Stochastic multi-configuration time-dependent Hartree for dissipative quantum dynamics with strong intramolecular coupling.

In this article, we explore the dissipation dynamics of a strongly coupled multidimensional system in contact with a Markovian bath, following a system-bath approach. We use in this endeavor the recently developed stochastic multi-configuration time-dependent Hartree approach within the Monte Carlo wave packet formalism [S. Mandal et al., J. Chem. Phys. 156, 094109 (2022)]. The method proved to yield thermalized ensembles of wave packets when intramolecular coupling is weak. To treat strongly coupled systems, new Lindblad dissipative operators are constructed as linear combinations of the system coordinates and associated momenta. These are obtained by a unitary transformation to a normal mode representation, which reduces intermode coupling up to second order. Additionally, we use combinations of generalized raising/lowering operators to enforce the Boltzmann distribution in the dissipation operators, which yield perfect thermalization in the harmonic limit. The two ansatz are tested using a model two-dimensional Hamiltonian, parameterized to disentangle the effects of intramolecular potential coupling, of strong mode mixing observed in Fermi resonances, and of anharmonicity.

The quantum mean square displacement of thermalized CO on Cu(100) in the short time approximation.

The mean square displacement 〈(x(t) - x(0))2〉 of the position x of a CO molecule adsorbed at thermal equilibrium on a Cu(100) substrate and moving along the 〈100〉 direction is evaluated quantum mechanically. The problem is treated in the independent particle formalism via the numerical solution of the time dependent Schrödinger equation with an initial thermal wave packet. The results are discussed in relation to observables from neutron scattering or helium-3 spin-echo experiments, and their interpretation in terms of classical or quantum mechanical expressions for the mean square displacement.

Rovibrational investigation of a new high-lying 0u + state of Cu2 by using two-color resonant four-wave-mixing spectroscopy.

A highly excited electronic state of dicopper is observed and characterized for the first time. The [39.6]0u +-X1Σg +(0g +) system is measured at rotational resolution by using degenerate and two-color resonant four-wave-mixing, as well as laser induced fluorescence spectroscopy. Double-resonance experiments are performed by labeling selected rotational levels of the ground state by tuning the probe laser wavelength to transitions in the well-known (1-0) band of the B0u +-X1Σg +(0g +) electronic system. Spectra obtained by scans of the pump laser in the UV wavelength range were then assigned unambiguously by the stringent double-resonance selection rules. The absence of a Q-band suggests a parallel transition (ΔΩ = 0) and determines the term symbol of the state as 0u + in Hund's case (c) notation. The equilibrium constants for 63Cu2 are Te = 39 559.921(92) cm-1, ωe = 277.70(14) cm-1, Be = 0.104 942(66) cm-1, and re = 2.2595(11) Å. These findings are supported by high-level ab initio calculations at the MRCI+Q level, which clearly identifies this state as resulting from a 4p ← 3d transition. In addition, three dark perturber states are found in the v = 1 and v = 2 vibrational levels of the new state. A deperturbation analysis characterizes the interaction and rationalizes the anomalous dips in the excitation spectrum of the [39.6]0u +-X1Σg +(0g +) system.

Multidimensional stochastic dissipative quantum dynamics using a Lindblad operator.

In this paper, multidimensional dissipative quantum dynamics is studied within a system-bath approach in the Markovian regime using a model Lindblad operator. We report on the implementation of a Monte Carlo wave packet algorithm in the Heidelberg version of the Multi-Configuration Time-Dependent Hartree (MCTDH) program package, which is henceforth extended to treat stochastic dissipative dynamics. The Lindblad operator is represented as a sum of products of one-dimensional operators. The new form of the operator is not restricted to the MCTDH formalism and could be used with other multidimensional quantum dynamical methods. As a benchmark system, a two-dimensional coupled oscillators model representing the internal stretch and the surface-molecule distance in the O2/Pt(111) system coupled to a Markovian bath of electron-hole-pairs is used. The simulations reveal the interplay between coherent intramolecular coupling due to anharmonic terms in the potential and incoherent relaxation due to coupling to an environment. It is found that thermalization of the system can be approximately achieved when the intramolecular coupling is weak.

Material properties particularly suited to be measured with helium scattering: selected examples from 2D materials, van der Waals heterostructures, glassy materials, catalytic substrates, topological insulators and superconducting radio frequency materials.

