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We present equations of motion (EOMs) for general time-dependent wave functions with exponentially parametrized biorthogonal basis sets. The equations are fully bivariational in the sense of the time-dependent bivariational principle (TDBVP) and offer an alternative, constraint free formulation of adaptive basis sets for bivariational wave functions. We simplify the highly non-linear basis set equations using Lie algebraic techniques and show that the computationally intensive parts of the theory are in fact identical to those that arise with linearly parametrized basis sets. Our approach thus offers easy implementation on top of existing code with minimal computational overhead in the context of both nuclear dynamics and time-dependent electronic structure. Computationally tractable working equations are provided for single and double exponential parametrizations of the basis set evolution. The EOMs are generally applicable for any value of the basis set parameters, unlike the approach of transforming the parameters to zero at each evaluation of the EOMs. We show that the basis set equations contain a well-defined set of singularities, which are identified and removed by a simple scheme. The exponential basis set equations are implemented in conjunction with time-dependent vibrational coupled cluster with time-dependent modals (TDMVCC) and we investigate the propagation properties in terms of the average integrator step size. For the systems we test, the exponentially parametrized basis sets yield slightly larger step sizes compared to linearly parametrized basis set., Comment: The following article has been submitted to the Journal of Chemical Physics

We derive general bivariational equations of motion (EOMs) for time-dependent wave functions with biorthogonal time-dependent basis sets. The time-dependent basis functions are linearly parameterized and their fully variational time evolution is ensured by solving a set of so-called constraint equations, which we derive for arbitrary wave function expansions. The formalism allows division of the basis set into an active basis and a secondary basis, ensuring a flexible and compact wave function. We show how the EOMs specialize to a few common wave function forms, including coupled cluster and linearly expanded wave functions. It is demonstrated, for the first time, that the propagation of such wave functions is not unconditionally stable when a secondary basis is employed. The main signature of the instability is a strong increase in non-orthogonality, which eventually causes the calculation to fail; specifically, the biorthogonal active bra and ket bases tend toward spanning different spaces. Although formally allowed, this causes severe numerical issues. We identify the source of this problem by reparametrizing the time-dependent basis set through polar decomposition. Subsequent analysis allows us to remove the instability by setting appropriate matrix elements to zero. Although this solution is not fully variational, we find essentially no deviation in terms of autocorrelation functions relative to the variational formulation. We expect that the results presented here will be useful for the formal analysis of bivariational time-dependent wave functions for electronic and nuclear dynamics in general and for the practical implementation of time-dependent CC wave functions in particular.

Self-assembled monolayers of 7-mercapto 4-methylcoumarin (MMC) on a flat gold surface were studied by Molecular Dynamics (MD) simulations, reference-free grazing incidence X-ray fluorescence (GIXRF) and X-ray photoemission spectroscopy (XPS), to determine the maximum monolayer density and to investigate the nature of the molecule/surface interface. In particular, the protonation state of the sulfur atom upon adsorption was analyzed, since some recent literature presented evidences for physisorbed thiols (preserving the S-H bond), unlike the common picture of chemisorbed thiyls (losing the hydrogen). MD with a specifically tailored force field was used to simulate either thiol or thiyl monolayers with increasing number of molecules, to determine the maximum dynamically stable densities. This result was refined by computing the monolayer chemical potential as a function of the density with the Bennet Acceptance Ratio method, based again on MD simulations. The monolayer density was measured with GIXRF, which provided a quantitative estimate of the number of sulfur atoms on top of flat gold surfaces embedded in a solution of MMC, to allow the formation of a dense monolayer. The sulfur core level binding energies in the same monolayers were measured by XPS, fitting the recorded spectra with the binding energies proposed in the literature for free or adsorbed thiols and thiyls, to get insight on the nature of the molecular species present in the layer.

