Higher-accuracy schemes for approximating the Hessian from electronic structure calculations in chemical dynamics simulations

Efficient Method for Numerical Calculations of Molecular Vibrational Frequencies by Exploiting Sparseness of Hessian Matrix

Molecular vibrational frequency analysis plays an important role in theoretical and computational chemistry. However, in many cases, the analytical frequencies are unavailable, whereas frequency calculations using conventional numerical methods are very expensive. In this work, we propose an efficient method to numerically calculate the frequencies. Our main strategies are to exploit the sparseness of the Hessian matrix and to construct the N-fold two-variable potential energy surfaces to fit the parabola parameters, which are later used for the construction of Hessian matrices. A set of benchmark calculations is performed for typical molecules of different sizes and complexities using the proposed method. The obtained frequencies are compared to those calculated with the analytical methods and conventional numerical methods. It is shown that the results yielded with the new method are in very good agreement with corresponding accurate values (with a maximum error of ∼20 cm-1), while the required computation resource is largely reduced compared to that required by conventional numerical methods. For medium-sized molecules, the calculational scaling is lowered to O(N1.6) (this work) from that of O(N2) (conventional numerical methods). For even larger molecules, more computational savings can be achieved, and the scaling is estimated to be quasilinear with respect to the molecular size.

Molecular Hessian matrices from a machine learning random forest regression algorithm

In this article, we present a machine learning model to obtain fast and accurate estimates of the molecular Hessian matrix. In this model, based on a random forest, the second derivatives of the energy with respect to redundant internal coordinates are learned individually. The internal coordinates together with their specific representation guarantee rotational and translational invariance. The model is trained on a subset of the QM7 dataset but is shown to be applicable to larger molecules picked from the QM9 dataset. From the predicted Hessian, it is also possible to obtain reasonable estimates of the vibrational frequencies, normal modes, and zero point energies of the molecules.

Unsupervised Machine Learning Neural Gas Algorithm for Accurate Evaluations of the Hessian Matrix in Molecular Dynamics

The Hessian matrix of the potential energy of molecular systems is employed not only in geometry optimizations or high-order molecular dynamics integrators but also in many other molecular procedures, such as instantaneous normal mode analysis, force field construction, instanton calculations, and semiclassical initial value representation molecular dynamics, to name a few. Here, we present an algorithm for the calculation of the approximated Hessian in molecular dynamics. The algorithm belongs to the family of unsupervised machine learning methods, and it is based on the neural gas idea, where neurons are molecular configurations whose Hessians are adopted for groups of molecular dynamics configurations with similar geometries. The method is tested on several molecular systems of different dimensionalities both in terms of accuracy and computational time versus calculating the Hessian matrix at each time-step, that is, without any approximation, and other Hessian approximation schemes. Finally, the method is applied to the on-the-fly, full-dimensional simulation of a small synthetic peptide (the 46 atom N-acetyl-l-phenylalaninyl-l-methionine amide) at the level of DFT-B3LYP-D/6-31G* theory, from which the semiclassical vibrational power spectrum is calculated.

Ab Initio Direct Dynamics

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this "on-the-fly" approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. This approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH₂O → H₂ + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

Semiclassical vibrational spectroscopy with Hessian databases

We report on a new approach to ease the computational overhead of ab initio "on-the-fly" semiclassical dynamics simulations for vibrational spectroscopy. The well known bottleneck of such computations lies in the necessity to estimate the Hessian matrix for propagating the semiclassical pre-exponential factor at each step along the dynamics. The procedure proposed here is based on the creation of a dynamical database of Hessians and associated molecular geometries able to speed up calculations while preserving the accuracy of results at a satisfactory level. This new approach can be interfaced to both analytical potential energy surfaces and on-the-fly dynamics, allowing one to study even large systems previously not achievable. We present results obtained for semiclassical vibrational power spectra of methane, glycine, and N-acetyl-L-phenylalaninyl-L-methionine-amide, a molecule of biological interest made of 46 atoms.

