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Density-functional-theory-based chemical reactivity indicators are formulated for degenerate and near-degenerate ground states. For degenerate states, the functional derivatives of the energy with respect to the external potential do not exist, and must be replaced by the weaker concept of functional variation. The resultant reactivity indicators depend on the specific perturbation. Because it is sometimes impractical to compute reactivity indicators for a specific perturbation, we consider two special cases: point-charge perturbations and Dirac delta function perturbations. The Dirac delta function perturbations provide upper bounds on the chemical reactivity. Reactivity indicators using the common used 'average of degenerate states approximation' for degenerate states provide a lower bound on the chemical reactivity. Unfortunately, this lower bound is often extremely weak. Approximate formulas for the reactivity indicators within the frontier-molecular-orbital approximation and special cases (two or three degenerate spatial orbitals) are presented in the supplementary material. One remarkable feature that arises in the frontier molecular orbital approximation, and presumably also in the exact theory, is that removing electrons sometimes causes the electron density to increase at the location of a negative (attractive) Dirac delta function perturbation. That is, the energetic response to a reduction in the external potential can increase even when the number of electrons decreases. [ABSTRACT FROM AUTHOR]

This work follows a companion article, which will be referred to as Paper I [Campeggio et al., J. Chem. Phys. 158, 244104 (2023)] in which a quantum-stochastic Liouville equation for the description of the quantum–classical dynamics of a molecule in a dissipative bath has been formulated in curvilinear internal coordinates. In such an approach, the coordinates of the system are separated into three subsets: the quantum coordinates, the classical relevant nuclear degrees of freedom, and the classical irrelevant (bath) coordinates. The equation has been derived in natural internal coordinates, which are bond lengths, bond angles, and dihedral angles. The resulting equation needs to be parameterized. In particular, one needs to compute the potential energy surfaces, the friction tensor, and the rate constants for the nonradiative jumps among the quantum states. While standard methods exist for the calculation of energy and dissipative properties, an efficient evaluation of the transition rates needs to be developed. In this paper, an approximated treatment is introduced, which leads to a simple explicit formula with a single adjustable parameter. Such an approximated expression is compared with the exact calculation of transition rates obtained via molecular dynamics simulations. To make such a comparison possible, a simple sandbox system has been used, with two quantum states and a single internal coordinate (together with its conjugate momentum). Results show that the adjustable parameter, which is an effective decoherence time, can be parameterized from the effective relaxation times of the autocorrelation functions of the conjugated momenta of the relevant nuclear coordinates. [ABSTRACT FROM AUTHOR]

The rotationally resolved infrared (IR) spectrum of the He– H 3 + complex has been measured in a cryogenic ion trap experiment at a nominal temperature of 4 K. Predissociation of the stored complex has been invoked by excitation of the degenerate ν2 mode of the H 3 + sub-unit using a pulsed optical parametric oscillator system. An assignment of the experimental spectrum became possible through one-to-one correlations with bands of the spectrum theoretically predicted in Paper I [Harding et al., J. Chem. Phys. 156, 144307 (2022)]. 19 bands have been assigned and analyzed, and the energy term diagram of the lower states of this floppy molecular complex has been derived from combination differences (CDs) in the experimental spectrum. Ground state combination differences (GSCDs) reveal a large part of the energy term diagram for the He– H 3 + complex in its vibrational ground state, v = 0. Experimental and theoretical term energies agree within experimental accuracy for the rotational fine structure associated with the total angular momentum quantum number J and the parity e/f as well as for the coarse spacing of the lowest K states of the complex. This favorable comparison shows that the potential energy surface (PES) calculated in Paper I is accurate. The barriers between the three equivalent global minima in this PES are relatively low and the He– H 3 + complex is extremely floppy, with nearly unhindered internal rotation of the H 3 + sub-unit. The resulting Coriolis interactions couple the internal and end-over-end rotation of the complex and contribute significantly to the energy terms. They are observed both in experiment and theory and are, e.g., the origin of different rotational constants for states of e and f parity. Also in this respect, experiment and theory agree very well. Despite the assignment and analysis of many bands of the extremely rich IR spectrum of He– H 3 + , higher levels of excitation, including the complex stretching mode, need further attention. [ABSTRACT FROM AUTHOR]

This paper concerns the representation of angular momentum operators in the Born–Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born–Oppenheimer parameter κ = (m/M)1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born–Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born–Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space. [ABSTRACT FROM AUTHOR]

Efficient energy transport in photosynthetic antenna is a long-standing source of inspiration for artificial light harvesting materials. However, characterizing the excited states of the constituent chromophores poses a considerable challenge to mainstream quantum chemical and semiempirical excited state methods due to their size and complexity and the accuracy required to describe small but functionally important changes in their properties. In this paper, we explore an alternative approach to calculating the excited states of large biochromophores, exemplified by a specific method for calculating the Qy transition of bacteriochlorophyll a, which we name Chl-xTB. Using a diagonally dominant approximation to the Casida equation and a bespoke parameterization scheme, Chl-xTB can match time-dependent density functional theory's accuracy and semiempirical speed for calculating the potential energy surfaces and absorption spectra of chlorophylls. We demonstrate that Chl-xTB (and other prospective realizations of our protocol) can be integrated into multiscale models, including concurrent excitonic and point-charge embedding frameworks, enabling the analysis of biochromophore networks in a native environment. We exploit this capability to probe the low-frequency spectral densities of excitonic energies and interchromophore interactions in the light harvesting antenna protein LH2 (light harvesting complex 2). The impact of low-frequency protein motion on interchromophore coupling and exciton transport has routinely been ignored due to the prohibitive costs of including it in simulations. Our results provide a more rigorous basis for continued use of this approximation by demonstrating that exciton transition energies are unaffected by low-frequency vibrational coupling to exciton interaction energies. [ABSTRACT FROM AUTHOR]

Some diarylethene molecular switches have a low quantum yield for cycloreversion when excited by a single photon, but react more efficiently following sequential two-photon excitation. The increase in reaction efficiency depends on both the relative time delay and the wavelength of the second photon. This paper examines the wavelength-dependent mechanism for sequential excitation using excited-state resonance Raman spectroscopy to probe the ultrafast (sub-30 fs) dynamics on the upper electronic state following secondary excitation. The approach uses femtosecond stimulated Raman scattering (FSRS) to measure the time-gated, excited-state resonance Raman spectrum in resonance with two different excited-state absorption bands. The relative intensities of the Raman bands reveal the initial dynamics in the higher-lying states, Sn, by providing information on the relative gradients of the potential energy surfaces that are accessed via secondary excitation. The excited-state resonance Raman spectra reveal specific modes that become enhanced depending on the Raman excitation wavelength, 750 or 400 nm. Many of the modes that become enhanced in the 750 nm FSRS spectrum are assigned as vibrational motions localized on the central cyclohexadiene ring. Many of the modes that become enhanced in the 400 nm FSRS spectrum are assigned as motions along the conjugated backbone and peripheral phenyl rings. These observations are consistent with earlier measurements that showed higher efficiency following secondary excitation into the lower excited-state absorption band and illustrate a powerful new way to probe the ultrafast dynamics of higher-lying excited states immediately following sequential two-photon excitation. [ABSTRACT FROM AUTHOR]

