Molecular Potential Energy Surfaces Research Articles

Theory and Examples of Catch Bonds.

We discuss slip bonds, catch bonds, and the tug-of-war mechanism using mathematical arguments. The aim is to explain the theoretical tool of molecular potential energy surfaces (PESs). For this, we propose simple 2-dimensional surface models to demonstrate how a molecule under an external force behaves. Examples are selectins. Catch bonds, in particular, are explained in more detail, and they are contrasted to slip bonds. We can support special two-dimensional molecular PESs for E- and L-selectin which allow the catch bond property. We demonstrate that Newton trajectories (NT) are powerful tools to describe these phenomena. NTs form the theoretical background of mechanochemistry.

Potential energy surfaces and dynamic properties via ab initio composite and density functional approaches.

Vibrational spectroscopy enables critical insight into the structural and dynamic properties of molecules. Presently, the majority of theoretical approaches to spectroscopy employ wavefunction-based ab initio or density functional methods that rely on the harmonic approximation. This approximation breaks down for large molecules with strongly anharmonic bonds or for molecules with large internuclear separations. An alternative to these methods involves generating molecular anharmonic potential energy surfaces (potentials) and using them to extrapolate the vibrational frequencies. This study examines the efficacy of density functional theory (DFT) and the correlation consistent Composite Approach (ccCA) in generating anharmonic frequencies from potentials of small main group molecules. Vibrational self-consistent field Theory (VSCF) and post-VSCF methods were used to calculate the fundamental frequencies of these molecules from their potentials. Functional choice, basis set selection, and mode-coupling are also examined as factors in influencing accuracy. The absolute deviations for the calculated frequencies using potentials at the ccCA level of theory were lower than the potentials at the DFT level. With DFT resulting in bending modes that are better described than those of ccCA, a multilevel DFT:ccCA approach where DFT potentials are used for single vibrational mode potentials and ccCA is used for vibrational mode-mode couplings can be utilized for larger polyatomic systems. The frequencies obtained with this multilevel approach using VCIPSI-PT2 were closer to experimental frequencies than the scaled harmonic frequencies, indicating the success of utilizing post-VSCF methods to generate more accurate representations of computed infrared spectra.

Efficient vibrationally correlated calculations using n-mode expansion-based kinetic energy operators.

Due to its efficiency and flexibility, the n-mode expansion is a frequently used tool for representing molecular potential energy surfaces in quantum chemical simulations. In this work, we investigate the performance of n-mode expansion-based models of kinetic energy operators in general polyspherical coordinate systems. In particular, we assess the operators with respect to accuracy in vibrationally correlated calculations and their effect on potential energy surface construction with the adaptive density guided approach. Our results show that the n-mode expansion-based operator variants are reliable and systematically improvable approximations of the full kinetic energy operator. Moreover, we introduce a workflow to generate the n-mode expanded kinetic energy operators on-the-fly within the adaptive density guided approach. This scheme can be applied in studies of species and coordinate systems, for which an analytical form of the kinetic energy operator is not available.

Solid state synthesis of zwitterionic cocrystal 5-fluorouracil L-phenylalanine explicated via structural, spectroscopy, quantum chemicals, Hirshfeld and docking analysis

