Newton-X is a general program for molecular dynamics simulations beyond the Born-Oppenheimer approximation. It has been primarily used for simulations of ultrafast processes (femtosecond to picosecond time scale) in photoexcited molecules. It has also been used for simulation of band envelops of absorption and emission spectra. Newton-X uses the trajectory surface hopping method, a semi-classical approximation in which the nuclei are treated classically by Newtonian dynamics, while the electrons are treated as a quantum subsystem via a local approximation of the Time-dependent Schrödinger Equation. Nonadiabatic effects (the spread of the nuclear wave packet between several states) are recovered by a stochastic algorithm, which allows individual trajectories to change between different potential energy states during the dynamics.
Capabilities Newton-X is designed as a platform to perform all steps of the nonadiabatic dynamics simulations, from the initial conditions generation, through trajectories computation, to the statistical analysis of the results. It works interfaced to a number of electronic structure programs available for computational chemistry, including Gaussian, Turbomole, Gamess, and Columbus. Its modular development allows to create new interfaces and integrate new methods. Users’ new developments are encouraged and are in due course included into the main branch of the program. Nonadiabatic couplings, the central quantity in nonadiabatic simulations, can be either provided by a third-party program or computed by Newton-X. When computed by Newton-X, it is done with a numerical approximation based on overlap of electronic wavefunctions obtained in sequential time steps. A local diabatization method is also available to provide couplings in the case of weak nonadiabatic interactions. Hybrid combination of methods is possible in Newton-X. Forces computed with different methods for different atomic subsets can be linearly combined to generate the final force driving the dynamics. These hybrid forces may, for instance, be combined into the popular electrostatic-embedding quantum-mechanical/molecular-mechanical method (QM/MM). Important options for QM/MM simulations, such as link atoms, boundaries, and thermostats are available as well. As part of the initial conditions module, Newton-X can simulate absorption, emission, and photoelectron spectra, using the Nuclear Ensemble approach, which provides full spectral widths and absolute intensities.
Methods and Interfaces to Third-Party Programs Newton-X can simulate surface-hopping dynamics with the following programs and quantum-chemical methods:
Nonadiabatic couplings The surface hopping probability depends on the values of the nonadiabatic couplings between electronic states. Newton-X can either compute nonadiabatic couplings during the dynamics or read them from an interfaced third-party program. The computation of the couplings in Newton-X is done by finite differences, following the Hammes-Schiffer-Tully approach. In this approach, the key quantity for computation of the surface hopping probability, the inner product between the nonadiabatic couplings (τLM) and the nuclear velocities (v) at time t, is given by
τ L M ⋅ v ≈ 1 4 Δ t ( 3 S L M ( t ) − 3 S M L ( t ) − S L M ( t − Δ t ) + S M L ( t − Δ t ) ) {\displaystyle {\boldsymbol {\tau }}_{LM}\cdot \mathbf {v} \approx {\frac {1}{4\Delta t}}\left(3S_{LM}(t)-3S_{ML}(t)-S_{LM}(t-\Delta t)+S_{ML}(t-\Delta t)\right)} , where the terms S L M ( t ) ≡ ⟨ Ψ L ( t − Δ t ) ∣ Ψ M ( t ) ⟩ {\displaystyle S_{LM}(t)\equiv \left\langle \Psi _{L}(t-\Delta t)\mid \Psi _{M}(t)\right\rangle } are wavefunction overlaps between states L and M in different time steps. This method can be generally used for any electronic-structure method, provided that a configuration interaction representation of the electronic wavefunction can be worked out. In Newton-X, it is used with a number of quantum-chemical methods, including MCSCF (Multiconfigurational Self-Consistent Field), MRCI (Multi-Reference Configuration Interaction), CC2 (Coupled Cluster to Approximated Second Order), ADC(2) (Algebraic Diagrammatic Construction to Second Order), TDDFT (Time-Dependent Density Functional Theory), and TDA (Tamm-Dankov Approximation). In the case of MCSCF and MRCI, the configuration interaction coefficients are directly used for computation of couplings. For the other methods, the linear-response amplitudes are used as the coefficients of a configuration interaction wavefunction with single excitations.
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