Featured Researches

Chemical Physics

"On-the-fly" calculation of the Vibrational Sum-frequency Generation Spectrum at the Air-water Interface

In the present work, we provide an electronic structure based method for the "on-the-fly" determination of vibrational sum frequency generation (v-SFG) spectra. The predictive power of this scheme is demonstrated at the air-water interface. While the instantaneous fluctuations in dipole moment are obtained using the maximally localized Wannier functions, the fluctuations in polarizability are approximated to be proportional to the second moment of Wannier functions. The spectrum henceforth obtained captures the signatures of hydrogen bond stretching, bending, as well as low-frequency librational modes.

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Chemical Physics

1 H-NMR Dipole-Dipole Relaxation in Fluids: Relaxation of Individual 1 H- 1 H Pairs versus Relaxation of Molecular Modes

The intra-molecular 1 H-NMR dipole-dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP) theory of NMR intra-molecular relaxation. The BPP theory draws upon Debye's theory for describing the rotational diffusion of the 1 H- 1 H pair and predicts a mono-exponential decay of the 1 H- 1 H dipole-dipole autocorrelation function between distinct spin pairs. Using molecular dynamics (MD) simulations, we show that for both n -heptane and water this is not the case. In particular, the autocorrelation function of individual 1 H- 1 H intra-molecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However for the high-symmetry molecule neopentane, the individual 1 H- 1 H intra-molecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The inter-molecular autocorrelation functions for n -heptane, water, and neopentane also do not admit a mono-exponential behavior of individual 1 H- 1 H inter-molecular pairs at distinct initial separations. We suggest expanding the auto-correlation function in terms of molecular modes, where the molecular modes do have an exponential relaxation behavior. With care, the resulting Fredholm integral equation of the first kind can be inverted to recover the probability distribution of the molecular modes. The advantages and limitations of this approach are noted.

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Chemical Physics

A General Automatic Method for Optimal Construction of Matrix Product Operators Using Bipartite Graph Theory

Constructing matrix product operators (MPO) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For DMRG to be conveniently used in different problems described by different Hamiltonians, in this work we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) It is automatic in that only the definition of the operator is required; (ii) It is symbolic thus free of any numerical error; (iii) The complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; (iv) The symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature.

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Chemical Physics

A Grid-free Approach for Simulating Sweep and Cyclic Voltammetry

We present a new computational approach to simulate linear sweep and cyclic voltammetry experiments that does not require a discretized grid in space to quantify diffusion. By using a Green's function solution coupled to a standard implicit ordinary differential equation solver, we are able to simulate current and redox species concentrations using only a small grid in time. As a result, where benchmarking is possible, we find that the current method is faster (and quantitatively identical) to established techniques. The present algorithm should help open the door to studying adsorption effects in inner sphere electrochemistry.

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Chemical Physics

A Markov theoretic description of stacking disordered aperiodic crystals including ice and opaline silica

We review the Markov theoretic description of 1D aperiodic crystals, describing the stacking-faulted crystal polytype as a special case of an aperiodic crystal. Under this description we generalise the centrosymmetric unit cell underlying a topologically centrosymmetric crystal to a reversible Markov chain underlying a reversible aperiodic crystal. We show that for the close-packed structure, almost all stackings are irreversible when the interaction reichweite is greater than 4. Moreover, we present an analytic expression of the scattering cross section of a large class of stacking disordered aperiodic crystals, lacking translational symmetry of their layers, including ice and opaline silica (opal CT). We then relate the observed stackings and their underlying reichweite to the physics of various nucleation and growth processes of disordered ice.