In this paper, a global and full-dimensional potential energy surface at the 2A″ ground state for the Al + O2 → AlO + O reaction was constructed, for the first time, based on extensive electronic structure calculations using the doubly hybrid functional XYG3 and potential energy surface fittings by neural networks. Details of the reaction paths have been analyzed. It was found that both two intermediates, the cyclic-AlO2 and the linear-OAlO, were able to dissociate to the AlO + O products, and the isomerization process between these two intermediates was controlled by conical intersections between two 2A″ states. Ro-vibrational state resolved integral cross sections have also been calculated at collision energies from 1.0 to 10.0 kcal/mol. The results support the harpooning mechanism in this metal-oxidant-involved reaction. [ABSTRACT FROM AUTHOR]

Chemical and photochemical reactivity, as well as supramolecular organization and several other molecular properties, can be modified by strong interactions between light and matter. Theoretical studies of these phenomena require the separation of the Schrödinger equation into different degrees of freedom as in the Born–Oppenheimer approximation. In this paper, we analyze the electron–photon Hamiltonian within the cavity Born–Oppenheimer approximation (CBOA), where the electronic problem is solved for fixed nuclear positions and photonic parameters. In particular, we focus on intermolecular interactions in representative dimer complexes. The CBOA potential energy surfaces are compared with those obtained using a polaritonic approach, where the photonic and electronic degrees of freedom are treated at the same level. This allows us to assess the role of electron–photon correlation and the accuracy of CBOA. [ABSTRACT FROM AUTHOR]

This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I [A. K. Bacher et al., J. Chem. Phys. 149, 114501 (2018)] with a focus on isomorphs in the low- temperature gas and liquid phases. As expected from the EXP system's strong virial potential-energy correlations, the reduced-unit structure and dynamics are isomorph invariant to a good approximation. Three methods for generating isomorphs are compared: the small-step method that is exact in the limit of small density changes and two versions of the direct-isomorph-check method that allows for much larger density changes. Results from the latter two approximate methods are compared to those of the small-step method for each of the three isomorphs generated by 230 one percent density changes, covering one decade of density variation. Both approximate methods work well [ABSTRACT FROM AUTHOR]

It is uncontested that a machine learning scheme cannot correctly reproduce physical properties that vary on a manifold in configuration space if the fingerprint, used as an input for the machine learning scheme, is constant on this manifold. In our original paper, we found several manifolds whose fingerprint variation is sufficiently small to prevent machine learning based on a standard training scheme even if some 40 configurations on the manifold are included in the training set. Response to "Comment on 'Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions'" [J. Chem. Phys. [Extracted from the article]

In this paper, we have developed a unitary variant of a double exponential coupled cluster theory, which is capable of handling molecular strong correlation with arbitrary electronic complexity. With the Hartree–Fock determinant taken as the reference, we introduce a sequential product of parameterized unitary Ansätze. While the first unitary, containing the excitation operators, acts directly on the reference determinant, the second unitary, containing a set of rank-two, vacuum-annihilating scattering operators, has nontrivial action only on certain entangled states. We demonstrate the theoretical bottleneck of such an implementation in a classical computer, whereas the same is implemented in the hybrid quantum–classical variational quantum eigensolver framework with a reasonably shallow quantum circuit without any additional approximation. We have further introduced a number of variants of the proposed Ansatz with different degrees of sophistication by judiciously approximating the scattering operators. With a number of applications on strongly correlated molecules, we have shown that all our schemes can perform uniformly well throughout the molecular potential energy surface without significant additional implementation cost over the conventional unitary coupled cluster approach with single and double excitations. [ABSTRACT FROM AUTHOR]

This paper presents the experimental and theoretical analyses of ArICl(IP,vIP,nIP) states' population and decay at energies lower than the ArICl(E,vE = 0,nE) dissociation limit (IP = E0+, D′2, β1), vIP = 0, 1, and nIP are the quantum numbers of the van der Waals (vdW) modes. We have measured the excitation spectra of the ArICl(E,vE = 0,1,nE → X,vX,nX) and ArICl(β,0,nβ → A and/or D ′ , v D ′ , n D ′ → A ′ luminescence as well as luminescence spectra themselves. To construct potential energy surfaces (PESs) for valence (A1, A′2) and ion-pair (E, β, and D′) electronic states of the complex, we utilized the intermolecular diatomic-in-molecule perturbation theory first order method. The experimental and calculated spectroscopic characteristics of the T-shaped ArICl valence and E, β states agree well. The ArICl(D′) state PES has no vdW levels in the T-shaped configuration, and collinear ArICl(D′) binding energy is larger than that of the T-shaped ArICl(β) state. We calculated vibrational state energies and the ArICl(IP → valence states) luminescence excitation spectra, as well as luminescence spectra themselves, by using the Heidelberg MCTDH code. The comparison of the experimental and calculated excitation spectra shows that the latter describe their principal features. The bound–bound ArICl(E,0,nE → X and β,0,nβ → A) parts of experimental luminescence spectra are described adequately by the calculated spectra, whereas bound-free ArICl(E,0,nE → X, D′, 0, nD′ → A′) parts are not described since the bound-free transitions occur in repulsive parts of the ArICl(X, A ′ PESs, which we cannot describe accurately. [ABSTRACT FROM AUTHOR]

In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules. We show that HCISCF nuclear gradients are fairly insensitive to the size of the "selected" variational space, which allows us to reduce the computational cost without introducing significant errors. The ability of the HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems, which require a larger active space than possible with a complete active space self-consistent field. Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT). We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional. We also use the HCISCF gradients to optimize geometries for this species and study the adiabatic singlet–triplet gap. During geometry optimization, we find that multiple near-degenerate local minima exist on the triplet potential energy surface. [ABSTRACT FROM AUTHOR]