The single crystal 5-Fluorouracil l-phenylalanine (5FUPA) was synthesized using solid state technique and crystallized at room temperature using the slow evaporation method. The crystal with orthorhombic structure and P212121 space group was obtained. Quantum chemical studies were used to compute the structural parameters and various spectroscopic properties for 5FUPA using the B3LYP/6–311++G (d, p). The structural parameters from reported single crystal XRD and calculated from DFT were compared, and they were showing good agreement with each other. The peaks obtained by experimental FTIR and modes calculated by theoretical DFT method have a good degree of consistency. The UV–Visible absorption spectrum of 5FUPA shown to have maximum absorption peak at 266 nm. The NBO analysis was used to calculate the interaction between bonding and anti-bonding orbitals and their stabilization energy in 5FUPA. The most reactive sites of the 5FUPA cocrystal were investigated by Fukui function descriptor and Molecular Electrostatic Potential (MEP) energy surface calculated using Mulliken charges. Inter- and intra-molecular interactions of the 5FUPA were investigated using the Hirshfeld surface and finger print methods. The topological studies ELF, LOL and thermodynamic parameters at different temperatures were performed. The molecular docking outcomes indicate that, cocrystal 5FUPA have better inhibitory effects on breast cancer proteins when compared to 5-fluorouracil and l-phenylalanine. The 5FUPA cocrystal has performed better compared to the other two molecules in terms of docking affinity, having a better binding score range of -8.3 kcal/mol to -9.4 kcal/mol. This demonstrates that 5FUPA cocrystal has unveiled more bioactivity and reactivity when compared with 5-fluorouracil and l-phenylalanine, and can be further considered as a breast cancer medication after clinical trials.

Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer.

In this work, we present a full-dimensional potential energy surface for AlF-AlF. We apply a general machine learning approach for full-dimensional potential energy surfaces, employing an active learning scheme trained on abinitio points, whose size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As a result, it is possible to provide the full-dimensional AlF-AlF potential energy surface, requiring ≲0.01% of the configurations to be calculated abinitio. Furthermore, we analyze the general properties of the AlF-AlF system, finding critical differences with other reported results on CaF or bi-alkali dimers.

Molecular structure, physicochemical properties, impact of solvents ionization potential, electron occupancy, inhibition constant, and stabilization energy investigations of 4-acetamido benzoic acid

A novel heterocyclic organic compound, 4-Acetamido benzoic acid (4AMBA) had a wide range of applications in the field of drug discovery arena. The molecular structural stability conformation had been carried out using the Molecular Potential Energy Surface (MPES) scan with chosen suitable dihedral angle. For both the calculated and experimental procedures, the identifications of the chemical bonds of pertinent functional groups were investigated using spectral measurements (FT-IR and FT-Raman). The DFT/B3LYP/6–311++G(d,p) basis set, which is a highly compatible technique, was implemented to execute the quantum computational studies. Further, to enhance the molecular (inter and intra) interactions, reactivity regions between the atoms were performed using reactivity sites such as MEP, NBO, NLMO, NHO, and Hirshfeld surface analysis. In addition, the topological analysis for the various solvents and the electronic properties of the appropriate wavelength, the energy gap of the UV–Visible spectrum (both theoretical (various solvents) and experimental), FMO theories (HOMO and LUMO) energies and topological analyses were attained. The significant features that explain the biological behavior of the header composite were computed with the least possible binding energy using protein-ligand interactions with appropriate protein receptors, such as 1J1R, 1G1K, and 1J1Q.

Orders-of-coupling representation achieved with a single neural network with optimal neuron activation functions and without nonlinear parameter optimization

Orders-of-coupling representations (representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates corresponding to different orders of coupling) are useful in many applications, for example, in computational chemistry and other applications, especially where integration is needed. Examples include N-mode approximations and many-body expansions. Such representations can be conveniently built with machine learning methods, and previously, methods building the lower-dimensional terms of such representations with neural networks [e.g. Comput. Phys. Commun. 180 (2009) 2002] and Gaussian process regressions [e.g. Mach. Learn. Sci. Technol. 3 (2022) 01LT02] were proposed. Here, we show that neural network models of orders-of-coupling representations can be easily built by using a recently proposed neural network with optimal neuron activation functions computed with a first-order additive Gaussian process regression [arXiv:2301.05567] and avoiding non-linear parameter optimization. Examples are given of representations of molecular potential energy surfaces.

Fitting Potential Energy Surfaces by Learning the Charge Density Matrix with Permutationally Invariant Polynomials.