Helium Atom Scattering (HAS) and Helium Spin-Echo scattering (HeSE), together helium scattering, are well established, but non-commercial surface science techniques. They are characterised by the beam inertness and very low beam energy (<0.1 eV) which allows essentially all materials and adsorbates, including fragile and/or insulating materials and light adsorbates such as hydrogen to be investigated on the atomic scale. At present there only exist an estimated less than 15 helium and helium spin-echo scattering instruments in total, spread across the world. This means that up till now the techniques have not been readily available for a broad scientific community. Efforts are ongoing to change this by establishing a central helium scattering facility, possibly in connection with a neutron or synchrotron facility. In this context it is important to clarify what information can be obtained from helium scattering that cannot be obtained with other surface science techniques. Here we present a non-exclusive overview of a range of material properties particularly suited to be measured with helium scattering: (i) high precision, direct measurements of bending rigidity and substrate coupling strength of a range of 2D materials and van der Waals heterostructures as a function of temperature, (ii) direct measurements of the electron-phonon coupling constant λ exclusively in the low energy range (<0.1 eV, tuneable) for 2D materials and van der Waals heterostructures (iii) direct measurements of the surface boson peak in glassy materials, (iv) aspects of polymer chain surface dynamics under nano-confinement (v) certain aspects of nanoscale surface topography, (vi) central properties of surface dynamics and surface diffusion of adsorbates (HeSE) and (vii) two specific science case examples - topological insulators and superconducting radio frequency materials, illustrating how combined HAS and HeSE are necessary to understand the properties of quantum materials. The paper finishes with (viii) examples of molecular surface scattering experiments and other atom surface scattering experiments which can be performed using HAS and HeSE instruments.

Controlling tunneling in ammonia isotopomers.

We report results of full-dimensional variational rovibrational quantum-dynamical computations for several ammonia isotopomers, based on selected potential energy and electric dipole moment hypersurfaces. The variational rovibrational eigenstates have been used as a basis for the solution of the time-dependent Schrödinger equation for nuclear motion including coherent infrared multiphoton excitation. The theoretical and computational framework developed during this study enables the investigation of the coherent inhibition or enhancement of tunneling in ammonia isotopomers by appropriately chosen laser fields. Our quantum-dynamical computations include all vibrational and rotational degrees of freedom and assume neither the alignment nor the orientation of the molecules under investigation. Specific results include accurate rotational-vibrational levels for NH2D, NHD2, NHDMu, and NHDT, probability densities for structural parameters as a function of time from the full-dimensional wavepacket results, time-dependent chirality for the isotopically chiral molecule NHDT, and detailed analyses of the enhancement and inhibition of stereomutation dynamics.

A Global Analytical Representation of the Potential Energy Surface of the FHF(-) Anion.

A global analytical representation of the potential energy hypersurface of the lowest adiabatic electronic state of the FHF(-) anion is derived from ab initio calculations at the coupled cluster level of theory with full single and double and perturbative triple excitations using explicitly correlated atomic basis functions. The new compact function of interatomic distances combines covalent short-range and long-range electrostatic interaction forms and assesses accurately both the lowest reaction channels between the F(-) and HF fragments, with reaction enthalpies to within 1 kJ mol(-1), as well as vibrational terms to within 1.5 cm(-1) deviation from experimental values.

Diffusion Rates for Hydrogen on Pd(111) from Molecular Quantum Dynamics Calculations.

The van Hove formula for the dynamical structure factor (DSF) related to particle scattering at mobile adsorbates is extended to include the relaxation of the adsorbates' vibrational states. The total rate obtained from the DSF is assumed to be the sum of a diffusion and a relaxation rate. A simple kinetic model to support this assumption is presented. To illustrate its potential applicability, the formula is evaluated using wave functions, energies, and lifetimes of vibrational states obtained for H/Pd(111) from first-principle calculations. Results show that quantum effects can be expected to be important even at room temperature.

Global analytical potential energy surface for the electronic ground state of NH3 from high level ab initio calculations.