Self-assembled monolayers (SAM) of 7-mercapto-4-methylcoumarin (MMC) on a flat gold surface were studied by molecular dynamics (MD) simulations, reference-free grazing incidence X-ray fluorescence (GIXRF) and X-ray photoelectron spectroscopy (XPS), to determine the maximum monolayer density and to investigate the nature of the molecule/surface interface. In particular, the protonation state of the sulfur atom upon adsorption was analyzed, since some recent literature presented evidence for physisorbed thiols (preserving the S-H bond), unlike the common picture of chemisorbed thiyls (losing the hydrogen). MD with a specifically tailored force field was used to simulate either thiol or thiyl monolayers with increasing number of molecules, to determine the maximum dynamically stable densities. This result was refined by computing the monolayer chemical potential as a function of the density with the bennet acceptance ratio method, based again on MD simulations. The monolayer density was also measured with GIXRF, which provided the absolute quantification of the number of sulfur atoms in a dense self-assembled monolayer (SAM) on flat gold surfaces. The sulfur core level binding energies in the same monolayers were measured by XPS, fitting the recorded spectra with the binding energies proposed in the literature for free or adsorbed thiols and thiyls, to get insight on the nature of the molecular species present in the layer. The comparison of theoretical and experimental SAM densities, and the XPS analysis strongly support the picture of a monolayer formed by chemisorbed, dissociated thiyls.

Polystyrene samples with different molar mass and narrow polydispersity index were prepared by nitroxide-mediated polymerization using N-tert-butyl-N-[1-diethylphosphono(2,2-dimethylpropyl)] nitrox...

We develop time-dependent vibrational coupled cluster with time-dependent modals (TDMVCC), where an active set of one-mode basis functions (modals) is evolved in time alongside coupled-cluster wave-function parameters. A biorthogonal second quantization formulation of many-mode dynamics is introduced, allowing separate biorthogonal bases for the bra and ket states, thus ensuring complex analyticity. We employ the time-dependent bivariational principle to derive equations of motion for both the one-mode basis functions and the parameters describing the cluster (T) and linear de-excitation (L) operators. The choice of constraint (or gauge) operators for the modal time evolution is discussed. In the case of untruncated cluster expansion, the result is independent of this choice, but restricting the excitation space removes this invariance; equations for the variational determination of the constraint operators are derived for the latter case. We show that all single-excitation parts of T and L are redundant and can be left out in the case of variationally determined constraint-operator evolution. Based on a pilot implementation, test computations on Henon–Heiles model systems, the water molecule, and a reduced-dimensionality bi-thiophene model are presented, showing highly encouraging results for TDMVCC. It is demonstrated how TDMVCC in the limit of a complete cluster expansion becomes equivalent to multiconfiguration time-dependent Hartree for the same active-space size. Similarly, it is discussed how TDMVCC generally gives better and more stable results than its time-independent-modals counterpart, while equivalent results are obtained for complete expansions and full one-mode basis sets.

We describe theoretically the structure and properties of layered lead organohalide perovskites, considering purely bi-dimensional (2D) PbI4 layers, and quasi-2D systems where the inorganic layers are formed by more than one lead iodide sheet. The intercalating organic dications were designed to have low lying virtual orbitals (LUMO), so as to induce in the perovskite the appearance of virtual bands, localized in the organic layer, either close to the inorganic conduction band bottom or valence band top, or in some cases in the middle of the inorganic band gap. Such a feature is quite uncommon for this class of materials, and deserves attention since it allows one to tune the effective band gap of the material, possibly leading to the absorption of visible light and influencing the optical properties deeply. We discuss the effect of functional groups on the organic cations, and of the different symmetries used in geometry optimizations: a careful analysis of the contributions to the dispersion curves and band gaps was performed. The charge carrier mobility is also discussed, computing the conductivity over relaxation time and the effective masses for all the systems, with particular attention to the features related to the unusual organic intra-gap bands. All the structures were optimized at the DFT level, with inclusion of dispersion effects; dispersion curves were computed with full relativistic potentials, and the band gaps corrected for long range coulombic effects at the GW level. A semiempirical approach, based on the integration of charge carrier group velocities over a dense grid of k-points, was used to compute the conductivities and effective masses.

