1. CF14 EGI-XSEDE Workshop Session Tuesday, May 20 Helsinki, Findland Usecase 2 TTU-COMPCHEM Collaboration on Direct Classical and Semiclassical Dynamics Calculations William L. Hase Department of Chemistry and Biochemistry Texas Tech University Lubbock, TX USA Collaborators Yu Zhuang, Texas Tech University Michele Ceotto, University of Milan

3. DIRECT DYNAMICS SIMULATIONS – trajectories are integrated “on the fly” with the potential energy and derivatives obtained directly from electronic structure theory. Review: Bolton et al. in Modern Methods for Multidimensional Dynamics Computations in Chemistry, edited by D. L. Thompson (World Scientific, Singapore, 1998), p 143. Car-Parinello Direct Dynamics – electronic motion and nuclear motion are propagated simultaneously; Phys. Rev. Lett. 55, 4271 (1985). DFT – wavefunction is propagated by using fictitious electronic degrees of freedom with sufficiently small masses. Ab initio and semiempirical theories – the wavefunction’s expansion coefficients are propagated; Hartke and Carter, J. Chem. Phys. 97, 6569 (1992). Born-Oppenheimer Direct Dynamics – at each step of the integration V(q) and  V/  q i are obtained by optimizing the wavefunction. CNDO theory: Wang and Karplus, J. Am. Chem. Soc. 95, 8160 (1973). HF/STO-3G: Leforestier, J. Chem. Phys. 68, 4406 (1978). Semiclassical Initial Value Representation (SC-IVR) Direct Dynamics CO 2 : Ceotto, Zhang, and WLH, J. Chem. Phys. 138, 054116 (2013).

4. Semiclassical-IVR Direct Dynamics for Power Spectra and Vibrational Energy Levels Heller-Herman-Kluk-Kay SC-IVR Propagator C t, the pre-exponential factor, is determined from the monodromy matrix, which depends upon the Hessian. Time-Dependent Power Spectra Importance sampling for the reference states χ to reduce the number of trajectories. Ceotto, Zhuang, and Hase, J. Chem. Phys. 138, 054116 (2013). Ceotto, Tantardini, and Aspuru-Guzik, J. Chem. Phys. 135, 214108 (2011).

5. Hessian Updating for Approximating the Hessian from Electronic Structure Theory (EST) Calculations Quasi – Newton (qN) Method J. M. Bofill, J. Comput. Chem. 15, 1 (1994) Error EST calculation of gradient G at each integration step EST calculation of Hessian H at step K and then update for K-1 steps Compact Finite Difference (CFD) Method Y. Zhuang and co-workers, J. Chem. Phys. 133, 074101 (2010) Error

6. Approximation is Required for Solving qN and CFD Equations Y. Zhuang and co-workers, J. Chem. Phys. 133, 074101 (2010) ● For a m x m Hessian matrix H, there are m(m+1)/2 unknown H ij ● There are only m CFD equations ● Solution in a lower dimensional subspace is required ● Following Bofill ΔH J+1 = H(X J+1 ) – H(X J ) is given by where R J+1 = ΔH J+1 ΔX J+1, ΔX J+1 = X J+1 – X J. The parameter λ (0-1) defines a family of Hessian update schemes.

7. Computational Details Trajectories calculated from an analytic potential energy function are run in serial and are well-suited for grid computing. The SC-IVR method and MM analytic potentials may be used to calculate quantum anharmonic vibrational energy levels for biological molecules. Direct dynamics trajectories calculated using VENUS/NWChem require parallel computation for the electronic structure theory calculations of the energy, gradient, and Hessian if needed. With direct dynamics an analytic potential energy function is not required. Use the results of the direct dynamics trajectories to fit an analytic potential energy function or to develop an interpolated representation of the potential energy surface.

8. Semiclassical-IVR Direct Dynamics for Power Spectrum I(E) and Vibrational Energy Levels Ceotto, Zhuang, and Hase, J. Chem. Phys. 138, 054116 (2013). Direct dynamics for CO 2 at the B3LYP/cc-pVDZ level of theory. Accurate power spectrum obtained with eight trajectories and Hessian updated every 60 time steps. Current Simulation Glycine with the AMBER MM potential and B3LYP/6-31G(d,p) direct dynamics.

9. The simulations were performed with the MC-SC-IVR method using 8 trajectories. The black line is the spectrum without the Hessian CFD approximation and the colored lines are for different levels of the CFD Hessian approximation B3LYP/cc-pVDZ Direct Dynamics Power Spectrum for CO 2 at Different Levels of the CFD-Bofill Hessian Update Scheme.