fitting to extensive CASPT2 and EOM-CCSD calculations. A detailed analysis of the structure of pyrrole's electronic spectrum in the range 5.5 to 6.5 eV is made. The role of intensity borrowing from transitions to ππ(*) states by lower-lying 3s and 3p Rydberg states is assessed, and reassignments of much of the spectrum are subsequently made which indicate that most of the states in the spectrum are predominantly Rydberg in character. The resulting conclusions drawn serve to highlight the limitations of assignments based on the matching of calculated vertical excitation energies and the positions of peak maxima observed in electronic spectra.

Quantum dynamics study of photoexcited aniline.

A model Hamiltonian based on the quadratic vibronic coupling model is developed to describe the photoinduced dynamics of aniline excited to the manifold of states comprising its first six singlet electronic states. The model Hamiltonian is parametrized by fitting to the results of extensive EOM-CCSD calculations and its validity tested through the calculation of the first two bands in the electronic absorption spectrum of aniline. It is found that two previously neglected 3p Rydberg states play an important role in the dynamics of aniline following excitation into the first two (1)ππ* states. Assignments of the vibrational structure seen in the experimental spectrum is made, and the role played by the Herzberg-Teller effect in excitation to the first (1)ππ* state is analyzed.

Quantum dynamics study of the competing ultrafast intersystem crossing and internal conversion in the "channel 3" region of benzene.

Time-resolved photoelectron spectroscopy can obtain detailed information about the dynamics of a chemical process on the femtosecond timescale. The resulting signal from such detailed experiments is often difficult to analyze and therefore theoretical calculations are important in providing support. In this paper we continue our work on the competing pathways in the photophysics and photochemistry of benzene after excitation into the "channel 3" region [R. S. Minns, D. S. N. Parker, T. J. Penfold, G. A. Worth, and H. H. Fielding, Phys. Chem. Chem. Phys. 12, 15607 (2010)] with details of the calculations shown previously, building on a vibronic coupling Hamiltonian [T. J. Penfold and G. A. Worth, J. Chem. Phys. 131, 064303 (2009)] to include the triplet manifold. New experimental data are also presented suggesting that an oscillatory signal is due to a hot band excitation. The experiments show that signals are obtained from three regions of the potential surfaces, three open channels, which are assigned with the help of simulations showing that following excitation into vibrationally excited-states of S(1) the wavepacket not only crosses through the prefulvenoid conical intersection back to the singlet ground state, but also undergoes ultrafast intersystem crossing to low lying triplet states. The model is, however, not detailed enough to capture the full details of the oscillatory signal due to the hot band.

Competing ultrafast intersystem crossing and internal conversion in the "channel 3" region of benzene.

We report new, detailed, femtosecond time-resolved photoelectron spectroscopy experiments and calculations investigating the competition between ultrafast internal conversion and ultrafast intersystem crossing in electronically and vibrationally excited benzene at the onset of "channel 3". Using different probe energies to record the total photoelectron yield as a function of pump-probe delay we are able to confirm that S(1), T(1) and T(2) electronic states are involved in the excited state dynamics. Time-resolved photoelectron spectroscopy measurements then allow us to unravel the evolution of the S(1), T(1) and T(2) components of the excited state population and, together with complementary quantum chemistry and quantum dynamics calculations, support our earlier proposal that ultrafast intersystem crossing competes with internal conversion (Chem. Phys. Lett., 2009, 469, 43).

Local control of multidimensional dynamics.

The control of chemical reactions has been a target for researchers since the development of lasers which operated on a timescale fast enough to follow nuclear motion. Since then a number of schemes have been developed, each proving successful in a selection of systems. In this paper we present results obtained following the implementation of local control theory together with the multi-configuration time dependent Hartree quantum dynamics algorithm, aiming to efficiently design control pulses for polyatomic systems. Control of multidimensional models of cyclobutadiene and pyrazine are presented and discussed. These results represent a starting point for further studies, showing the distinct advantages of using this approach for controlling chemical reactions.

Multimode quantum dynamics using Gaussian wavepackets: The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method applied to the absorption spectrum of pyrazine.

The Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH) method is applied to calculate the S(2)(pipi( *)) absorption spectrum of the pyrazine molecule, whose diffuse structure results from the ultrafast nonadiabatic dynamics at the S(2)-S(1) conical intersection. The 24-mode second-order vibronic-coupling model of Raab et al. [J. Chem. Phys. 110, 936 (1999)] is employed, along with 4-mode and 10-mode reduced-dimensional variants of this model. G-MCTDH can be used either as an all-Gaussian approach or else as a hybrid method using a partitioning into primary modes, treated by conventional MCTDH basis functions, and secondary modes described by Gaussian particles. Comparison with standard MCTDH calculations shows that the method converges to the exact result. The variational, nonclassical evolution of the moving Gaussian basis is a key element in obtaining convergence. For high-dimensional systems, convergence is significantly accelerated if the method is employed as a hybrid scheme.

