Full-dimensional MCTDH/MGPF study of the ground and lowest lying vibrational states of the bihydroxide H3O2(-) complex

Using a pruned basis and a sparse collocation grid with more points than basis functions to do efficient and accurate MCTDH calculations with general potential energy surfaces

We propose a new collocation multi-configuration time-dependent Hartree (MCTDH) method. It reduces point-set error by using more points than basis functions. Collocation makes it possible to use MCTDH with a general potential energy surface without computing any integrals. The collocation points are associated with a basis larger than the basis used to represent wavefunctions. Both bases are obtained from a direct product basis built from single-particle functions by imposing a pruning condition. The collocation points are those on a sparse grid. Heretofore, collocation MCTDH calculations with more points than basis functions have only been possible if both the collocation grid and the basis set are direct products. In this paper, we exploit a new pseudo-inverse to use both more points than basis functions and a pruned basis and grid. We demonstrate that, for a calculation of the lowest 50 vibrational states (energy levels and wavefunctions) of CH2NH, errors can be reduced by two orders of magnitude by increasing the number of points, without increasing the basis size. This is true also when unrefined time-independent points are used.

Automatic Determination of the Non-Covalent Stable Conformations of the NO2-Pyrene Cluster in Full Dimensionality (81D) Using the vdW-TSSCDS Approach

We present the detailed topographical characterisation (stationary points and minimum energy paths connecting them) of the full dimensional (81D) intermolecular potential energy surface associated with the non-covalent interactions between the NO2 radical and the pyrene (C16H10) molecule. The whole procedure is (quasi) fully automated. We have used our recent algorithm vdW-TSSCDS as implemented on the freely-available AutoMekin software package. To this end, a series of inexpensive classical trajectories using forces from a low-level (semi-empirical) theory are used to sample the configuration space of the system in the search for candidates to first order saddle points. These guess structures are determined by means of a graph-theory based algorithm using the concept of adjacency matrix. Low-level optimizations are followed by re-optimizations at a final high-level of theory (DFT and CCSD(T)-F12 in our case.). The resulting set of stationary points and paths connecting them constitutes the so-called reaction network. In the case of NO2-pyrene, this network exhibits four major basins which can be characterized by their point-group symmetry. A central one, of global C2 symmetry, comprises the global minimum (as well as all other permutationally related conformers) together with the corresponding C2v saddle points connecting them. This central basin is connected to three others of lower C1 symmetry. The latter can be distinguished by the projection of the position of the NO2 nitrogen atom on the pyrene plane in combination with the relative orientation of the oxygen pair pointing either inwards, outwards, upwards or downwards.

Nuclear Quantum Effects in Hydroxide Hydrate Along the H-Bond Bifurcation Pathway

Path integral (PI) simulations are used to explore nuclear quantum effects (NQEs) in hydroxide hydrate and its perdeuterated isotopomer along the H-bond bifurcation pathway. Toward this, a new potential energy surface using the symmetric gradient domain machine learning method with ab initio data at the CCSD(T)/aug-cc-pVTZ level is built. From PI umbrella sampling (US) simulations, free energy profiles along the bifurcation coordinate are explored as a function of temperature. At ambient temperature, the bifurcation barrier is increased upon inclusion of NQEs. At low temperatures in the deep tunneling regime, the barrier is strongly decreased and flattened. These trends are examined, and the role of the O-O distance is also investigated through two-dimensional US simulations.

Analytical high-dimensional operators in canonical polyadic finite basis representation (CP-FBR)

In the present work, we introduce a simple means of obtaining an analytical (i.e., grid-free) canonical polyadic (CP) representation of a multidimensional function that is expressed in terms of a set of discrete data. For this, we make use of an initial CP guess, even not fully converged, and a set of auxiliary basis functions [finite basis representation (FBR)]. The resulting CP-FBR expression constitutes the CP counterpart of our previous Tucker sum-of-products-FBR approach. However, as is well-known, CP expressions are much more compact. This has obvious advantages in high-dimensional quantum dynamics. The power of CP-FBR lies in the fact that it requires a grid much coarser than the one needed for the dynamics. In a subsequent step, the basis functions can be interpolated to any desired density of grid points. This is useful, for instance, when different initial conditions (e.g., energy content) of a system are to be considered. We show the application of the method to bound systems of increased dimensionality: H₂ (3D), HONO (6D), and CH₄ (9D).