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Chemical Physics

A Minimal Experimental Bias on the Hydrogen Bond Greatly Improves Ab Initio Molecular Dynamics Simulations of Water

Experiment Directed Simulations (EDS) is a method within a class of techniques seeking to improve molecular simulations by minimally biasing the system Hamiltonian to reproduce certain experimental observables. In a previous application of EDS to ab initio molecular dynamics (AIMD) simulation-based on electronic density functional theory (DFT), the AIMD simulations of water were biased to reproduce its experimentally derived solvation structure. In particular, by solely biasing the O-O pair correlation functions, other structural and dynamical properties that were not biased were improved. In this work, the hypothesis is tested that directly biasing the OH pair correlation, will provide an even better improvement of DFT-based water properties in AIMD simulations. The logic behind this hypothesis is that for most electronic DFT descriptions of water the hydrogen bonding is known to be deficient due to anomalous charge transfer and over polarization in the DFT. Using recent advances to the EDS learning algorithm, we thus train a minimal bias on AIMD water that reproduces the O-H radial distribution function derived from the highly accurate MB-pol model of water. It is then confirmed that biasing the O-H pair correlation alone can lead to improved AIMD water properties, with structural and dynamical properties in even closer to experiment than the previous EDS-AIMD model.

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Chemical Physics

A Multi-Center Quadrature Scheme for the Molecular Continuum

A common way to evaluate electronic integrals for polyatomic molecules is to use Becke's partitioning scheme [J. Chem. Phys.88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron-molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke's partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

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Chemical Physics

A Neural Network Inspired Formulation of Chemical Kinetics

A method which casts the chemical source term computation into an artificial neural network (ANN)-inspired form is presented. This approach is well-suited for use on emerging supercomputing platforms that rely on graphical processing units (GPUs). The resulting equations allow for a GPU-friendly matrix-multiplication based source term estimation where the leading dimension (batch size) can be interpreted as the number of chemically reacting cells in the domain; as such, the approach can be readily adapted in high-fidelity solvers for which an MPI rank offloads the source term computation task for a given number of cells to the GPU. Though the exact ANN-inspired recasting shown here is optimal for GPU environments as-is, this interpretation allows the user to replace portions of the exact routine with trained, so-called approximate ANNs, where the goal of these approximate ANNs is to increase computational efficiency over the exact routine counterparts. Note that the main objective of this paper is not to use machine learning for developing models, but rather to represent chemical kinetics using the ANN framework. The end result is that little-to-no training is needed, and the GPU-friendly structure of the ANN formulation during the source term computation is preserved. The method is demonstrated using chemical mechanisms of varying complexity on both 0-D auto-ignition and 1-D channel detonation problems, and the details of performance on GPUs are explored.

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Chemical Physics

A Protocol for Spectroscopists to Isolate The Effect of Berry Geometric Magnetic Forces on Molecular Dynamics

We propose a novel means to isolate and quantify the effects of Berry force on molecular dynamics using two reasonably strong continuous wave (CW) laser fields with frequencies ω and 2ω . For molecules or materials with three frequency-matching bright transitions ( |0⟩→|1⟩ , |1⟩→|2⟩ , |0⟩→|2⟩ ) at frequencies ( ω , ω , 2ω ) respectively, the effects of Berry curvature can be isolated by varying the phase between the two laser fields ( Δϕ ) and monitoring the dynamics. Moreover, we find that the resulting chemical dynamics can depend critically on the sign of Δϕ ; in other words, the effects of Berry curvature can be enormous. Thus, this manuscript represents an unusual step forward towards using light-matter interactions to affect chemical dynamics, suggesting that topological concepts usually invoked in adiabatic quantum optics and condensed matter can be directly applied to non-adiabatic chemical excited state dynamics.

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Chemical Physics

A Self Consistent Field Formulation of Excited State Mean Field Theory

We show that, as in Hartree Fock theory, the orbitals for excited state mean field theory can be optimized via a self-consistent one-electron equation in which electron-electron repulsion is accounted for through mean field operators. In addition to showing that this excited state ansatz is sufficiently close to a mean field product state to admit a one-electron formulation, this approach brings the orbital optimization speed to within roughly a factor of two of ground state mean field theory. The approach parallels Hartree Fock theory in multiple ways, including the presence of a commutator condition, a one-electron mean-field working equation, and acceleration via direct inversion in the iterative subspace. When combined with a configuration interaction singles Davidson solver for the excitation coefficients, the self consistent field formulation dramatically reduces the cost of the theory compared to previous approaches based on quasi-Newton descent.

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