Gareth W Richings

University of Birmingham, Birmingham, England, United Kingdom

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Publications (9)26.88 Total impact

  • Gareth W Richings · Graham A Worth
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    ABSTRACT: A method for diabatising multiple electronic states on-the-fly within the direct dynamics variational multi-configuration Gaussian method for calculating quantum nuclear dynamics is presented. The method is based upon the propagation of the adiabatic-diabatic transformation matrix along the paths followed by the Gaussian basis functions which constitute the nuclear wavefunction, by use of a well known differential equation relating the matrix and the non-adiabatic vector coupling terms between the electronic states. The implementation of the method is described and test calculations are presented using the ground and first-excited states of the butatriene cation as an example, allowing comparison to the earlier regularisation diabatisation scheme as well as to full nuclear dynamics on a pre-computed potential energy surface. The new scheme is termed propagation diabatisation.
    No preview · Article · Sep 2015 · The Journal of Physical Chemistry A
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    ABSTRACT: Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrödinger equation (TDSE). They have an underlying trajectory picture that has a natural connection to semi-classical mechanics, allowing a simple pictorial interpretation of an evolving wavepacket. They also have better scaling with system size compared to conventional grid-based techniques. Here we review the variational multi-configurational Gaussian (vMCG) method. This is a variational solution to the TDSE, with explicit coupling between the Gaussian basis functions, resulting in a favourable convergence on the exact solution. The implementation of the method and its performance will be discussed with examples from non-adiabatic photo-excited dynamics and tunneling to show that it can correctly describe both of these strongly quantum mechanical processes. Particular emphasis is given to the implementation of the direct dynamics variant, DD-vMCG, where the potential surfaces are calculated on-the-fly via an interface to quantum chemistry programs.
    No preview · Article · Apr 2015 · International Reviews in Physical Chemistry
  • Gareth W Richings · Graham A Worth
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    ABSTRACT: A theoretical study of the intra-molecular vibrational-energy redistribution of toluene using time-resolved photo-electron spectra calculated using nuclear quantum dynamics and a simple, two-mode model is presented. Calculations have been carried out using the multi-configuration time-dependent Hartree method, using three levels of approximation for the calculation of the spectra. The first is a full quantum dynamics simulation with a discretisation of the continuum wavefunction of the ejected electron, whilst the second uses first-order perturbation theory to calculate the wavefunction of the ion. Both methods rely on the explicit inclusion of both the pump and probe laser pulses. The third method includes only the pump pulse and generates the photo-electron spectrum by projection of the pumped wavepacket onto the ion potential energy surface, followed by evaluation of the Fourier transform of the autocorrelation function of the subsequently propagated wavepacket. The calculations performed have been used to study the periodic population flow between the 6a and 10b16b modes in the S1 excited state, and compared to recent experimental data. We obtain results in excellent agreement with the experiment and note the efficiency of the perturbation method.
    No preview · Article · Dec 2014 · The Journal of Chemical Physics
  • Gareth W. Richings · Peter B. Karadakov
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    ABSTRACT: An augmented optimisation of a previously described (Richings and Karadakov in Mol Phys 105:2363, 2007), variationally stable, Hartree–Fock style excited-state wavefunction is presented. The matrix of second derivatives (Hessian) of the electronic energy with respect to the molecular orbital coefficients is derived, and the matrix elements, necessary for the evaluation of the derivatives, are explicitly laid out. The Hessian is then used in a second-order optimisation procedure to demonstrate the significant improvement, in comparison with the simple steepest descent method used previously, in the rate of convergence of the energies of the selection of small molecules from the earlier work. The improvement is both in terms of the computational time required and in the tighter convergence of the gradient norms. The former factor is particularly significant when using an unrestricted reference wavefunction. A brief discussion of the merits and disadvantages of the use of the Hessian, as well as ideas for future work to improve to further improve the method, is also included.
    No preview · Article · Nov 2013 · Theoretical Chemistry Accounts
  • Graham A. Worth · Gareth W. Richings
