Quasi-direct Quantum Molecular Dynamics: The Time-Dependent Adaptive Density-Guided Approach for Potential Energy Surface Construction.

We present a new quasi-direct quantum molecular dynamics computational method which offers a compromise between quantum dynamics using a precomputed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for constructing a PES on the fly during a dynamics simulation. This is achieved by acquisition of new single-point (SP) calculations and refitting of the PES, depending on the need of the dynamics. The TD-ADGA is a further development of the adaptive density-guided approach (ADGA) for PES construction where the placement of SPs is guided by the density of the nuclear wave function. In TD-ADGA, the ADGA framework has been integrated into the time propagation of the time-dependent nuclear wave function and we use the reduced one-mode density of this wave function to guide when and where new SPs are placed. The PES is thus extended or updated if the wave function moves into new areas or if a certain area becomes more important. Here, we derive equations for the reduced one-mode density for the time-dependent Hartree (TDH) method and for multiconfiguration time-dependent Hartree (MCTDH) methods, but the TD-ADGA can be used with any time-dependent wave function method as long as a density is available. The TD-ADGA method has been investigated on molecular systems containing single- and double-minimum potentials and on single-mode and multi-mode systems. We explore different approaches to handle the fact that the TD-ADGA involves a PES that changes during the computation and show how results can be obtained that are in very good agreement with results obtained by using an accurate reference PES. Dynamics with TD-ADGA is essentially a black box procedure, where only the initialization of the system and how to compute SPs must be provided. The TD-ADGA thus makes it easier to carry out quantum molecular dynamics and the quasi-direct framework opens up the possibility to compute quantum dynamics accurately for larger molecular systems.

Cluster perturbation theory. VIII. First order properties for a coupled cluster state.

We have extended cluster perturbation (CP) theory to comprehend the calculation of first order properties (FOPs). We have determined CP FOP series where FOPs are determined as a first energy derivative and also where the FOPs are determined as a generalized expectation value of the external perturbation operator over the coupled cluster state and its biorthonormal multiplier state. For S(D) orbital excitation spaces, we find that the CP series for FOPs that are determined as a first derivative, in general, in second order have errors of a few percent in the singles and doubles correlation contribution relative to the targeted coupled cluster (CC) results. For a SD(T) orbital excitation space, we find that the CP series for FOPs determined as a generalized expectation value in second order have errors of about ten percent in the triples correlation contribution relative to the targeted CC results. These second order models, therefore, constitute viable alternatives for determining high quality FOPs.

Cluster perturbation theory. VII. The convergence of cluster perturbation expansions.

The convergence of the recently developed cluster perturbation (CP) expansions [Pawlowski et al., J. Chem. Phys. 150, 134108 (2019)] is analyzed with the double purpose of developing the mathematical tools and concepts needed to describe these expansions at general order and to identify the factors that define the rate of convergence of CP series. To this end, the CP energy, amplitude, and Lagrangian multiplier equations as a function of the perturbation strength are developed. By determining the critical points, defined as the perturbation strengths for which the Jacobian becomes singular, the rate of convergence and the intruder and critical states are determined for five small molecules: BH, CO, H2O, NH3, and HF. To describe the patterns of convergence for these expansions at orders lower than the high-order asymptotic limit, a model is developed where the perturbation corrections arise from two critical points. It is shown that this model allows for rationalization of the behavior of the perturbation corrections at much lower order than required for the onset of the asymptotic convergence. For the H2O, CO, and HF molecules, the pattern and rate of convergence are defined by critical states where the Fock-operator underestimates the excitation energies, whereas the pattern and rate of convergence for BH are defined by critical states where the Fock-operator overestimates the excitation energy. For the NH3 molecule, both forms of critical points are required to describe the convergence behavior up to at least order 25.

Cluster perturbation theory. VI. Ground-state energy series using the Lagrangian.

