*Highly Parallelized Large Scale Atomistic Simulations
for Design of Materials*

Department of Chemistry, Beckman Institute (139-74),

Caltech, Pasadena, CA 91125

Richard Friesner, rich@cucbs.chem.columbia.edu

Department of Chemistry, Columbia University, New York, NY 10027

Zhen-Gang Wang, zgw@macpost.caltech.edu

Department of Chemical Engineering (210-41),

Caltech, Pasadena, CA 91125

Abhinandan Jain, jain@telerobotics.jpl.nasa.gov

Robotics, Jet Propulsion Laboratory (198-219),

Pasadena, CA 91109

Stephen Taylor, steve@cs.caltech.edu

Department of Computer Science (256-80),

Caltech, Pasadena, CA 91125

**Quantum Mechanics (QM)**

First principles solution of the Schrodinger equation (H F = E F) leads to accurate predictions of properties (structures, chemical reactions, excited states); however, this was limited to small systems (10 to 20 atoms) limiting the time and distance scale to 1 ps and 1 nm.**Force Fields (FF)**

By averaging over the electrons from QM we can obtain parameters (charges, force constants) while allowing materials to be described in terms of atoms rather than electrons.**Molecular Dynamics (MD)**

Using force fields (FF) the fundamental equations become Newton's equations (F = MA) rather than the Schrodinger equations. This allows practical calculations on 1000 to 5000 atoms rather than 10 to 20, extending the time and distance scale to 1 ns and 10 nm.**Coarse Graining (CG)**

By averaging over the atoms for MD, we can obtain parameters representing groups of atoms (molecules, segments), considerably simplifying the calculations.**Statistical Mechanics (SM)**

Using the CG description we can examine materials in terms of the large scale motions relevant to macroscopic experiments. This extends the time and distance scales to 1 microseconds and microns.**Continuum Parameters (CP)**

The results from SM are combined to obtain macroscopic or continuum parameters (free energies, phase diagrams, partition coefficients, solubility parameters) suitable for practical chemical engineering software (e.g., ASPEN-PLUS) for design of unit processes.

*QM - FINITE.*

For finite molecules we are focussing upon developing a new methodology (PS-GVB) combining pseudospectral (PS) multi-grid and dealiasing strategies with sophisticated many-body wavefunctions [generalized valence bond (GVB)]. PS-GVB leads to considerably better scaling with size (N^2 rather than the N^3, N^4, N^5, N^6 characteristic of alternative methods) and simpler parallelization. The basic PS-GVB program has been commercialized and parallelized. PS-GVB has been extended to*treat all atoms of the periodic table (using core effective potentials),**handle new sophisticated wavefunctions (GVB-RCI, MP2),*and*describe important properities (solvation energies, hyperpolarizabilities).*

Next we will (1) optimize these methods for parallel implementations, (2) extend the methodology to include GVB-RCI-MP2 and self-consistent GVB-RCI.

*QM - INFINITE.*

Most practical materials properties require a description of infinite systems using periodic boundary conditions (PBC). This is three-dimensional (3D) for bulk properties or two-dimensional (2D) for surface growth and interfaces. For this purpose we have developed a new method, Gaussian dual space density functional theory (GDS-DFT), in which most parts scale linearly with $N$. In implementating this we have developed a new separable pseudopotential that can be applied to all atoms of the periodic table. The GDS-DFT program is now being used for several projects. We will next optimize it for parallel environments.*MD/CMM-KSR.*

The focus here is on extending the methods of MD to treat molecules with 1 million atoms or crystals with 1 million atoms per unit cell, while accurately treating long-range interactions. The new methodology is the cell multipole method (CMM). The CMM methodology has been efficiently implemented into a general MD code on the KSR parallel supercomputer (part of the Caltech NSF-GCAG project). CMM/MD-KSR was written in an object oriented fashion to be portable and efficient for parallel computers using a global memory model such as KSR and CRAY T3D. We can now do routine molecular dynamic calculations up to 1.5 million atoms with the KSR and now are in production for industrially important problems (diffusion, glass temperature) for realistic description for amorphous polymers. This constitutes a great leap forward, allowing accurate atomistic simulations on systems 40 times larger than previous methods.*CMM/MD - INTEL, J-Machine.*