Direct Canonical-Polyadic-Decomposition of the Potential Energy Surface from Discrete Data by Decoupled Gaussian Process Regression

A Gaussian process regression (GPR) approach for directly constructing the canonical polyadic decomposition (CPD) of a multidimensional potential energy surface (PES) by discrete training energies is proposed and denoted by CPD-GPR. The present CPD-GPR method requires the kernel function in a product of a series of one-dimensional functions. To test CPD-GPR, the reactive probabilities of H + H₂ as a function of kinetics energy are performed. Comparing the dynamics results computed by the CPD-GPR PES with those by the original PES, a good agreement between these results can be clearly found. Discussions on the previous algorithms for building the decomposed form are also given. We further show that the CPD-GPR method might be the general algorithm for building the decomposed form. However, further development is needed to reduce the CPD rank. Therefore, the present CPD-GPR method might be helpful to inspire ideas for developing new tools in building decomposed potential functions.

Adaptive Fitting of Potential Energy Surfaces of Small to Medium-Sized Molecules in Sum-of-Product Form: Application to Vibrational Spectroscopy

A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting relies on energies only and can be used for re-fitting existing analytic potential energy surfaces in sum-of-product form or for direct fits from ab initio computa- tions. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based upon ab initio computations at the CCSD(T)-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg MCTDH package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules, in terms of accuracy, including of resulting vibrational states, required numbers of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.

Helium Nanodroplet Infrared Action Spectroscopy of the Proton-Bound Dimer of Hydrogen Sulfate and Formate: Examining Nuclear Quantum Effects

The proton-bound dimer of hydrogen sulfate and formate is an archetypal structure for ionic hydrogen-bonding complexes that contribute to biogenic aerosol nucleation. Of central importance for the structure and properties of this complex is the location of the bridging proton connecting the two conjugate base moieties. The potential energy surface for bridging proton translocation features two local minima, with the proton localized at either the formate or hydrogen sulfate moiety. However, electronic structure methods reveal a shallow potential energy surface governing proton translocation, with a barrier on the order of the zero-point energy. This shallow potential complicates structural assignment and necessitates a consideration of nuclear quantum effects. In this work, we probe the structure of this complex and its isotopologues, utilizing infrared (IR) action spectroscopy of ions captured in helium nanodroplets. The IR spectra indicate a structure in which a proton is shared between the hydrogen sulfate and formate moieties, HSO₄^-···H⁺···^-OOCH. However, because of the nuclear quantum effects and vibrational anharmonicities associated with the shallow potential for proton translocation, the extent of proton displacement from the formate moiety remains unclear, requiring further experiments or more advanced theoretical treatments for additional insight.

Non long-range corrected density functionals incorrectly describe the intensity of the CH stretching band in polycyclic aromatic hydrocarbons

We present a comprehensive study of the most relevant numerical aspects influencing frequencies and intensities in the infrared spectrum of isolated polycyclic aromatic hydrocarbons (PAHs) regarding the overestimate of the IR CH-stretching bands. We use naphthalene as benchmark and show the validity of our results to different members of the PAH family. Our analysis relies on widely employed density functional theory methods and second-order vibrational perturbational theory for the computation of vibrational eigenstates. We have focused on the elucidation of the origin of the systematic overestimate of the intensities in the CH-stretching region. To rule out nonfundamental numerical errors, we have initially considered the influence of the electronic basis set and various other parameters on the different stages of the vibrational analysis. In a second stage, we have benchmarked the results of different density functional theory functionals with respect to the aforementioned overestimate taken as the ratio between the most prominent features of the spectrum, the CH-bending and the CH-stretching bands. Our results unambiguously indicate that the long-range correction plays a major role in this spurious numerical issue. More specifically, this phenomenon is due to an incorrect description of the charge distribution (and hence dipole) within the symmetrically relevant CH bonds. Long-range correction specifically remedies this issue. It improves the description of the intensities in the stretching region while at the same time it does not perturb significantly the rest of the spectrum. With respect to the frequencies, we have observed an overall improvement when compared to noncorrected functionals.