Direct quantum dynamics using variational multi-configuration Gaussian wavepackets. Implementation details and test case.

We present here a direct quantum dynamics method using variational multi-configuration Gaussian wavepackets. Based on the efficient multi-configuration time-dependent Hartree wavepacket propagation algorithm, it uses on-the-fly quantum chemical calculation of the potential energy and its derivatives rather than fitted surfaces. Intermediate results are stored in a database so that expensive quantum chemical computations can be recycled. This method is intended to treat quantum effects in the photochemistry of large molecules and the use of Cartesian coordinates to perform direct dynamics is discussed with a comparison between Cartesian coordinates of Jacobi vectors and Cartesian coordinates of the nuclei, using various free and constrained approaches depending on the way the rotation is treated. As a test calculation to be compared to full quantum dynamics it is applied here to the computation of the photodissociation spectrum of nitrosyl chloride (NOCl).

A novel algorithm for non-adiabatic direct dynamics using variational Gaussian wavepackets.

In a recent paper (G. Worth, P. Hunt and M. Robb, J. Phys. Chem. A, 2003, 107, 621), we used surface hopping direct dynamics calculations to study the molecular dynamics of the butatriene radical cation in the X/A manifold, which is coupled by a conical intersection. Here, we present the first direct dynamics calculations using a novel algorithm, again using this ideal test system. The algorithm, which is based on the powerful multi-configuration time-dependent Hartree (MCTDH) wavepacket propagation method, uses a variational basis of coupled frozen Gaussian functions that optimally represent the evolving nuclear wavepacket at all times. Each Gaussian function follows a "quantum trajectory", along which the potential surface is evaluated by quantum chemistry calculations. As far fewer Gaussian functions are needed than classical trajectories in a semi-classical method, the number of quantum chemical calculations is drastically reduced. A crucial point in direct dynamics. To validate the method, initial calculations have been made using an analytic model Hamiltonian, where it is shown to reproduce the main features of the state population transfer with 8-16 basis functions per state. Coupled to the GAUSSIAN quantum chemistry program, the method is then shown to provide a feasible direct dynamics algorithm for the description of this non-adiabatic process.

Local interactions of aromatic residues in short peptides in aqueous solution: a combined database and energetic analysis.

Although short peptides are usually structurally disordered in aqueous solution, particular peptide sequences display local structure. We performed database and conformational searches, along with molecular dynamics simulations, to study two local interactions detected by 1H-NMR in tetrapeptides excised from bovine pancreatic trypsin inhibitor: aromatic-(i+2)amide and (i-1)cisproline-aromatic. For both types of interaction, at least two major and distinct peptide conformations are identified in the folded state. The aromatic-(i+2)amide interaction can have parallel and perpendicular arrangements of the N-H bond and the aromatic ring. The (i-1)cisproline-aromatic interaction can have close packing of the aromatic ring to the (i-2)C alpha H or the (i-1)C gamma H but not both simultaneously. Although these local aromatic interactions are weak, they may influence folding and binding properties. The combination of search and simulation techniques provides a useful route towards obtaining an atomic-detail description of peptides exhibiting these interactions.

TRAJAN: a tool for analyzing trajectories from molecular simulations.

Molecular dynamics simulations of biological systems are notoriously difficult to analyze because of the complexity of the information that contain. We describe a new method for analyzing trajectories from simulations in order to extract important features of the motion. The trajectory of each atom is partitioned into conformation wells, in each of which its motion is assumed to be predominantly harmonic oscillation around an average position. Thus each atom moves anharmonically through a sequence of wells during the trajectory. The movement of atoms between wells, their ellipsoids of motion within each well, and correlations in the motion of atoms are quantified and can be visualized with molecular graphics. The TRAJAN analysis procedure is applicable to trajectories from equilibrium and nonequilibrium simulations and is not restricted to molecular dynamics simulations. Its application is demonstrated for a range of model systems.

Histamine tautomerism and its mode of action.

An established combination of quantum mechanical calculations and molecular dynamics simulations (Worth, C.A., King, P.M. and Richards, W.G. (1989) Biochim. Biophys. Acta 993, 134-136; Cieplak, P., Singh, U.C. and Kollman, P.A. (1987) Int. J. Quant. Chem. QBS14, 65-74; Reynolds, C.A., King, P.M. and Richards, W.G. (1988) Nature 334, 80-82) has been used to calculate the tautomer ratios of histamine species in aqueous solution. The results are in good agreement with experiment and provide a bridge between experimental data and earlier theoretical calculations.

Theoretical calculation of tautomer equilibria in solution: 4-(5-)methylimidazole.

A combination of quantum mechanical calculations and molecular dynamics simulations has been used to calculate the tautomer ratio of 4-(5-)methyl imidazole in solution, and the results are in good agreement with experiment.