The electronic energy in the Hartree-Fock (HF) theory is the trace of the product of the charge density matrix (CDM) with the one-electron and two-electron matrices represented in an atomic orbital basis, where the two-electron matrix is also a function of the same CDM. In this work, we examine a formalism of analytic representation of a generic molecular potential energy surface (PES) as a sum of a linearly parameterized HF and a correction term, the latter formally representing the electron correlation energy, also linearly parameterized, by expressing the elements of CDM using permutationally invariant polynomials (PIPs). We show on a variety of numerical examples, ranging from exemplary two-electron systems HeH+ and H3+ to the more challenging cases of methanium (CH5+) fragmentation and high-energy tautomerization of formamide to formimidic acid that such a formulation requires significantly fewer, 10-20% of PIPs, to accomplish the same accuracy of the fit as the conventional representation at practically the same computational cost.

Rectangularization of Gaussian process regression for optimization of hyperparameters

Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and can be viewed as linear regression problem with equal numbers of training data and basis functions. When data are sparse, avoidance of overfitting and optimization of hyperparameters of GPR are difficult, in particular in high-dimensional spaces where the data sparsity issue cannot practically be resolved by adding more data. Optimal choice of hyperparameters, however, determines success or failure of the application of the GPR method. We show that parameter optimization is facilitated by rectangularization of the defining equation of GPR. On the example of a 15-dimensional molecular potential energy surface we demonstrate that this approach allows effective hyperparameter tuning even with very sparse data.

Anharmonicity and quantum nuclear effects in theoretical vibrational spectroscopy: a molecular tale of two cities

Anharmonic effects due to the shape of the molecular potential energy surface far from the equilibrium geometry are major responsible for the deviations of the actual frequencies of vibration from the harmonic estimates. However, anharmonic effects are not the solely responsible for this. Quantum nuclear effects also play a prominent role in theoretical vibrational spectroscopy as they contribute to drive away the molecular vibrational frequencies from their harmonic counterpart. The consequence of this is that anharmonicity and quantum effects may be difficult to separate spectroscopically and get often confused. In this work we show that anharmonicity can be detected by means of classical simulations, while quantum nuclear effects need to be identified by means of an approach originating from either the time independent or the time dependent Schroedinger equation of quantum mechanics. We show that classical methods are sensitive to the temperature or energy conditions under which they are undertaken. This leads to wrong frequency estimates, when dealing with few-Kelvin experiments, if one performs simulations simply matching the experimental temperature. Conversely, quantum approaches are not affected by this issue and they provide more and better information.

Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces

This paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C5H5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree-Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.

Explicit Learning of Derivatives with the KREG and pKREG Models on the Example of Accurate Representation of Molecular Potential Energy Surfaces.

The KREG and pKREG models were proven to enable accurate learning of multidimensional single-molecule surfaces of quantum chemical properties such as ground-state potential energies, excitation energies, and oscillator strengths. These models are based on kernel ridge regression (KRR) with the Gaussian kernel function and employ a relative-to-equilibrium (RE) global molecular descriptor, while pKREG is designed to enforce invariance under atom permutations with a permutationally invariant kernel. Here we extend these two models to also explicitly include the derivative information from the training data into the models, which greatly improves their accuracy. We demonstrate on the example of learning potential energies and energy gradients that KREG and pKREG models are better or on par with state-of-the-art machine learning models. We also found that in challenging cases both energy and energy gradient labels should be learned to properly model potential energy surfaces and learning only energies or gradients is insufficient. The models' open-source implementation is freely available in the MLatom package for general-purpose atomistic machine learning simulations, which can be also performed on the MLatom@XACS cloud computing service.