Nuclear dynamics in the coupled electronic states of mono-, di-(ortho and meta), and pentafluorobenzene molecules is investigated here. Attempts are specifically made to understand the complexity and broadening of the recorded gas phase electronic absorption spectra of these molecules. Justification is also provided for the low quantum yield of fluorescence emission with increasing number of fluorine substitutions. The nuclear dynamics is simulated from first principles both by time-independent and time-dependent quantum mechanical methods. Potential energy surfaces of the low-lying excited electronic states of these molecules constructed in Paper I [Mondal and Mahapatra, J. Chem. Phys. 133, 084304 (2010)] are employed for the purpose. Theoretical results presented in this paper are compared with the available experimental data and the agreement between the two is found to be excellent. While structured electronic absorption bands are observed for the S1 state of mono- and difluorobenzene molecules, the same for the pentafluorobenzene is broad and structureless. Occurrence of S1-S2 conical intersections in pentafluorobenzene leads to a nonradiative internal conversion of the S1 state in ∼165 fs and contributes to the broadening of the S1←S0 absorption band and a biexponential decay of its fluorescence emission. [ABSTRACT FROM AUTHOR]

The dissociating states of the triplet-excited CO-He complex are studied by means of scattering calculations on ab initio diabatic potential energy surfaces produced in the preceding paper (Paper I). With the aid of an effective transition dipole function and the bound states of the CO-He complex in the ground singlet state we obtain the photoabsorption cross section as a function of the excitation energy and generate the full UV spectrum of the singlet-triplet transition. It was found that the dominant contributions to the spectrum, in the energy range from -5 to +10 cm[SUP-1] relative to the band origin at 48 473.201 cm[SUP-1], originate from resonances that correspond to higher spin-orbit levels of the excited CO(a[SUP3]П) - He complex with approximate quantum number |Ω| = 1. Rapid predissociation, with the triplet CO fragment decaying into its lower spin-orbit levels with Ω = 0, limits the lifetime of these excited levels to, typically, 10-700 ps. We also predict the rotational and spin-orbit state distribution of the triplet CO fragment and the maximum deflection angle of the photodissociation products in a molecular beam experiment. [ABSTRACT FROM AUTHOR]

Computing the solubility of crystals in a solvent using atomistic simulations is notoriously challenging due to the complexities and convergence issues associated with free-energy methods, as well as the slow equilibration in direct-coexistence simulations. This paper introduces a molecular-dynamics workflow that simplifies and robustly computes the solubility of molecular or ionic crystals. This method is considerably more straightforward than the state-of-the-art, as we have streamlined and optimised each step of the process. Specifically, we calculate the chemical potential of the crystal using the gas-phase molecule as a reference state, and employ the S0 method to determine the concentration dependence of the chemical potential of the solute. We use this workflow to predict the solubilities of sodium chloride in water, urea polymorphs in water, and paracetamol polymorphs in both water and ethanol. Our findings indicate that the predicted solubility is sensitive to the chosen potential energy surface. Furthermore, we note that the harmonic approximation often fails for both molecular crystals and gas molecules at or above room temperature, and that the assumption of an ideal solution becomes less valid for highly soluble substances. [ABSTRACT FROM AUTHOR]

The analysis and modeling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian and group-theoretical formulation that differs significantly from that of more familiar rigid systems. Within the framework of Hougen–Bunker–Johns (HBJ) theory, this paper is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part. For the first time, a variational calculation from ab initio potential energy surfaces is performed using the HBJ kinetic energy operator built from vibrational, large-amplitude motion, and rotational tensor operators expressed in terms of curvilinear and normal coordinates. Group theory for nonrigid molecules plays a central role in the characterization of the overall tunneling splittings and is discussed in the present approach. The construction of the dipole moment operator is also examined. Validation tests consisting of a careful convergence study of the energy levels as well as a comparison of results obtained from independent computer codes are given for the nonrigid molecules CH2, CH3, NH3, and H2O2. This work paves the way for the modeling of high-resolution spectra of larger nonrigid systems. [ABSTRACT FROM AUTHOR]

Accurate modeling of anionic abundances in the interstellar and circumstellar media requires calculations of collisional data with the most abundant species that are usually He atoms and H2 molecules. In this paper, we focus on smaller cyclic molecular anion, c-C3H−, an astrophysical candidate, following the detection of larger CnH− carbon chains. From a new three-dimensional potential energy surface, the rotational (de-)excitation of the c-C3H−(X1A1) anion by collision with He is investigated. The surface is obtained in the supermolecular approach at the CCSD(T)-F12/aug-cc-pVTZ level of theory. Fully quantum close-coupling calculations of inelastic integral cross sections are performed on a grid of collisional energies large enough to ensure the convergence of the state-to-state rate coefficients for the 34 first rotational levels up to j K a , K c = 77,0 of c-C3H− and temperatures ranging from 5 to 100 K. For this collisional system, rate coefficients exhibit a strong dominance in favor of 21,2 → l1,1 downward transition. This transition was previously used for the detection of the cyclic parent c-C3H. The c-C3H−–He rate coefficients (∼10−11 cm3 s−1) are of the same order of magnitude as those of the detected anions CnH− (as C2H−, C4H−, and C6H−) in collision with He and one order of magnitude smaller than those with H2. The critical densities of H2 were also estimated, and a discussion on the validity of the local thermodynamic equilibrium conditions is carried out. This work represents the contribution to understanding and modeling abundances and chemistry of hydrocarbon radicals, CnH, in astrophysical media. [ABSTRACT FROM AUTHOR]

Recent work has demonstrated the promise of using machine-learned surrogates, in particular, Gaussian process (GP) surrogates, in reducing the number of electronic structure calculations (ESCs) needed to perform surrogate model based (SMB) geometry optimization. In this paper, we study geometry meta-optimization with GP surrogates where a SMB optimizer additionally learns from its past "experience" performing geometry optimization. To validate this idea, we start with the simplest setting where a geometry meta-optimizer learns from previous optimizations of the same molecule with different initial-guess geometries. We give empirical evidence that geometry meta-optimization with GP surrogates is effective and requires less tuning compared to SMB optimization with GP surrogates on the ANI-1 dataset of off-equilibrium initial structures of small organic molecules. Unlike SMB optimization where a surrogate should be immediately useful for optimizing a given geometry, a surrogate in geometry meta-optimization has more flexibility because it can distribute its ESC savings across a set of geometries. Indeed, we find that GP surrogates that preserve rotational invariance provide increased marginal ESC savings across geometries. As a more stringent test, we also apply geometry meta-optimization to conformational search on a hand-constructed dataset of hydrocarbons and alcohols. We observe that while SMB optimization and geometry meta-optimization do save on ESCs, they also tend to miss higher energy conformers compared to standard geometry optimization. We believe that further research into characterizing the divergence between GP surrogates and potential energy surfaces is critical not only for advancing geometry meta-optimization but also for exploring the potential of machine-learned surrogates in geometry optimization in general. [ABSTRACT FROM AUTHOR]

