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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]

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]

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]

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]

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]

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]

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]