Controlling the strong field fragmentation of ClCHO+ using two laser pulses -an ab initio molecular dynamics simulation

For a single, intense 7 μm linearly polarized laser pulse, we found that the branching ratio for the fragmentation of ClCHO⁺ → Cl + HCO⁺ , H + ClCO⁺ , HCl⁺ +CO depended strongly on the orientation of the molecule (J. Phys. Chem. Lett. 2012, 3 2541). The present study explores the possibility of controlling the branching ratio for fragmentation by using two independent pulses with different frequencies, alignment and delay. Born-Oppenheimer molecular dynamics simulations in the laser field were carried out with the B3LYP/6-311G(d,p) level of theory using combinations of 3.5, 7 and 10.5 μm sine squared pulses with field strengths of 0.03 au (peak intensity of 3.15×10¹³ W/cm² ) and lengths of 560 fs. A 3.5 μm pulse aligned with the C-H bond and a 10.5 μm pulse perpendicular to the C-H bond produced a larger branching ratio for HCl⁺ +CO than a comparable single 7 μm pulse. When the 10.5 μm pulse was delayed by one quarter of the pulse envelope, the branching ratio for the high energy product, (HCl⁺ +CO 73%) was a factor of three larger than the low energy product (Cl + HCO⁺ , 25%). By contrast, when the 3.5 μm pulse was delayed by one quarter of the pulse envelope, the branching ratio was reversed (HCl⁺ +CO 38%; Cl + HCO⁺ , 60%). Continuous wavelet analysis was used to follow the interaction of the laser with the various vibrational modes as a function of time. © 2018 Wiley Periodicals, Inc.

Mechanism of Formation of the Nonstandard Product in the Prenyltransferase Reaction of the G115T Mutant of FtmPT1: A Case of Reaction Dynamics Calling the Shots?

FtmPT1 is a fungal indole prenyltransferase that affords Tryprostatin B from Brevianamide F and dimethylallyl pyrophosphate; however, when a single residue in the active site is mutated (Gly115Thr), a novel five-membered ring compound is obtained as the major product with Tryprostatin B as the minor product. Herein, we describe detailed studies of the catalysis of the Gly115Thr mutant of FtmPT1 with a focus on the observed regioselectivity of the reaction. We employ one- and two-dimensional potential of mean force simulations to explore the catalytic mechanism, along with molecular dynamics simulations exploring the reaction dynamics of the prenyl transfer reaction. Single-point electronic structure calculations were also used to explore the performance of the self-consistent charge density functional tight-binding method to model specific reaction steps. Importantly, we observe that the two reaction pathways have comparable activation parameters and propose that the origin of the novel product is predicated, at least in part, on the topology of the potential energy surface as revealed by reaction dynamics studies.

Controlling Chemical Reactions by Short, Intense Mid-Infrared Laser Pulses: Comparison of Linear and Circularly Polarized Light in Simulations of ClCHO(+) Fragmentation

Enhanced mode selective fragmentation of oriented ClCHO(+) → Cl + HCO(+), H + ClCO(+), HCl(+) + CO with linear polarized intense mid-IR pulses was demonstrated in our previous computational study ( J. Phys. Chem. Lett. 2012 , 3 , 2541 ). Simulations of angle-dependent strong field ionization of ClCHO indicate the ionization rate in the molecular plane is nearly twice as large as perpendicular to the plane, suggesting a degree of planar alignment can be obtained experimentally for ClCHO(+), starting from neutral molecules. Classical trajectory calculations with a 4 cycle 7 μm laser pulse (peak intensity of 1.26 × 10(14) W/cm(2)) show that circularly polarized light with the electric field in the plane of the molecule deposits more energy and yields larger branching ratios for higher energy fragmentation channels than linearly polarized light with the same maximum field strength. These results suggest circularly polarized mid-IR pulses can not only achieve control on reactions but also provide an experimentally accessible implementation.

A high order predictor–corrector integration algorithm for first principle chemical dynamics simulations

H. Wu submitted the paper without having obtained permissions for submission from some of the co-authors or some of the major contributors, and hereby requested to retract the publication.