Hybrid methods that combine molecular dynamics methods capable of analyzing dynamics with Monte Carlo (MC) methods that can efficiently treat thermodynamically stable states are valuable for understanding complex chemical processes in which an equilibrium state is reached through many elementary processes. The hybrid MC (HMC) method is one such promising method; however, it often fails to sample configurations properly from the canonical multimodal distribution due to the rugged potential energy surfaces. In this paper, we extend the HMC method to overcome this difficulty. The new method, which is termed potential scaling HMC (PS-HMC), makes use of an artificially modulated trajectory to propose a new configuration. The trajectory is generated from Hamilton's equations, but the potential energy surface is scaled to be gradually flattened and then recovered to the original surface, which facilitates barrier-crossing processes. We apply the PS-HMC method to three kinds of molecular processes: the thermal motion of argon particles, butane isomerization, and an atom transfer chemical reaction. These applications demonstrate that the PS-HMC method is capable of correctly constructing the canonical ensemble with a multimodal distribution. The sampling efficiency and accepted trajectories are examined to clarify the features of the PS-HMC method. Despite the potential scaling, many reactive atom transfer trajectories (elementary processes) pass through the vicinity of the minimum energy path. Furthermore, we demonstrate that the method can properly imitate the relaxation process owing to the inherent configurational continuity. By comparing the PS-HMC method with other relevant methods, we can conclude that the new method is a unique approach for studying both the dynamic and thermodynamic aspects of chemical processes. [ABSTRACT FROM AUTHOR]

The mechanism of vibrational relaxation and dissociation in the O2–O system at elevated temperatures is investigated by means of molecular dynamics. The most recent O3 potential energy surfaces (PESs), obtained from the first principles quantum mechanical calculations [Varga et al., J. Chem. Phys. 147, 154312 (2017)], are used to derive a complete set of state-specific rate coefficients of vibrational energy transfer and dissociation. Unlike most of the previous efforts that utilize only the lowest and supposedly most reactive 11A′ O3 PES [A. Varandas and A. Pais, Mol. Phys. 65, 843 (1988)], this paper demonstrates the necessity to account for a complete ensemble of all excited O3 PESs that correlate with O2(X) and O(3P) when high-temperature kinetics is of interest. At the same time, it is found that the Varandas 11A′ O3 PES adequately describes vibrational energy transfer and dissociating dynamics when compared to the most recent 11A′ O3 PES by Varga et al. [J. Chem Phys. 147, 154312 (2017)]. The differences between this new dataset and previous rate coefficients are quantified by the master equation model. [ABSTRACT FROM AUTHOR]

The results of an extensive ab initio study of the cyanobutadiyne cation, initially motivated by threshold-photoelectron spectroscopy experiments [see the study by Gans et al., J. Chem. Phys. 150, 244304 (2019)], are reported in the present paper. Calculations at the internally contracted multireference configuration interaction level of theory have been performed to derive the rovibronic properties of the seven lowest electronic states of HC5N+. Equilibrium geometries, rotational constants, vibrational frequencies, electric dipole moments, and spin-orbit constants have been calculated and compared with experimental data when available. Adiabatic and vertical ionization energies from the neutral ground state as well as transition energies within the cation electronic manifold are predicted, using the convergence to the complete basis set limit. The accurate description of the complex energy landscape up to 32 000 cm−1 above the ionization potential allows us to perform Franck-Condon simulations of the photoionization spectrum to the X+2Π, A+2Π, B+2Σ+, and C+2Π states and allows us to simulate the A+2Π → X+2Π emission spectrum. The vibronic perturbations occurring on the excited potential energy surfaces are revealed and discussed, in particular, for the 3 2Π surface, which presents a double-well topography. [ABSTRACT FROM AUTHOR]

Crystal structure prediction has been a subject of topical interest but remains a substantial challenge especially for complex structures as it deals with the global minimization of the extremely rugged high-dimensional potential energy surface. In this paper, a symmetry-orientated divide-and-conquer scheme was proposed to construct a symmetry tree graph, where the entire search space is decomposed into a finite number of symmetry dependent subspaces. An artificial intelligence-based symmetry selection strategy was subsequently devised to select the low-lying subspaces with high symmetries for global exploration and in-depth exploitation. Our approach can significantly simplify the problem of crystal structure prediction by avoiding exploration of the most complex P1 subspace on the entire search space and has the advantage of preserving the crystal symmetry during structure evolution, making it well suitable for predicting the complex crystal structures. The effectiveness of the method has been validated by successful prediction of the candidate structures of binary Lennard-Jones mixtures and the high-pressure phase of ice, containing more than 100 atoms in the simulation cell. The work therefore opens up an opportunity toward achieving the long-sought goal of crystal structure prediction of complex systems. [ABSTRACT FROM AUTHOR]

We present the computational methodology, which for the first time allows rigorous twelve-dimensional (12D) quantum calculations of the coupled intramolecular and intermolecular vibrational states of hydrogen-bonded trimers of flexible diatomic molecules. Its starting point is the approach that we introduced recently for fully coupled 9D quantum calculations of the intermolecular vibrational states of noncovalently bound trimers comprised of diatomics treated as rigid. In this paper, it is extended to include the intramolecular stretching coordinates of the three diatomic monomers. The cornerstone of our 12D methodology is the partitioning of the full vibrational Hamiltonian of the trimer into two reduced-dimension Hamiltonians, one in 9D for the intermolecular degrees of freedom (DOFs) and another in 3D for the intramolecular vibrations of the trimer, and a remainder term. These two Hamiltonians are diagonalized separately, and a fraction of their respective 9D and 3D eigenstates is included in the 12D product contracted basis for both the intra- and intermolecular DOFs, in which the matrix of the full 12D vibrational Hamiltonian of the trimer is diagonalized. This methodology is implemented in the 12D quantum calculations of the coupled intra- and intermolecular vibrational states of the hydrogen-bonded HF trimer on an ab initio calculated potential energy surface (PES). The calculations encompass the one- and two-quanta intramolecular HF-stretch excited vibrational states of the trimer and low-energy intermolecular vibrational states in the intramolecular vibrational manifolds of interest. They reveal several interesting manifestations of significant coupling between the intra- and intermolecular vibrational modes of (HF)3. The 12D calculations also show that the frequencies of the v = 1, 2 HF stretching states of the HF trimer are strongly redshifted in comparison to those of the isolated HF monomer. Moreover, the magnitudes of these trimer redshifts are much larger than that of the redshift for the stretching fundamental of the donor-HF moiety in (HF)2, most likely due to the cooperative hydrogen bonding in (HF)3. The agreement between the 12D results and the limited spectroscopic data for the HF trimer, while satisfactory, leaves room for improvement and points to the need for a more accurate PES. [ABSTRACT FROM AUTHOR]