We have extended cluster perturbation (CP) theory to comprehend the Lagrangian framework of coupled cluster (CC) theory and derived the CP Lagrangian energy series (LCP) where the 2n + 1/2n + 2 rules for the cluster amplitudes and multipliers are used to get the energy corrections. We have also developed the variational CP (LCP) series, where the total cluster amplitudes and multipliers are determined through the same orders as in the LCP series, but the energy is obtained by inserting the total cluster amplitudes and multipliers in the Lagrangian. The energies of the LCP series have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. With the exception of molecular systems that have a low lying doubly excited state compared to the electronic ground state configuration, we find that the fourth order models LCPS (D-4), LCPSD (T-4), and LCPSD(T-4) give energies of CC target state quality. For the LCPS (D-4) model, CC target state quality is obtained as the LCPS (D-4) calculation determines more than 99.7% of the coupled cluster singles and doubles (CCSD) correlation energy as the numerical deviations of the LCPS (D-4) energy from the CCSD energy were more than an order of magnitude smaller than the triples correlation contribution. For the LCPSD (T-4) and LCPSD(T-4) models, CC target state quality was obtained, given that the LCPSD (T-4) and LCPSD(T-4) calculations recover more than 99% of the coupled cluster singles doubles and triples (CCSDT) correlation contribution and as the numerical deviations of the LCPSD (T-4) and LCPSD(T-4) energies from the CCSDT energy were nearly and order of magnitude smaller than the quadruples correlation contribution. We, thus, suggest that the fourth order models may replace the full target CC models with no or very limited loss of accuracy.

Perturbation of the UV transitions of formaldehyde by TiO2 photocatalysts and Aun nanoclusters.

In the gas phase, formaldehyde has an electric-dipole forbidden transition that becomes allowed by vibronic coupling. In this paper we explore whether perturbation by surfaces could also enhance light absorption by CH2O. We investigate the electronic transitions of formaldehyde in the gas phase and interacting with rutile (110) TiO2, Aun nanoclusters, and Aun on (110)-TiO2. These surfaces are chosen as being representative of metals and metal-oxide minerals, and also because of specific interest in photocatalysts and noble metal nanocluster catalysts. The oscillator strength of the forbidden n → π* transition of formaldehyde in vacuum is investigated by modelling vibrational coupling to the electronic transition with equation-of-motion coupled cluster theory. The excitation energies and oscillator strengths of formaldehyde are calculated for different orientations and distances to the surfaces using the coupled cluster singles and doubles linear response method within the Quantum Mechanical and Molecular Mechanical (QM/MM) model using the aug-cc-pVTZ basis set and compared with the values calculated in vacuo. The electronic transitions of formaldehyde vary very little when placed near a pure TiO2-surface with only minor variations depending on the orientation of formaldehyde. Introducing a gold nanoparticle (by itself or supported by TiO2) induces dramatic changes in the absorption properties. This is due to vibronic interactions and the effect of the broken symmetry on the n → π* transition. We see a large redshift in the transition of 90 nm and oscillator strengths larger than 1.0 × 10-4 for CH2O interacting with Aun.

Optimization of the thermochemical properties of the norbornadiene/quadricyclane photochromic couple for solar energy storage using nanoparticles.

In this paper, we present an investigation concerning the prospects of using nanoparticles to improve solar energy storage properties of three different norbornadiene/quadricyclane derivatives. Computationally, we study how different nanoparticles influence the properties of the systems that relate to the storage of solar energy, namely, the storage energy and the back reaction barrier. Our approach employs hybrid quantum mechanical/molecular mechanical calculations in which the molecular systems are described using density functional theory while the nanoparticles are described using molecular mechanics. The interactions between the two subsystems are determined using polarization dynamics. The results show that the influence of the nanoparticles on the thermochemical properties largely depends on the type of nanoparticle used, the relative orientation with respect to the nanoparticle, and the distance between the the nanoparticle and the molecular system. Additionally, we find indications that copper and/or titanium dioxide nanoparticles can lower the energy barrier of the back reaction for all of the studied systems without significantly lowering the storage capability of the systems. Consequently, the study shows that nanoparticles can potentially be employed in the optimization of molecular photoswitches towards solar energy storage.