Starting with the CMM/MD-KSR code a communication layer was added for distributed memory applications based on the active message strategy for the J-Machine. This has been implemented on the Intel Touchstone Delta/512 at Caltech and will soon be tested on the J-Machine at Caltech. The design is based on the fine-grain programming concepts developed by the Scalable Concurrent Programming Group and should be portable to the J-Machine, CRAY T3D and other machines with active message libraries. Algorithms have been designed to systematically balance the load dynamically at intervals as the computation proceeds (due to atoms moving between cells assigned to other computers).*MD-NEIMO.*

For fast internal coordinate dynamics on a million atoms, we have developed the Newton-Euler Inverse Mass Operator (NEIMO) method. This methodology has been extended to handle periodic systems and has been incorporated into the advanced dynamics (Gibbs/Nose) codes for single processor computers. Next we need to- allow ring topologies and infinite chains
- parallelize the code.

*SM - Grand Canonical Monte Carlo.*

We have focussed on developing systematic methods for simulating mesoscopic and macroscopic properties of supramolecular structures formed from amphiphilic molecules. We use coarse-grained models with methods involving Monte Carlo and Brownian dynamics. This year we developed a grand canonical Monte Carlo method for simulating the forming and breaking of micelles, allowing full equilibrium among micelles of different sizes, between micelles and monomers, and between chains and rings. For the coming year our focus will be on the ordered structures in diblock copolymers and how they transform from one to another as a function of temperature.

*PS-GVB-SOLVATE.*

QM (PS-GVB) was combined with a Poisson-Boltzmann treatment of solvant to obtain self-consistent fully solvated wavefunctions. This was tested on 29 molecules and found to give excellent results (an accuracy of 0.03 electron volts).*PS-GVB-HYPERPOLARIZABILITY*

the PS-GVB method was extended to treat hyperpolarizability (for nonlinear optical materials) and applied to the best current organic materials with about 40 atoms. The results are excellent, indicating that theory can be used for designing materials with improved properties.*GDS-DFT*

A new generation of software (Gaussian dual space density functional theory) has been developed for predicting surface chemistry, thin film growth, adhesion, corrosion, and other properties. It is being applied to the CdTe and HgTe surfaces (in collaboration with Hughes) and to corrosion inhibitors on iron oxide (in collaboration with Chevron).*Glass Temperature of Polymers.*

A strategy has been developed for using MD to predict glass temperatures of polymers. It has been applied to eight polymers with excellent results. This is being extended to the study of copolymers and blends.*MD-CMM-KSR*

the new technology (CMM, RCMM) for million atom MD simulations has been successfully implemented on the KSR parallel supercomputer and is now in production for studies of melting of nylons (with Allied-Signal), diffusion of gases in polymers (Chevron), surface tension (Chevron), and glass temperatures of polymers (Goodrich, Chevron, Asahi Glass).

**PREDICTION OF GLASS TEMPERATURES OF POLYMERS.**

A key, potentially very significant industrial application for atomistic simulations is the prediction of glass temperatures, T_g. Above T_g the polymer is soft and can be formed or extruded; below T_g it is stiff. Industry would like to tune the glass temperature and the modulus to attain desired values by alloying the polymer with different monomers (forming copolymers), by cross linking, by blending or by using additives. Currently this is done empirically leading to costly and wasteful experiments. If theory could be used to predict the best choices there is the potential for considerably reducing the number of such experiments. Using the new MD techniques developed under the GCAG and working with industrial collaborators (Chevron, BF Goodrich, Asahi Glass), we have demonstrated (for eight cases) excellent predictions of the glass temperature. The simulations predict a glass temperature of 396K for teflon in good agreement with the experimental value of 400K. Equally exciting, analysis of the simulations explain the underlying phenomena controlling the glass temperature. Namely it is the point above which gauche-trans transformations compete with diffusion. Such concepts may allow new applications for rapid prediction of how the glass temperature is modified by changing the material (carrying out large scale calculations only for selected cases).**QUANTUM MECHANICS OF LARGE FINITE MOLECULES.**