Some chemical reactions proceed on multiple potential energy surfaces and are often accompanied by a change in spin multiplicity, being called spin-forbidden reactions, where the spin–orbit coupling (SOC) effects play a crucial role. In order to efficiently investigate spin-forbidden reactions with two spin states, Yang et al. [Phys. Chem. Chem. Phys. 20, 4129–4136 (2018)] proposed a two-state spin-mixing (TSSM) model, where the SOC effects between the two spin states are simulated by a geometry-independent constant. Inspired by the TSSM model, we suggest a multiple-state spin-mixing (MSSM) model in this paper for the general case with any number of spin states, and its analytic first and second derivatives have been developed for locating stationary points on the mixed-spin potential energy surface and estimating thermochemical energies. To demonstrate the performance of the MSSM model, some spin-forbidden reactions involving 5d transition elements are calculated using the density functional theory (DFT), and the results are compared with the two-component relativistic ones. It is found that MSSM DFT and two-component DFT calculations may provide very similar stationary-point information on the lowest mixed-spin/spinor energy surface, including structures, vibrational frequencies, and zero-point energies. For the reactions containing saturated 5d elements, the reaction energies by MSSM DFT and two-component DFT agree very well within 3 kcal/mol. As for the two reactions OsO+ + CH4 → OOs(CH2)+ + H2 and W + CH4 → WCH2 + H2 involving unsaturated 5d elements, MSSM DFT may also yield good reaction energies of similar accuracy but with some counterexamples. Nevertheless, the energies may be remarkably improved by a posteriori single point energy calculations using two-component DFT at the MSSM DFT optimized geometries, and the maximum error of about 1 kcal/mol is almost independent of the SOC constant used. The MSSM method as well as the developed computer program provides an effective utility for studying spin-forbidden reactions. [ABSTRACT FROM AUTHOR]

In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schro\der, and J. C. Dyre, 'NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface,' J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nosé-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times. [ABSTRACT FROM AUTHOR]

In a previous paper [J. L. McAfee and B. Poirier, J. Chem. Phys. 130, 064701 (2009)], using spin-polarized density functional theory (DFT), the authors reported a binding energy of 0.755 eV, for a single hydrogen atom adsorbed on a pristine (unrelaxed) (5,5) single-walled carbon nanotube (SWNT) substrate. A full three-dimensional (3D) potential energy surface (PES) for the SWNT-H system was also developed, and used in a quantum dynamics calculation to compute all rovibrational bound states, and associated equatorial and longitudinal adsorbate migration rates. A highly pronounced preference for the latter migration pathway at ambient temperatures was observed. In this work, we extend the aforementioned study to include multiple H-atom adsorbates. Extensive DFT calculations are performed, in order to ascertain the most relevant dynamical pathways. For two adsorbates, the SWNT-H-H system is found to exhibit highly site-specific binding, as well as long-range correlation and pronounced binding energy enhancement. The latter effect is even more pronounced in the full-hydrogenation limit, increasing the per-adsorbate binding energy to 2.6 eV. To study migration dynamics, a single-hole model is developed, for which the binding energy drops to 2.11 eV. A global 3D PES is developed for the hole migration model, using 40 radial × 18 cylindrical ab initio geometries, fit to a Fourier basis with radially dependent expansion coefficients (rms error 4.9 meV). As compared with the single-adsorbate case, the hole migration PES does not exhibit separate chemisorption and physisorption wells. The barrier to longitudinal migration is also found to be much lower. Quantum dynamics calculations for all rovibrational states are then performed (using a mixed spectral basis/phase-space optimized discrete variable representation), and used to compute longitudinal migration rates. Ramifications for the use of SWNTs as potential hydrogen storage materials are discussed. [ABSTRACT FROM AUTHOR]

The variational approach detailed in the previous paper (Paper I) for the treatment of the Renner–Teller effect in linear tetra-atomic molecules including all degrees of freedom and couplings between angular momenta is applied for HCCH+. The accurate six-dimensional potential energy surfaces of the X 2Πu electronic state, presented in Paper I is incorporated in the variational treatment in order to obtain all rovibronic levels including the spin-orbit coupling for 1/2≤J≤7/2 and up to 2600 cm-1 above the global zero point energy. The “pure” stretching levels are calculated up to 11 000 cm-1 from the stretching zero point energy. The calculated rovibronic energies are compared with previous theoretical and experimental data. The mean agreement with the zero kinetic energy photoelectron measurements of Tang et al. [J. Chem. Phys. 125, 133201 (2006)] is of 16.7 cm-1. The Renner–Teller parameters have been determined at νtrans=690.0 cm-1, εtrans=0.30, νcis=715.0 cm-1, and εcis=-0.063. A detailed analysis of the rovibronic Hund’s cases is presented and the rotational structures of some vibronic bands recorded by Yang and Mo [J. Phys. Chem. A 110, 11001 (2006)] are given. [ABSTRACT FROM AUTHOR]

By extending an earlier study [Gianturco et al., J. Chem. Phys. 154, 054311 (2021)] on the purely rotational excitation of HeH+ by He atoms, we report in this paper integral cross sections and rate coefficients for rovibrational excitation and de-excitation processes in HeH+ due to collisions with He. The data were obtained using a new ab initio potential energy surface that includes the vibrational degree of freedom. The results are compared with those computed using the earlier potential energy surface by Panda and Sathyamurthy [J. Phys. Chem. A 107, 7125 (2003)] that additionally accounts for the proton-exchange reaction between HeH+ and He. It is shown that the exchange channel contributes nearly as much as the inelastic channel to the vibrational excitation and de-excitation processes and that the total rate constants pertaining to the purely inelastic processes are largely of the same magnitude as those obtained when both inelastic and reactive channels are included in the dynamics. The inelastic rovibrational rate coefficients involving this astrophysical cation are also found to be much larger than those obtained for anions present in similar interstellar environments. [ABSTRACT FROM AUTHOR]

For molecules with more than three atoms, it is difficult to fit or interpolate a potential energy surface (PES) from a small number of (usually ab initio) energies at points. Many methods have been proposed in recent decades, each claiming a set of advantages. Unfortunately, there are few comparative studies. In this paper, we compare neural networks (NNs) with Gaussian process (GP) regression. We re-fit an accurate PES of formaldehyde and compare PES errors on the entire point set used to solve the vibrational Schrödinger equation, i.e., the only error that matters in quantum dynamics calculations. We also compare the vibrational spectra computed on the underlying reference PES and the NN and GP potential surfaces. The NN and GP surfaces are constructed with exactly the same points, and the corresponding spectra are computed with the same points and the same basis. The GP fitting error is lower, and the GP spectrum is more accurate. The best NN fits to 625/1250/2500 symmetry unique potential energy points have global PES root mean square errors (RMSEs) of 6.53/2.54/0.86 cm−1, whereas the best GP surfaces have RMSE values of 3.87/1.13/0.62 cm−1, respectively. When fitting 625 symmetry unique points, the error in the first 100 vibrational levels is only 0.06 cm−1 with the best GP fit, whereas the spectrum on the best NN PES has an error of 0.22 cm−1, with respect to the spectrum computed on the reference PES. This error is reduced to about 0.01 cm−1 when fitting 2500 points with either the NN or GP. We also find that the GP surface produces a relatively accurate spectrum when obtained based on as few as 313 points. [ABSTRACT FROM AUTHOR]

Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree–Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree–Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single Ms (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree–Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis. [ABSTRACT FROM AUTHOR]

We present a new collocation method for computing the vibrational spectrum of a polyatomic molecule. Some form of quadrature or collocation is necessary when the potential energy surface does not have a simple form that simplifies the calculation of the potential matrix elements required to do a variational calculation. With quadrature, better accuracy is obtained by using more points than basis functions. To achieve the same advantage with collocation, we introduce a collocation method with more points than basis functions. Critically important, the method can be used with a large basis because it is incorporated into an iterative eigensolver. Previous collocation methods with more points than functions were incompatible with iterative eigensolvers. We test the new ideas by computing energy levels of molecules with as many as six atoms. We use pruned bases but expect the new method to be advantageous whenever one uses a basis for which it is not possible to find an accurate quadrature with about as many points as there are basis functions. For our test molecules, accurate energy levels are obtained even using non-optimal, simple, equally spaced points. [ABSTRACT FROM AUTHOR]

Photo-induced relaxation processes leading to excimer formations or other traps are in the focus of many investigations of optoelectronic materials because they severely affect the efficiencies of corresponding devices. Such relaxation effects comprise inter-monomer distortions in which the orientations of the monomer change with respect to each other, whereas intra-monomer distortions are variations in the geometry of single monomers. Such distortions are generally neglected in quantum chemical investigations of organic dye aggregates due to the accompanied high computational costs. In the present study, we investigate their relevance using perylene-bisimide dimers and diindenoperylene tetramers as model systems. Our calculations underline the importance of intra-monomer distortions on the shape of the potential energy surfaces as a function of the coupling between the monomers. The latter is shown to depend strongly on the electronic state under consideration. In particular, it differs between the first and second excited state of the aggregate. Additionally, the magnitude of the geometrical relaxation decreases if the exciton is delocalized over an increasing number of monomers. For the interpretation of the vibronic coupling model, pseudo-Jahn–Teller or Marcus theory can be employed. In the first part of this paper, we establish the accuracy of density functional theory-based approaches for the prediction of vibrationally resolved absorption spectra of organic semiconductors. These investigations underline the accuracy of those approaches although shortcomings become obvious as well. These calculations also indicate the strength of intra-monomer relaxation effects. [ABSTRACT FROM AUTHOR]

In an infrequent metadynamics (iMetaD) simulation, a well-tempered metadynamics bias accumulates in the reactant basin, accelerating escapes to the product state. Like the earlier hyperdynamics strategy, iMetaD enables estimates of the unbiased escape rates. However, iMetaD applies the bias to visited locations in a collective variable (CV) space, not to the more specific visited locations in a full configuration space as done in hyperdynamics. This difference makes rate estimates from iMetaD sensitive to the choice of CVs, to parameters that control the bias deposition rate, and to the preparation of the initial state within the reactant basin. This paper uses an extremely simple discrete state model to illustrate complications that can arise in systems that exhibit fluxional transitions between sub-basins of the reactant state. Specifically, we show how the reactant-to-product escape time and relaxation times within the reactant basin(s) impose bounds on the admissible parameter choices for an iMetaD calculation. Predictions from the discrete state model are validated by iMetaD simulations on a corresponding two-dimensional potential energy surface. [ABSTRACT FROM AUTHOR]

The parameterization of torsional/dihedral angle potential energy terms is a crucial part of developing molecular mechanics force fields. Quantum mechanical (QM) methods are often used to provide samples of the potential energy surface (PES) for fitting the empirical parameters in these force field terms. To ensure that the sampled molecular configurations are thermodynamically feasible, constrained QM geometry optimizations are typically carried out, which relax the orthogonal degrees of freedom while fixing the target torsion angle(s) on a grid of values. However, the quality of results and computational cost are affected by various factors on a non-trivial PES, such as dependence on the chosen scan direction and the lack of efficient approaches to integrate results started from multiple initial guesses. In this paper, we propose a systematic and versatile workflow called TorsionDrive to generate energy-minimized structures on a grid of torsion constraints by means of a recursive wavefront propagation algorithm, which resolves the deficiencies of conventional scanning approaches and generates higher quality QM data for force field development. The capabilities of our method are presented for multi-dimensional scans and multiple initial guess structures, and an integration with the MolSSI QCArchive distributed computing ecosystem is described. The method is implemented in an open-source software package that is compatible with many QM software packages and energy minimization codes. [ABSTRACT FROM AUTHOR]

In this article, we propose a generalized non-equilibrium chemical kinetics model from ab initio simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air chemistry. First, we present a simple cross section model for dissociation that captures recent ab initio data accurately. The cross section model is analytically integrated over Boltzmann distributions and general non-Boltzmann distributions to derive a general non-equilibrium dissociation model. The general non-Boltzmann model systematically incorporates key physics such as dependence on translational energy, rotational energy, vibrational energy, internal energy, centrifugal barrier, and non-Boltzmann effects such as overpopulation and depletion of high energy states. The model is shown to reproduce the rates from quasi-classical trajectory calculations for Boltzmann distributions of internal energy states. The reduced rates in a non-equilibrium steady state due to depletion of high internal energy states are also predicted well by the model. Furthermore, the model predicts the enhanced rates as observed due to significant overpopulation of high vibrational states relative to Boltzmann distributions while the gas is in non-equilibrium in the transient phase. The model provides a computationally inexpensive way of incorporating non-equilibrium chemistry without incurring additional cost in the existing computational tools. Further comparisons of the model are carried out in Paper II, where simplifications to the model are proposed based on the results. [ABSTRACT FROM AUTHOR]

We have developed an algorithm to detect holes in multi-dimensional real-valued surfaces—such as the potential energy surfaces (PESs) that describe the nuclear motion of molecules in the context of the Born–Oppenheimer approximation. For our purposes, a PES "hole" is defined as an unphysical saddle point, beyond which the potential energy drops (typically) without limit to negative infinity. PES holes are numerical artifacts that can arise when fitting PES functional forms to discrete ab initio data—even when the data is of high quality, and/or for comparatively few degrees of freedom (DOF). Often undetected, PES holes can have devastating effects on subsequent dynamical calculations, especially if they occur at low energies. In this paper, we present a highly efficient algorithm designed to systematically identify hole configurations and energies. The method is applied to a variety of molecular PESs ranging up to 30 DOF. A number of evidently previously undetected PES holes are reported here—surprisingly, even for PESs that have been available for decades. The code itself (Crystal) is presented together with a user manual. These tools may be of great benefit for PES developers, who can use the information they provide to fix holes, once identified. More generally, the methodology can be applied in any context involving multi-dimensional surfaces. [ABSTRACT FROM AUTHOR]