The analytical, full-dimensional, and global representation of the potential energy surface of NH(3) in the lowest adiabatic electronic state developed previously (Marquardt, R.; et al. J. Phys. Chem. B 2005, 109, 8439­8451) is improved by adjustment of parameters to an enlarged set of electronic energies from ab initio calculations using the coupled cluster method with single and double substitutions and a perturbative treatment of connected triple excitations (CCSD(T)) and the method of multireference configuration interaction (MRCI). CCSD(T) data were obtained from an extrapolation of aug-cc-pVXZ results to the basis set limit (CBS), as described in a previous work (Yurchenko, S.N.; et al. J. Chem. Phys 2005, 123, 134308); they cover the region around the NH3 equilibrium structures up to 20,000 hc cm(­1). MRCI energies were computed using the aug-cc-pVQZ basis to describe both low lying singlet dissociation channels. Adjustment was performed simultaneously to energies obtained from the different ab initio methods using a merging strategy that includes 10,000 geometries at the CCSD(T) level and 500 geometries at the MRCI level. Characteristic features of this improved representation are NH3 equilibrium geometry r(eq)(NH(3)) ≈ 101.28 pm, α(eq)(NH(3)) ≈ 107.03°, the inversion barrier at r(inv)(NH(3)) ≈ 99.88 pm and 1774 hc cm(­1) above the NH(3) minimum, and dissociation channel energies 41,051 hc cm(­1) (for NH(3) → ((2)B(2))NH(2) + ((2)S(1/2))H) and 38,450 hc cm(­1) (for NH(3) → ((3)Σ(­))NH +((1)Σ(g)(+))H(2)); the average agreement between calculated and experimental vibrational line positions is 11 cm(­1) for (14)N(1)H(3) in the spectral region up to 5000 cm(­1). A survey of our current knowledge on the vibrational spectroscopy of ammonia and its isotopomers is also given.

Theoretical methods for ultrafast spectroscopy.

Time-resolved spectroscopy in the femtosecond and attosecond time domain is a tool to unravel the dynamics of nuclear and electronic motion in molecular systems. Theoretical insight into the underlying physical processes is ideally gained by solving the time-dependent Schrödinger equation. In this work, methods currently used to solve this equation are reviewed in a compact presentation. These methods involve numerical representations of wavefunctions and operators, the calculation of time evolution operators, the setting up of the Hamiltonian operators and the types of coordinates to be used hereto. The advantages and disadvantages of some methods are discussed.

Ab initio calculations of the lowest electronic states in the CuNO system.

The lowest singlet and triplet electronic levels of the A' and A" symmetry species of the neutral copper-nitrosyl (CuNO) system are calculated by ab initio methods at the multi-reference configuration interaction (MRCI) level of theory with single and double excitations, and at the coupled cluster level of theory with both perturbational (CCSD(T)) and full inclusion of triple excitations (CCSDT). Experimental data are difficult to obtain, hence the importance of carrying out calculations as accurate as possible to address the structure and dynamics of this system. This paper aims at validating a theoretical protocol to develop global potential energy surfaces for transition metal nitrosyl complexes. For the MRCI calculations, the comparison of level energies at linear structures and their values from C(2v) and C(s) symmetry restricted calculations has allowed to obtain clear settings regarding atomic basis sizes, active orbital spaces and roots obtained at the multi-configurational self-consistent field (MCSCF) level of theory. It is shown that a complete active space involving 18 valence electrons, 11 molecular orbitals and the prior determination of 12 roots in the MCSCF calculation is needed for overall qualitatively correct results from the MRCI calculations. Atomic basis sets of the valence triple-zeta type are sufficient. The present calculations yield a bound singlet A' ground state for CuNO. The CCSD(T) calculations give a quantitatively more reliable account of electronic correlation close to equilibrium, while the MRCI energies allow to ensure the qualitative assessment needed for global potential energy surfaces. Relativistic coupled cluster calculations using the Douglas-Kroll-Hess Hamiltonian yield a dissociation energy of CuNO into Cu and NO to be (59 ± 5) kJ mol(-1) ((4940 ± 400) hc cm(-1)). Favorable comparison is made with some of previous theoretical results and a few known experimental data.

Laser-induced enhancement of tunneling in NHD2.