Molecular dynamics of methylamine, methanol, and methyl fluoride cations in intense 7 micron laser fields

Fragmentation and isomerization of methylamine (CH3NH2(+)), methanol (CH3OH(+)), and methyl fluoride (CH3F(+)) cations by short, intense laser pulses have been studied by ab initio classical trajectory calculations. Born-Oppenheimer molecular dynamics (BOMD) on the ground-state potential energy surface were calculated with the CAM-B3LYP/6-31G(d,p) level of theory for the cations in a four-cycle laser pulse with a wavelengths of 7 μm and intensities of 0.88 × 10(14) and 1.7 × 10(14) W/cm(2). The most abundant reaction path was CH2X(+) + H (63-100%), with the second most favorable path being HCX(+) + H2 (0-33%), followed by isomerization to CH2XH(+) (0-8%). C-X cleavage after isomerization was observed only in methyl fluoride. Compared to random orientation, CH3X(+) with the C-X aligned with the laser polarization gained energy nearly twice as much from laser fields. The percentage of CH3(+) + X dissociation increased when the C-X bond was aligned with the laser field. Alignment also increased the branching ratio for H2 elimination in CH3NH2(+) and CH3OH(+) and for isomerization in CH3OH(+).

Synchronous concerted multiple-body photodissociation of oxalyl chloride explored by ab initio-based dynamics simulations

Photo-induced multiple body dissociation is of fundamental interest in chemistry and physics. A description of the mechanism associated with n-body (n ≥ 3) photodissociation has proven to be an intriguing and yet challenging issue in the field of chemical dynamics. Oxalyl chloride, (ClCO)2, is the sole molecule reported up to date that can undergo four-body dissociation following absorption of a single UV photon, with a rich history of mechanistic debate. In the present work, the combined electronic structure calculations and dynamics simulations have been performed at the advanced level, which provides convincing evidence for resolving the mechanistic debate. More importantly, synchronous and asynchronous concertedness were explored for the first time for the (ClCO)2 photodissociation, which is based on the simulated time constants for the C-C and C-Cl bond fissions. Upon photoexcitation of (ClCO)2 to the S1 state, the adiabatic C-C or C-Cl fission takes place with little possibility. The four-body dissociation to 2Cl((2)P) and 2CO((1)Σ) was determined to a dominant channel with its branch of ∼0.7, while the three-body dissociation to ClCO((2)A(')) + CO((1)Σ) + Cl((2)P) was predicted to play a minor role in the (ClCO)2 photodissociation at 193 nm. Both the four-body and three-body dissociations are non-adiabatic processes, which proceed in a synchronous concerted way as a result of the S1 → S0 internal conversion. There is a little possibility for two-body dissociation to occur in the S0 and S1 states.

Chemical dynamics simulations of X- + CH3Y → XCH3 + Y- gas-phase S(N)2 nucleophilic substitution reactions. Nonstatistical dynamics and nontraditional reaction mechanisms

Extensive classical chemical dynamics simulations of gas-phase X(-) + CH(3)Y → XCH(3) + Y(-) S(N)2 nucleophilic substitution reactions are reviewed and discussed and compared with experimental measurements and predictions of theoretical models. The primary emphasis is on reactions for which X and Y are halogen atoms. Both reactions with the traditional potential energy surface (PES), which include pre- and postreaction potential energy minima and a central barrier, and reactions with nontraditional PESs are considered. These S(N)2 reactions exhibit important nonstatistical atomic-level dynamics. The X(-) + CH(3)Y → X(-)---CH(3)Y association rate constant is less than the capture model as a result of inefficient energy transfer from X(-)+ CH(3)Y relative translation to CH(3)Y rotation and vibration. There is weak coupling between the low-frequency intermolecular modes of the X(-)---CH(3)Y complex and higher frequency CH(3)Y intramolecular modes, resulting in non-RRKM kinetics for X(-)---CH(3)Y unimolecular decomposition. Recrossings of the [X--CH(3)--Y](-) central barrier is important. As a result of the above dynamics, the relative translational energy and temperature dependencies of the S(N)2 rate constants are not accurately given by statistical theory. The nonstatistical dynamics results in nonstatistical partitioning of the available energy to XCH(3) +Y(-) reaction products. Besides the indirect, complex forming atomic-level mechanism for the S(N)2 reaction, direct mechanisms promoted by X(-) + CH(3)Y relative translational or CH(3)Y vibrational excitation are possible, e.g., the roundabout mechanism.