Automated reaction kinetics and network exploration (Arkane): A statistical mechanics, thermodynamics, transition state theory, and master equation software

AbstractThe open‐source statistical mechanics software described here, Arkane–Automated Reaction Kinetics and Network Exploration–facilitates computations of thermodynamic properties of chemical species, high‐pressure limit reaction rate coefficients, and pressure‐dependent rate coefficient over multi‐well molecular potential energy surfaces (PES) including the effects of collisional energy transfer on phenomenological kinetics. Arkane can use estimates to fill in information for molecules or reactions where quantum chemistry information is missing. The software solves the internal energy master equation for complex unimolecular reaction systems. Inputs to the software include converged electronic structure computations performed by the user using a variety of supported software packages (Gaussian, Molpro, Orca, TeraChem, Q‐Chem, Psi4). The software outputs high‐pressure limit rate coefficients and pressure‐dependent phenomenological rate coefficients, as well as computed thermodynamic properties (enthalpy, entropy, and constant pressure heat capacity) with added energy corrections. Some of the key features of Arkane include treatment of 1D, 2D or ND hindered internal rotation modes, treatment of free internal rotation modes, quantum tunneling effect consideration, transition state theory (TST) and Rice‐Ramsperger‐Kassel‐Marcus (RRKM) rate coefficient computations, master equation solution with four implemented methods, inverse‐Laplace transform of high‐pressure limit rate coefficients into the energy domain, energy corrections based on bond‐additivity or isodesmic reactions, automated and efficient PES exploration, and PES sensitivity analysis. The present work describes the design of Arkane, how it should be used, and refers to the theory that it employs. Arkane is distributed via the RMG‐Py software suite (https://github.com/ReactionMechanismGenerator/RMG‐Py).

PESPIP: Software to fit complex molecular and many-body potential energy surfaces with permutationally invariant polynomials.

We wish to describe a potential energy surface by using a basis of permutationally invariant polynomials whose coefficients will be determined by numerical regression so as to smoothly fit a dataset of electronic energies as well as, perhaps, gradients. The polynomials will be powers of transformed internuclear distances, usually either Morse variables, exp(-ri,j/λ), where λ is a constant range hyperparameter, or reciprocals of the distances, 1/ri,j. The question we address is how to create the most efficient basis, including (a) which polynomials to keep or discard, (b) how many polynomials will be needed, (c) how to make sure the polynomials correctly reproduce the zero interaction at a large distance, (d) how to ensure special symmetries, and (e) how to calculate gradients efficiently. This article discusses how these questions can be answered by using a set of programs to choose and manipulate the polynomials as well as to write efficient Fortran programs for the calculation of energies and gradients. A user-friendly interface for access to monomial symmetrization approach results is also described. The software for these programs is now publicly available.

The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces.

Kernel-based methods, including Gaussian process regression (GPR) and generally kernel ridge regression, have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density functionals in high-dimensional feature spaces. Kernels of the Matern family, such as Gaussian-like kernels (basis functions), are often used which allow imparting to them the meaning of covariance functions and formulating GPR as an estimator of the mean of a Gaussian distribution. The notion of locality of the kernel is critical for this interpretation. It is also critical to the formulation of multi-zeta type basis functions widely used in computational chemistry. We show, on the example of fitting of molecular potential energy surfaces of increasing dimensionality, the practical disappearance of the property of locality of a Gaussian-like kernel in high dimensionality. We also formulate a multi-zeta approach to the kernel and show that it significantly improves the quality of regression in low dimensionality but loses any advantage in high dimensionality, which is attributed to the loss of the property of locality.

Copper coordination compounds based on bis-quinolylhydrazone of 2,6-diacetylpyridine: Synthesis, structure and cytotoxic activity

Bis-hetarylhydrazone H2L (1), a condensation product of 2,6-diacetylpyridine with 2-hydrazinoquinoline, has been synthesized. By reaction of 1 with Cu(II) nitrate and perchlorate binuclear mixed-valence coordination compounds [CuICuII(H2L)2](NO3)3⋅2H2O (2) and [CuICuII(H2L)2](ClO4)3 (3) were obtained. Cu(I) Ion in the compounds 2, 3 is in the distorted tetrahedral N-donor environment, while Cu(II) center is in the distorted octahedral one. Cu(II) Chloride and bromide form with 1 asymmetric mononuclear compounds with composition [Cu(H2L)Cl]Cl (4) and [Cu(H2L)Br]Br (5) with tetragonal–pyramidal coordination polyhedron. The structures of the compounds were studied by means of NMR, IR, ESR, UV–vis, X-ray absorption spectroscopy and X-ray single crystal diffraction methods. The effect of compounds on viability of the Hep-2 and HepG2 cell lines was investigated in vitro. The study showed that 1 is non-toxic at tested concentrations (1–100 μM), while all the complexes exhibit significant dose-dependent cytotoxic effect. It is shown that compounds 2–5 demonstrate higher cytotoxicity towards considered cancer cell cultures than widely used commercial anticancer pharmaceuticals – cisplatin and carboplatin. Quantum-chemical modeling of the structure of the ligand 1 and its complexes was performed using density functional theory at B3LYP/6-311G(d) level of theory. Molecular electrostatic potential (MEP) and average local ionization energy (ALIE) surfaces were calculated to rationalize the reactive properties of the compounds.