The enhancement factor (EF) is an essential parameter in the field of surface-enhanced Raman spectroscopy (SERS), indicating the magnification of the Raman signal of molecules interacting with the surface of plasmonic nanostructures. The calculation of EF requires a careful evaluation of both the signal intensities and the number of molecules in SERS and normal Raman conditions. The determination of the surface density of molecules adsorbed on the plasmonic substrate is a challenging task, but essential for the estimation of the number of SERS-active molecules. This paper describes the determination of EF using 7-mercapto-4-methylcoumarin (MMC) as the probe molecule on gold-coated silicon nanowires, integrating SERS and normal Raman spectroscopy with X-ray fluorescence (RF-XRF) data that provide a reference-free quantitative measurement of the molecular surface density. In addition, the surface coverage of MMC on the substrate is modelled by molecular mechanics (MM) and molecular dynamics (MD) simulations.

We derive equations for describing the time evolution of variational wave functions in linear and exponential parameterization with a second-quantization (SQ) formulation. The SQ formalism covers time-dependent Hartree (TDH), while exact states and approximate vibrational configuration interaction wave functions are described using state-transfer operators. We present detailed expressions for efficient evaluation of TDH in linear (L-TDH) and exponential (X-TDH) parametrization and an efficient implementation supporting linear scaling with respect to the number of degrees of freedom M when the Hamiltonian operator contains a constant number of terms per mode independently of the size of the system. The computational cost of the X-TDH method is reduced significantly compared to the L-TDH method for systems with many operator terms per mode such as is typical for accurate molecular potential-energy surfaces. Numerical results for L-TDH and X-TDH are presented which confirm the theoretical reduction of the M scaling compared to standard first-quantization formulations. Calculations on Henon-Heiles potentials with more than 105 dimensions and polycyclic aromatic hydrocarbons with up to 264 modes have been performed. Thus, the SQ formulation and the X-TDH method pave the way for studying the time-resolved quantum dynamics of large molecules.

Equations are derived for the time evolution of time-dependent vibrational coupled cluster (TDVCC) wave functions covering both the TDVCC ket state and the associated so-called Λ bra state. The equations are implemented in the special case of both the Hamiltonian and the cluster operator containing at most two-mode coupling terms. The nontrivial behavior of the evolution of norm, energy, and expectation values due to the nonunitary time-evolution of the nonvariational TDVCC theory is analyzed theoretically and confirmed in numerical experiments that also include time-dependent Hamiltonians. In the spirit of time-independent size-consistency analysis, the separability of both the coupled cluster and Λ states for noninteracting systems is studied. While the coupled cluster state clearly has the correct behavior, the behavior of the Λ state is more intricate, and the consequence for different properties is shown theoretically and numerically. Overall, the numerical experiments show that TDVCC in incomplete expansions gives higher accuracy than a standard linear variational wave function parameterization with the same number of independent parameters, while equivalent results are obtained for complete expansions. The efficiency of the methodology is illustrated in computations on polycyclic aromatic hydrocarbons with up to 156 modes.

We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the critical population required to correctly sample the wavefunction for a range of systems and excitation levels and hence leads to a substantial reduction in the computational cost. This development has the potential to substantially extend the range of the method, enabling it to be used to treat larger systems with excitation levels not easily accessible with conventional deterministic methods.

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo̸ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.

In this work we show how the vibrational coupled-cluster method at the two-mode coupling level can be used to calculate zero-point vibrational averages of properties. A technique is presented, where any expectation value can be calculated using a single set of Lagrangian multipliers computed solving iteratively a single linear set of equations. Sample calculations are presented which show that the resulting algorithm scales only with the third power of the number of modes, therefore making large systems accessible. Moreover, we present applications to water, pyrrole, and para-nitroaniline.

In this paper we set up a method called overlap decoherence correction (ODC) to take into account the quantum decoherence effect in a surface hopping framework. While keeping the standard surface hopping approach based on independent trajectories, our method allows to account for quantum decoherence by evaluating the overlap between frozen Gaussian wavepackets, the time evolution of which is obtained in an approximate way. The ODC scheme mainly depends on the parameter σ, which is the Gaussian width of the wavepackets. The performance of the ODC method is tested versus full quantum calculations on three model systems, and by comparison with full multiple spawning (FMS) results for the S(1)→S(0) decay in the azobenzene molecule.