A rectangular collocation multi-configuration time-dependent Hartree (MCTDH) approach with time-independent points for calculations on general potential energy surfaces

We introduce a collocation-based multi-configuration time-dependent Hartree (MCTDH) method that uses more collocation points than basis functions. We call it the rectangular collocation MCTDH (RC-MCTDH) method. It does not require that the potential be a sum of products. RC-MCTDH has the important advantage that it makes it simple to use time-independent collocation points. When using time-independent points, it is necessary to evaluate the potential energy function only once and not repeatedly during an MCTDH calculation. It is inexpensive and straightforward to use RC-MCTDH with combined modes. Using more collocation points than basis functions enables one to reduce errors in energy levels without increasing the size of the single-particle function basis. On the contrary, whenever a discrete variable representation is used, the only way to reduce the quadrature error is to increase the basis size, which then also reduces the basis-set error. We demonstrate that with RC-MCTDH and time-independent points, it is possible to calculate accurate eigenenergies of CH₃ and CH₄.

Low-rank sum-of-products finite-basis-representation (SOP-FBR) of potential energy surfaces

The sum-of-products finite-basis-representation (SOP-FBR) approach for the automated multidimensional fit of potential energy surfaces (PESs) is presented. In its current implementation, the method yields a PES in the so-called Tucker sum-of-products form, but it is not restricted to this specific ansatz. The novelty of our algorithm lies in the fact that the fit is performed in terms of a direct product of a Schmidt basis, also known as natural potentials. These encode in a non-trivial way all the physics of the problem and, hence, circumvent the usual extra ad hoc and a posteriori adjustments (e.g., damping functions) of the fitted PES. Moreover, we avoid the intermediate refitting stage common to other tensor-decomposition methods, typically used in the context of nuclear quantum dynamics. The resulting SOP-FBR PES is analytical and differentiable ad infinitum. Our ansatz is fully general and can be used in combination with most (molecular) dynamics codes. In particular, it has been interfaced and extensively tested with the Heidelberg implementation of the multiconfiguration time-dependent Hartree quantum dynamical software package.

Franck–Condon simulations of transition-state spectra for the OH + H2O and OD + D2O reactions

Quantum wave packet calculations in reduced dimensions were performed to analyze the experimentally measured transition-state spectra of the OH + H₂O and OD + D₂O hydrogen exchange reactions.

Reactivity of Hydrated Hydroxide Anion Clusters with H and Rb: An ab Initio Study

We present a theoretical investigation of the hydrated hydroxide anion clusters, OH(H₂O)_n^-, and of the collisional complexes, H-OH(H₂O)_n^- and Rb-OH(H₂O)_n^- (with n = 1-4). The MP2 and CCSD(T) methods are used to calculate interaction energies, optimized geometries, and vertical detachment energies. Parts of the potential energy surfaces are explored with a focus on the autodetachment region. We point out the importance of diffuse functions to correctly describe the latter. We use our results to discuss the different water loss and electronic detachment channels, which are the main reaction routes at room temperature and below. In particular, we have considered a direct and an indirect process for the electronic detachment, depending on whether water loss follows or precedes the detachment of the excess electron. We use our results to discuss the implications for astrochemistry and hybrid trap experiments in the context of cold chemistry.

Specific Reaction Parameter Multigrid POTFIT (SRP-MGPF): Automatic Generation of Sum-of-Products Form Potential Energy Surfaces for Quantum Dynamical Calculations

We present Specific Reaction Parameter Multigrid POTFIT (SRP-MGPF), an automated methodology for the generation of global potential energy surfaces (PES), molecular properties surfaces, e.g., dipole, polarizabilities, etc. using a single random geometry as input. The SRP-MGPF workflow integrates: (i) a fully automated procedure for the global topographical characterization of a (intermolecular) PES based on the Transition State Search Using Chemical Dynamical Simulations (TSSCDS) family of methods;i (ii) the global optimization of the parameters of a semiempirical Hamiltonian in order to reproduce a given level of electronic structure theory; and (iii) a tensor decomposition algorithm which turns the resulting SRP-PES into sum of products (Tucker) form with the Multigrid POTFIT algorithm. The latter is necessary for quantum dynamical studies within the Multiconfiguration Time-Dependent Hartree (MCTDH) quantum dynamics method. To demonstrate our approach, we have applied our methodology to the cis-trans isomerization reaction in HONO in full dimensionality (6D). The resulting SRP-PES has been validated through the computation of classical on-the-fly dynamical calculations as well as calculations of the lowest vibrational eigenstates of HONO as well as high-energy wavepacket propagations.