Algorithmic Design of Geometric Data for Molecular Potential Energy Surfaces

A code MolecGeom, based on algorithms for stepwise distortions of bond lengths, bond angles and dihedral angles of polyatomic molecules, is presented. Potential energy surfaces (PESs) are curated in terms of the energy for each molecular geometry. PESs based on the Born–Oppenheimer approximation, by which the atomic nuclei within a molecule are assumed stationary with respect to the motion of its electrons, are calculated. Applications requiring PESs involve the effects of nuclear motion on molecular properties. These include determining equilibrium geometries corresponding to stationary and saddle point energies, calculating reaction rates and predicting vibrational spectra. This multi-objective study focuses on the development of a new method for the calculation of PESs and the analysis of the molecular geometry components in terms of incremental changes that provide comprehensive sampling while preserving the precision of PES points. MolecGeom is applied to generate geometric data to calculate PESs for theoretical calculations of vibrational-rotational spectra of water and formaldehyde. An ab initio PES comprising 525 and 2160 intramolecular nuclear configurations results in vibrational frequencies in agreement with experiment, having errors less than 0.08% and 0.8%, respectively. Vinyl alcohol, with a total of 14 internal coordinates, generates a PES of 1458 unique geometries. Ascorbic acid, with 54 internal coordinates, generates a 1,899,776 point PES.

Calculations of molecular properties of 2-(2'-hydroxyphenyl)benzoxazole by semi-empirical tight-binding methods

The semi-empirical tight-binding methods GFN1-xTB and GFN2-xTB are applied to calculations of structure, energy and normal vibrations of the molecule of 2-(2'-hydroxyphenyl)benzoxazole undergoing excited state intramolecular proton transfer. The results are compared with ones obtained by the density-functional tight-binding methods with hydrogen interaction corrections and density functional theory. The GFN2-xTB method is found to provide good correspondence to the results obtained by more accurate but much slower density functional theory method for geometrical parameters of hydrogen bond, relative energy of molecular conformations and potential energy surface.

Dual exponential coupled cluster theory: Unitary adaptation, implementation in the variational quantum eigensolver framework and pilot applications.

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.

General Analytical Nuclear Forces and Molecular Potential Energy Surface from Full Configuration Interaction Quantum Monte Carlo.

The full configuration interaction quantum Monte Carlo (FCIQMC) is a state-of-the-art stochastic electronic structure method, providing a methodology to compute FCI-level state energies of molecular systems within a quantum chemical basis. However, especially to probe dynamics at the FCIQMC level, it is necessary to devise more efficient schemes to produce nuclear forces and potential energy surfaces (PES) from FCIQMC. In this work, we derive the general formula for nuclear forces from FCIQMC, and clarify different contributions of the total force. This method to obtain FCIQMC forces eliminates previous restrictions and can be used with frozen core approximation and free selection of orbitals, making it promising for more efficient nuclear forces calculations. After some numerical checks of this procedure on the binding curve of N2 molecule, we use the FCIQMC energy and force to obtain the full-dimensional ground state PES of the water molecule via Gaussian processes regression. The new water FCIQMC PES can be used as the basis for H2O ground state nuclear dynamics, structure optimization, and rotation-vibrational spectrum calculation.