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    ABSTRACT: The use of computer simulations studying how laser light can control the behaviour of atoms and molecules is reviewed. A variety of control schemes have been developed and we focus on three commonly used approaches: optimal control, local control and strong-field control. An overview is given of the types of control that can be achieved of interest to chemists, namely molecular alignment and orientation, isomerisation and bond breaking and forming. The calculations are very computer intensive and results from both exact solutions to the time-dependent Schrödinger equation and approximate solutions using the commonly employed trajectory surface hopping approach are covered. Of particular interest is the recent work using strong-field control, which promises to be more general and powerful than approaches based on weak-fields that do not perturb the molecular potential energy surfaces.
    No preview · Article · Jun 2013 · Annual Reports Section C"" (Physical Chemistry)"""
  • Gareth W Richings · Graham A Worth
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    ABSTRACT: Control of the photodissociation of ammonia, by the nonresonant dynamic Stark effect, has been studied theoretically by the numerically exact propagation of wavepackets on ab initio potential energy surfaces. An assessment of the feasibility of controlling the proportion of the wavepacket which dissociates to produce ground or electronically excited state NH(2) fragments, mediated by a conical intersection, has been made by use of a simple two-dimensional, two-state model. It was found that modest control was possible for nonresonant pulses applied during and after excitation, and that the control was caused not by alteration of the position or nature of the conical intersection but by modification of the energy surfaces around the Franck-Condon region. This is made possible by the predissociative nature of the mechanism for hydrogen ejection. The control effect is frequency independent but dependent on pulse, i.e., electric field, strength, indicating that it is indeed due to the Stark effect. Analysis of the control is, however, complicated by the presence of vibrational effects which can come into play if the control pulse frequency is not carefully chosen. By systematically varying the excitation energy, it was also found that the capacity for control is only significant at low energies.
    No preview · Article · Aug 2012 · The Journal of Physical Chemistry A
  • Cristina Sanz-Sanz · Gareth W Richings · Graham A Worth
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    ABSTRACT: The Stark effect is produced when a static field alters molecular states. When the field applied is time dependent, the process is known as the dynamic Stark effect. Of particular interest for the control of molecular dynamics is the Non-Resonant Dynamic Stark Effect (NRDSE), in which the time dependent field is unable to effect a one-photon excitation. The intermediate strength laser pulse instead shapes the potential energy surfaces (PES) and so guides the evolution of the system. A prototype control scheme uses the NRDSE to change the topography of PES in regions where they intersect, thus providing control over photochemistry. Following earlier experimental work, in this paper we study the NRDSE on a new 3 state model of the IBr molecule to gain insight into the mechanism of control at the avoided crossing that governs the branching ratio of the photodissociation.
    No preview · Article · Oct 2011 · Faraday Discussions
  • Andreas Köhn · Gareth W Richings · David P Tew
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    ABSTRACT: An implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 using a single Slater-type geminal has been obtained with the aid of automated term generation and evaluation techniques. In contrast to a previously reported computer code [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], our implementation features a reduced dependence on the auxiliary basis set due to the use of a reformulated evaluation of the so-called Z-intermediate rather than straight forward insertion of an auxiliary basis expansion, which allows an unambiguous comparison to more approximate CCSD-F12 models. First benchmark results for total correlation energies and reaction energies indicate an excellent performance of the much cheaper CCSD(F12) model.
    No preview · Article · Dec 2008 · The Journal of Chemical Physics
  • Gareth W. Richings · Peter B. Karadakov
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    ABSTRACT: A compact approximate wavefunction for a non-degenerate first excited state constructed as a Slater determinant from which the ground state Hartree–Fock (HF) wavefunction has been projected out explicitly is introduced, together with all expressions required for its calculation through gradient-based energy optimization schemes. The explicit projection makes this wavefunction suitable for the description of a non-degenerate first excited state which is of the same symmetry as the HF ground state without any danger of a variational collapse to the lower energy ground state. The equations allowing the calculation of a spin-unrestricted version of the proposed wavefunction have been implemented in code. The results of excited state calculations on HeH+, H2, C2, N2, H2O and H2O2 show that this excited state wavefunction which, effectively, is comprised of just two Slater determinants, only one of which is optimized variationally, is capable of producing results which compare favourably to those coming from standard approaches such as single-excitation configuration interaction (CIS), time-dependent HF (TDHF), symmetry-adapted-cluster CI (SAC-CI) and equations-of-motion coupled-cluster with singles and doubles (EOM-CCSD).
    No preview · Article · Sep 2007 · Molecular Physics