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Register a new userEfficient and Accurate Simulations of Vibrational and Electronic Spectra with Symmetry-Preserving Neural Network Models for Tensorial Properties
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Machine learning has revolutionized the high-dimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant. Here, we propose tensorial neural network (NN) models to learn both tensorial response and transition properties, in which atomic coordinate vectors are multiplied with scalar NN outputs or their derivatives to preserve the rotationally covariant symmetry. This strategy keeps structural descriptors symmetry invariant so that the resulting tensorial NN models are as efficient as their scalar counterparts. We validate the performance and universality of this approach by learning response properties of water oligomers and liquid water, and transition dipole moment of a model structural unit of proteins. Machine learned tensorial models have enabled efficient simulations of vibrational spectra of liquid water and ultraviolet spectra of realistic proteins, promising feasible and accurate spectroscopic simulations for biomolecules and materials.
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We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical embedded atom method (EAM) model used in condensed phase. It simply replaces the scalar embedded atom density in EAM with a Gaussian-type orbital based density vector, and represents the complex relationship between the embedded density vector and atomic energy by neural networks. We demonstrate that the EANN approach is equally accurate as several established ML models in representing both big molecular and extended periodic systems, yet with much fewer parameters and configurations. It is highly efficient as it implicitly contains the three-body information without an explicit sum of the conventional costly angular descriptors. With high accuracy and efficiency, EANN potentials can vastly accelerate molecular dynamics and spectroscopic simulations in complex systems at ab initio level.
Vibrational spectra can be computed without storing full-dimensional vectors by using low-rank sum-of-products (SOP) basis functions. We introduce symmetry constraints in the SOP basis functions to make it possible to separately calculate states in different symmetry subgroups. This is done using a power method to compute eigenvalues and an alternating least squares method to optimize basis functions. Owing to the fact that the power method favours the convergence of the lowest states, one must be careful not to exclude basis functions of some symmetries. Exploiting symmetry facilitates making assignments and improves the accuracy. The method is applied to the acetonitrile molecule.
Efficient computational methods that are capable of supporting experimental measures obtained at constant values of pH and redox potential are important tools as they serve to, among other things, provide additional atomic level information that cannot be obtained experimentally. Replica Exchange is an enhanced sampling technique that allows converged results to be obtained faster in comparison to regular molecular dynamics simulations. In this work we report the implementation, also available with GPU-accelerated code, of pH and redox potential (E) as options for multidimensional REMD simulations in AMBER. Previous publications have only reported multidimensional REMD simulations with the temperature and Hamiltonian dimensions. In this work results are shown for N-acetylmicroperoxidase-8 (NAcMP8) axially connected to a histidine peptide. This is a small system that contains only a single heme group. We compare results from E,pH-REMD, E,T-REMD and E,T,pH-REMD to one dimensional REMD simulations and to simulations without REMD. We show that 2D-REMD simulations improve sampling convergence in comparison to 1D-REMD simulations, and that 3D-REMD further improves convergence in comparison to 2D-REMD simulations. Also, our computational benchmarks show that our multidimensional REMD calculations have a small and bearable computational performance, essentially the same as one dimensional REMD. However, in multidimensional REMD a significantly higher number of replicas is required as the number of replicas scales geometrically with the number of dimensions, which requires additional computational resources. In addition to the pH dependence on standard redox potential values and the redox potential dependence on pKa values,we also investigate the influence of the temperature in our results. We observe an agreement between our computational results and theoretical predictions.
Vibrational spectra and wavefunctions of polyatomic molecules can be calculated at low memory cost using low-rank sum-of-product (SOP) decompositions to represent basis functions generated using an iterative eigensolver. Using a SOP tensor format does not determine the iterative eigensolver. The choice of the interative eigensolver is limited by the need to restrict the rank of the SOP basis functions at every stage of the calculation. We have adapted, implemented and compared different reduced-rank algorithms based on standard iterative methods (block-Davidson algorithm, Chebyshev iteration) to calculate vibrational energy levels and wavefunctions of the 12-dimensional acetonitrile molecule. The effect of using low-rank SOP basis functions on the different methods is analyzed and the numerical results are compared with those obtained with the reduced rank block power method introduced in J. Chem. Phys. 140, 174111 (2014). Relative merits of the different algorithms are presented, showing that the advantage of using a more sophisticated method, although mitigated by the use of reduced-rank sum-of-product functions, is noticeable in terms of CPU time.
We describe our efforts of the past few years to create a large set of more than 500 highly-accurate vertical excitation energies of various natures ($pi to pi^*$, $n to pi^*$, double excitation, Rydberg, singlet, doublet, triplet, etc) in small- and medium-sized molecules. These values have been obtained using an incremental strategy which consists in combining high-order coupled cluster and selected configuration interaction calculations using increasingly large diffuse basis sets in order to reach high accuracy. One of the key aspect of the so-called QUEST database of vertical excitations is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating theoretical cross comparisons. Following this composite protocol, we have been able to produce theoretical best estimate (TBEs) with the aug-cc-pVTZ basis set for each of these transitions, as well as basis set corrected TBEs (i.e., near the complete basis set limit) for some of them. The TBEs/aug-cc-pVTZ have been employed to benchmark a large number of (lower-order) wave function methods such as CIS(D), ADC(2), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, ADC(3), CC3, NEVPT2, and others (including spin-scaled variants). In order to gather the huge amount of data produced during the QUEST project, we have created a website [https://lcpq.github.io/QUESTDB_website] where one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the type of basis set, etc. We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited-state methods.
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