In this third paper of the series, which started with Bailey et al. [J. Chem. Phys. 129, 184507 (2008); ibid. 129, 184508 (2008)], we continue the development of the theoretical understanding of strongly correlating liquids—those whose instantaneous potential energy and virial are more than 90% correlated in their thermal equilibrium fluctuations at constant volume. The existence of such liquids was detailed in previous work, which identified them, based on computer simulations, as a large class of liquids, including van der Waals liquids but not, e.g., hydrogen-bonded liquids. We here discuss the following: (1) the scaling properties of inverse power-law and extended inverse power-law potentials (the latter includes a linear term that “hides” the approximate scale invariance); (2) results from computer simulations of molecular models concerning out-of-equilibrium conditions; (3) ensemble dependence of the virial/potential-energy correlation coefficient; (4) connection to the Grüneisen parameter; and (5) interpretation of strong correlations in terms of the energy-bond formalism. [ABSTRACT FROM AUTHOR]

The multimode multistate vibronic interactions between the five lowest electronic states of all three isomers of the difluorobenzene radical cation are investigated theoretically, based on ab initio electronic structure data, and employing a well-established vibronic coupling model. The approach rests on the linear vibronic coupling scheme, augmented by quadratic coupling terms for the totally symmetric modes. The underlying ionization potentials and coupling constants are obtained from ab initio coupled-cluster calculations. Low-energy conical intersections and strong vibronic couplings are found to prevail within the sets of X-Ã and B-C-D cationic states, while the interactions between these two sets of states are found to be weaker and depend on the isomer. The inclusion of the aforementioned quadratic couplings is found to be essential to correctly reproduce the lowest-energy conical intersections between the two different sets of electronic states. Differences between the three isomers regarding these quantities are pointed out. The results will be used as basis for multidimensional wave-packet dynamical simulations for these coupled potential energy surfaces to be presented in the following paper (Paper II). [ABSTRACT FROM AUTHOR]

The multistate vibronic dynamics in the X-D electronic states of all three difluorobenzene radical cations are investigated theoretically by an ab initio quantum dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from Paper I [S. Faraji and H. Köppel, J. Chem. Phys. 129, 074310 (2008)]. Extensive calculations by wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Five coupled electronic potential energy surfaces and 10 (11 in the case of the orthoisomer) vibrational degrees of freedom have been included in these calculations. The nonadiabatic interactions lead to the restructuring of the photoelectron spectral envelopes. Ultrafast internal conversion processes within the electronic manifolds in question demonstrate the strength of the nonadiabatic coupling effects and complement the analogous findings for the electronic spectra. The internal conversion dynamics is characterized by a stepwise transfer of the electronic population to the lowest electronic state on a time scale of femtoseconds to picoseconds. A difference between the three isomers is found to be related to the weaker interaction between the sets of X-Ã and B-C-D states (with high-energy conical intersections) in the meta isomer, as compared to the other isomers. The implications of these findings for the qualitative understanding of the fluorescence dynamics of fluorinated benzene radical cations are discussed. [ABSTRACT FROM AUTHOR]

We report the vibrational energy levels of vinyl radical (VR) that are computed with a Lanczos eigensolver and a contracted basis. Many of the levels of the two previous VR variational calculations differ significantly and differ also from those reported in this paper. We identify the source of and correct symmetry errors on the potential energy surfaces used in the previous calculations. VR has two equivalent equilibrium structures. By plotting wavefunction cuts, we show that two tunneling paths play an important role. Using the computed wavefunctions, it is possible to assign many states and thereby to determine tunneling splittings that are compared with their experimental counterparts. Our computed red shift of the hot band at 2897.23 cm−1, observed by Dong et al. [J Chem. Phys. 128, 044305 (2008)], is 4.47 cm−1, which is close to the experimental value of 4.63 cm−1. [ABSTRACT FROM AUTHOR]

A generalized Frenkel–Holstein Hamiltonian is constructed to describe exciton migration in oligo(para-phenylene vinylene) chains, based on excited state electronic structure data for an oligomer comprising 20 monomer units (OPV-20). Time-dependent density functional theory calculations using the ωB97XD hybrid functional are employed in conjunction with a transition density analysis to study the low-lying singlet excitations and demonstrate that these can be characterized to a good approximation as a Frenkel exciton manifold. Based on these findings, we employ the analytic mapping procedure of Binder et al. [J. Chem. Phys. 141, 014101 (2014)] to translate one-dimensional (1D) and two-dimensional (2D) potential energy surface (PES) scans to a fully anharmonic, generalized Frenkel–Holstein (FH) Hamiltonian. A 1D PES scan is carried out for intra-ring quinoid distortion modes, while 2D PES scans are performed for the anharmonically coupled inter-monomer torsional and vinylene bridge bond length alternation modes. The kinetic energy is constructed in curvilinear coordinates by an exact numerical procedure, using the TNUM Fortran code. As a result, a fully molecular-based, generalized FH Hamiltonian is obtained, which is subsequently employed for quantum exciton dynamics simulations, as shown in Paper II [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)]. [ABSTRACT FROM AUTHOR]

Although very useful, the original multi-configuration time-dependent Hartree (MCTDH) method has two weaknesses: (1) its cost scales exponentially with the number of atoms in the system; (2) the standard MCTDH implementation requires that the potential energy surface (PES) be in the sum-of-product (SOP) form in order to reduce the cost of computing integrals in the MCTDH basis. One way to deal with (1) is to lump coordinates into groups. This is mode combination (MC). One way to deal with (2) is to reformulate MCTDH using collocation so that there are no integrals. In this paper, we combine MC and collocation to formulate a MC collocation multi-configuration time-dependent Hartree (MC-C-MCTDH) method. In practice, its cost does not scale exponentially with the number of atoms, and it can be used with any general PES; the PES need not be an SOP and need not have a special form. No integrals and, hence, no quadratures are necessary. We demonstrate the accuracy and efficiency of the new method by computing vibrational energy eigenstates of methyl radical, methane, and acetonitrile. To do this, we use MC-C-MCTDH with a variant of improved relaxation, derived by evaluating a residual at points. Because the MC basis functions are multivariate, collocation points in multi-dimensional spaces are required. We use two types of collocation points: (1) discrete variable representation-like points obtained from (approximate) simultaneous diagonalization of matrices and (2) Leja points, which are known to be good interpolation points, determined from a generalized recipe suitable for any basis. [ABSTRACT FROM AUTHOR]

Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore the potential energy surface of the system of interest. These simulations can be very demanding due to the high-dimensional configurational search space. The effective search space can be reduced by utilizing grids for the atomic positions, but at the cost of possibly biasing the results if fixed grids are employed. In this paper, we present a flexible grid algorithm for global optimization that allows us to exploit the efficiency of grids without biasing the simulation outcome. The method is general and applicable to very heterogeneous systems, such as interfaces between two materials of different crystal structures or large clusters supported at surfaces. As a benchmark case, we demonstrate its performance for the well-known global optimization problem of Lennard-Jones clusters containing up to 100 particles. Despite the simplicity of this model potential, Lennard-Jones clusters represent a challenging test case since the global minima for some "magic" numbers of particles exhibit geometries that are very different from those of clusters with only a slightly different size. [ABSTRACT FROM AUTHOR]

The nuclear-electronic orbital (NEO) framework enables the incorporation of nuclear quantum effects by treating both electrons and specific key nuclei quantum-mechanically. The conventional NEO method predicates on the controversial Born–Oppenheimer separation between classical and quantum nuclei, and its potential energy surface only depends on the coordinates of classical nuclei. In this paper, based on the fact that quantum nuclei are relatively localized, we develop the constrained nuclear-electronic orbital density functional theory (cNEO-DFT) by imposing a constraint on the expectation value of the quantum nuclear position. In this way, an extended NEO energy surface is obtained, which also depends on the quantum nuclear position. Compared to the potential energy surface obtained from conventional DFT, the extended NEO energy surface incorporates the nuclear quantum effects, which have notable impacts on the energy profile. Furthermore, cNEO-DFT can facilitate the location of NEO stationary states. It potentially can be used in geometry optimization, transition states search, and the calculation of reaction dynamics. [ABSTRACT FROM AUTHOR]

A full-dimensional ab initio intermolecular potential energy surface (IPES) is reported in this paper for van der Waals complex N2–HF. The calculations were performed by employing the explicitly correlated coupled cluster [CCSD (T)-F12a] method with the augmented correlation-consistent aug-cc-pVTZ basis set plus bond functions. The basis set superposition error was corrected by the full counterpoise procedure. About 55 000 ab initio points were calculated and then fitted by the permutation invariant polynomial neural network approach with a root-mean-square error of 0.433 cm−1. The potential energy surface features two equivalent linear minima with a well depth of 811.012 cm−1 separated by a barrier of 635.836 cm−1. The ro-vibrational energy levels for N2–HF and N2–DF were calculated based on the vibrationally averaged 4D IPESs with the radial discrete variable representation/angular finite basis representation method and Lanczos propagation algorithm. The calculated frequencies and the relative line intensities in the HF (DF) stretching band agree well with the available observed spectra. The theoretical band origins are all red shifted relative to the isolated HF (DF) molecule and reproduce the experimental values well. The results of ro-vibrational state calculations demonstrate the high accuracy of our new PES. [ABSTRACT FROM AUTHOR]

In this paper, we examine decay and fragmentation of core-excited and core-ionized water molecules combining quantum chemical calculations and electron-energy-resolved electron–ion coincidence spectroscopy. The experimental technique allows us to connect electronic decay from core-excited states, electronic transitions between ionic states, and dissociation of the molecular ion. To this end, we calculate the minimum energy dissociation path of the core-excited molecule and the potential energy surfaces of the molecular ion. Our measurements highlight the role of ultra-fast nuclear motion in the 1 a 1 − 1 4 a 1 core-excited molecule in the production of fragment ions. OH+ fragments dominate for spectator Auger decay. Complete atomization after sequential fragmentation is also evident through detection of slow H+ fragments. Additional measurements of the non-resonant Auger decay of the core-ionized molecule (1 a 1 − 1 ) to the lower-energy dication states show that the formation of the OH+ + H+ ion pair dominates, whereas sequential fragmentation OH+ + H+ → O + H+ + H+ is observed for transitions to higher dication states, supporting previous theoretical investigations. [ABSTRACT FROM AUTHOR]

Sulfurous acid (H2SO3) is an infamously elusive molecule. Although some theoretical papers have supposed possible roles for it in more complicated systems, it has yet to be experimentally observed. To aid experiment in detecting this molecule, we have examined the H2O + SO2 potential energy surface at the CCSDT(Q)/CBS//CCSD(T)-F12b/cc-pVTZ-F12b level of theory to resolve standing discrepancies in previous reports and predict the gas-phase vibrational spectrum for H2SO3. We find that sulfurous acid has two potentially detectable rotamers, separated by 1.1 kcal mol−1 ΔH0K with a torsional barrier of 1.6 kcal mol−1. The sulfonic acid isomer is only 6.9 kcal mol−1 above the lowest enthalpy sulfurous acid rotamer, but the barrier to form it is 57.2 kcal mol−1. Error in previous reports can be attributed to misidentified stationary points, the use of density functionals that perform poorly for this system, and, most importantly, the basis set sensitivity of sulfur. Using VPT2+K, we determine that the intense S=O stretch fundamental of each species is separated from other intense peaks by at least 25 cm−1, providing a target for identification by infrared spectroscopy. [ABSTRACT FROM AUTHOR]

This paper presents two new adiabatic, global potential energy surfaces (PESs) for the two lowest 3A′ and 3A″ electronic states of the O(3P) + H2 system. For each of these states, ab initio electronic energies were calculated for more than 5000 geometries using internally contracted multireference configuration interaction methods. The calculated points were then fitted using the ansatz by Aguado et al. [Comput. Phys. Commun. 108, 259 (1998)] leading to very accurate analytical potentials well adapted to perform reaction dynamics studies. Overall, the topographies of both PESs are in good agreement with the benchmark potentials of Rogers et al. [J. Phys. Chem. A 104, 2308 (2000)], but those presented in this work reproduce better the height and degeneracy of the two states at the saddle point. Moreover, the long range potential in the entrance channel does not require any cutoff. These features make the new PESs particularly suitable for a comparison of the dynamics on each of them. The new set of PESs was then used to perform quantum mechanics and quasiclassical trajectory calculations to determine differential and integral cross sections, which are compared to the experimental measurements by Garton et al. [J. Chem. Phys. 118, 1585 (2003)]. [ABSTRACT FROM AUTHOR]

This paper is the first application of the tensor-train (TT) cross approximation procedure for potential energy surface fitting. In order to reduce the complexity, we combine the TT-approach with another technique recently introduced in the field of numerical analysis: an affine transformation of Cartesian coordinates into the active subspaces where the PES function has the most variability. The numerical experiments for the water molecule and for the nitrous acid molecule confirm the efficiency of this approach. [ABSTRACT FROM AUTHOR]