We apply and explore techniques aiming at enhancing the tunneling by laser fields, originally developed for a one-dimensional model, to a complete six-dimensional vibrational model of the inversion motion in NHD(2). The computational study is performed with the multi-configuration time-dependent Hartree method. Assuming an ideal three-dimensional alignment we obtain a driven tunneling time twenty times smaller than the natural one, in rather good agreement with an oversimplified three-state model. In the case of one-dimensional alignment, a linearly polarized field leads to a poor enhancement of the tunneling probability, after averaging over the rotation about the alignment axis, whereas a circularly polarized field improves the rotationally averaged tunneling probability at the end of the pulse.

Full-dimensional quantum dynamics of vibrationally highly excited NHD2.

We report on full-dimensional vibrational quantum dynamics of the highly excited ammonia isotopologue NHD(2) using a newly developed potential energy surface and the MCTDH program package. The calculations allow to realistically simulate an infrared laser induced stereomutation reaction at the pyramidal nitrogen atom in the femtosecond time domain. Our results allow for a thorough qualitative and quantitative understanding of infrared photoinduced stereomutation kinetics, the underlying quantum dynamics, and the reaction mechanisms. Comparison is made with a previous, reduced dimensionality study of the same reaction [R. Marquardt, M. Quack, I. Thanopulos, and D. Luckhaus, J. Chem. Phys. 118, 643 (2003)], and it is shown that slight variances of reduced spaces lead to significantly different kinetics. Because the quantum dynamics depends subtly on variances of reduced spaces, reduced dimensionality treatments are not reliable even for qualitative predictions of the stereomutation kinetics. The first direct comparison between the Multiconfigurational Time Dependent Hartree [M. H. Beck, A. Jäckle, G. A. Worth et al., Phys. Rep. 324, 1 (2000)] and Unimolecular Reactions Induced by Monochromatic Infrared Radiation [M. Quack and E. Sutcliffe, QCPE Bulletin 6, 98 (1986)] program packages on a specific, four dimensional quantum dynamical problem allows for their full validation in the present work.

A new analytical potential energy surface for the adsorption system CO/Cu(100).

Electronic structure data and analytical representations of the potential energy surface for the adsorption of carbon monoxide on a crystalline copper Cu(100) substrate are reviewed. It is found that a previously published and widely used analytical hypersurface for this process [J. C. Tully, M. Gomez, and M. Head-Gordon, J. Vac. Sci. Technol. A 11, 1914 (1993)] represents rather poorly the data obtained from a slab type calculation of the electronic structure. A new, global analytical representation of the potential energy surface for this process is derived via a nonlinear adjustment of parameters. It is more general and fits qualitatively better the electronic structure data. Key characteristic elements of the new surface are the "top" equilibrium adsorption site in the perpendicular arrangement Cu-C-O with Cu-C and C-O distances of 184 and 115 pm, the desorption energy of 0.76 eV and the barrier for lateral diffusion of 33 meV, including approximative corrections for the variation of zero point energy. Anharmonic vibrational fundamentals and overtones are also calculated from six dimensional variational calculations. All these values agree equally well or better with experimental data than previous published theoretical data within estimated uncertainties. The analytical representation is compact and robust, and may be used to describe other adsorption processes of diatomic molecules, including dissociative chemisorption.

Global analytical potential energy surface for large amplitude nuclear motions in ammonia.

An analytical, full-dimensional, and global representation of the potential energy surface of NH(3) in the lowest adiabatic electronic state is developed, and parameters are determined by adjustment to ab initio data and thermochemical data for several low-lying dissociation channels. The electronic structure is calculated at the CASPT2 level within an [8,7] active space. The representation is compared to other recently published potential energy surfaces for this molecule. The present representation is distinguished by giving a qualitatively correct description of the potential energy for very large amplitude displacements of the nuclei from equilibrium. Other characteristic features of the present surface are the equilibrium geometries r(eq)(NH(3)) approximately 101.24 pm, r(eq)(NH(2)) approximately 102.60 pm, alpha(eq)(NH(3)) approximately 106.67 degrees, and the inversion barrier at r(inv)(NH(3)) approximately 99.80 pm and 1781 cm(-1) above the NH(3) minimum. The barrier to linearity in NH(2) is 11,914 cm(-1) above the NH(2)((2)B(1)) minimum. While the quartic force field for NH(3) from the present representation is significantly different from that of the other potential energy surfaces, the vibrational structures obtained from perturbation theory are quite similar for all representations studied here.