We have developed a new methodology (PS-GVB) combining pseudospectral (PS) multi-grid and dealiasing strategies with sophisticated many-body wavefunctions [e.g., generalized valence bond (GVB)]. PS-GVB has been extended to treat all atoms of the periodic table. This combined a valence bond formulation for estimating initial guesses of wavefunctions, core effective potentials to treat the core electrons, and new grid and dealiasing functions. These methods scale with size as N^2 (rather than the N^3 of standard programs) and are 10 to 100 times faster than standard programs (depending on size). The PS-GVB method has been extended to treat solvation effects self-consistently using dielectric continuum methods, a Poisson-Boltzmann solver, and a self-consistent reaction field method. Like DelPhi, PS-GVB's Poisson-Boltzmann solver uses a cavity based on the real molecular surface, rather than the spherical cavity used by other programs. PS-GVB has been extended to calculate hyperpolarizabilities and applied to the new high-beta NLO organics. Second-order Moller-Plesset perturbation theory (MP2) has been implemented into PS-GVB, leading to improvements by a factor of 10 to 100, depending on size of the system. Licenses of this technology from Caltech and Columbia to Schrodinger Inc. have been arranged. Schrodinger has added a user-friendly interface and extended the program in many ways. On October 15, 1994 the first full commercial release will be made. It is anticipated that in two years PS-GVB will be in use at 100 US industrial sites plus 100 US university sites.**NONLINEAR OPTICAL MATERIALS.**

We have developed a simple valence bond theory (VB-CT) for predicting the trends in nonlinear optical properties (hyperpolarization) of new organic materials as a function of donor, acceptor, linker length, and solvent. VB-CT provides a way for experimentalists to quickly select the proper combination to maximize the various hyperpolarizabilities. This theory explains the derivative relationship of various polarizabilities observed experimentally for these materials. Using PS-GVB we have now succeeded in accurately predicting the hyperpolarizabilities of the newest extremely high hyperpolarizability materials, thus confirming both the experiment and the simple theory.**QUANTUM MECHANICS OF CHEMICAL PROPERTIES ON SOLID SURFACES.**

We have developed and tested a new methodology for predicting the chemical properties at surfaces and interfaces which should be useful in optimizing thin film growth. This methodology, GDS-DFT, extends density functional theory to use of Gaussian type functions by using a dual space strategy. This has been tested successfully on CdTe(100), HgTe(100), GaAs(110), and is being used in two industrial projects (HgCdTe with Hughes, corrosion inhibitors with Chevron).

*PS-GVB.*

Parallelize the solvate, hyperpolarizability, and GVB-RCI methods. Further develop and optimize the MP2, self-consistent GVB-RCI, and GVB-RCI-MP2 methods. Apply to important industrial problems.*GDS-DFT.*

Vectorize and parallelize for the CRAY T3D. Apply to important industrial problems.*CMM-MD-INTEL.*

Further develop and optimize. Test on the prototype J-Machine. This should allow up to 12 million atoms on the Intel-Paragon.*MD-NEIMO.*

Extend to ring topologies and to infinite chains. Parallize for KSR and Intel.*SM.*

Extend grand canonical Monte Carlo for studying phase transitions in diblock copolymers as a function of temperature and pressure.

Schrodinger Inc., Pasadena CA (contact Dr. Murco Ringnalda, ph: 818-568-9392, fax: 818-568-9778, email: info@psgvb.com) has licensed the PS-GVB technology from Caltech and Columbia. They have added a user-friendly interface, extensive user guide, and extended the program in many ways. On October 15, 1994 the first full commercial release will be made. It is anticipated that in two years PS-GVB will be in use at 100 US industrial sites plus 100 US university sites.

Chevron Petroleum Technology Co., La Habra, CA (Dr. Yongchun Tang, ph: 310-694-7550) uses PS-GVB, GDS-DFT, and MD-CMM to design new scale inhibitors and corrosion inhibitors for oil recovery applications (designing new and more effective calculations).

Allied-Signal, Morristown, NJ (Dr. Willis Hammond, ph: 201-455-4914) uses MD-CMM to predict structure and moduli of nylon polymers.

Hughes Research Labs., Malibu, CA (Dr. Jenna Zinck, ph: 310-317-5913) uses GDS-DFT to design metallorganics for MO-MBE deposition of HgCdTe single crystal films.

**DATE PROPOSAL: September 20, 1994**

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