Research

My Research Work

My research involves a cross-disciplinary problem in Physics, Chemistry and Material Sciences. The topic is generically known as “Multi-Scale Modeling”.
Physics provides the fundamental laws of nature; chemistry addresses the consequences of these laws for complex molecular systems; and material science is concerned with the macroscopic consequences of physics and chemistry. This logical sequence is quite disconnected in its practical implementation, being supplanted in practice by phenomenology based on a mix of experiment, intuition, and speculation. My research is designed to bring the Physics component to the forefront of a class of complex problems: the experimentally known strong effects of chemistry on the dynamical response of real materials to mechanical distortion (stress, strain). More specifically, I address questions of how to wed the fundamental quantum mechanical description at small scales (fundamental physics) to more practical mesoscale descriptions (classical physics). In the following this is referred to as the problem of the Quantum Mechanical / Classical Mechanical interface.

Phenomena like crack propagation, enzymatic reactions and chemo-mechanical processes such as stress corrosion, surface etching, hydrolytic weakening of silica etc., require a very accurate description at one scale while at another scale a coarser description might be satisfactory. For example, one needs ab initio quantum mechanical method at the crack tip where chemical bonds are breaking between neighboring atoms thereby bringing marked deformation in the electron density but far from the crack tip where deformation is less, atoms are described using classical potentials. However ab initio methods are extremely computationally intensive to be applied to study such phenomena in a macroscopic sample. To reduce the computational effort, one commonly used tactic is multi-scale modeling, which combines different levels of theory for various scales of calculations. One fundamental problem of multi-scale modeling is the coupling of these different scales. My project focuses on the science and systematic for such mutli-scale modeling.(see pdf )

Other Projects: Comparative studies of DFT and Transfer-Hamiltonian methods (view pdf), Developing a classical potential from ab initio quantum data(view pdf)

Conference Proceedings and Presentations

Mallik A, Muralidharan K, Runge K, Dufty J.W. “Choosing a Potential for Multi-Scale Modeling”. Oral Presentation at APS Annual March Meeting, March 21, 2005.
Mallik A, Taylor C, Runge K., Dufty J.W. “An Embedding Potential for Multi-Scale Modeling in Silica”. Poster Presentation at Sanibel Symposium, March 6 – 11, 200.
Mallik A, Taylor D E, Runge K, Cheng H-P, Dufty J.W. “A Comparison of Transfer Hamiltonian vs. DFT Methods in QM/CM Multi-Scale Modeling” Oral Presentation at SESAPS Meeting, Nov, 2004.
Mallik A, Taylor D. E., Runge K, Dufty J. W.: "A Method for Consistent Embedding in Quantum Mechanical (QM)/ Classical Mechanical (CM) Simulations". Poster Presentation at NSF DMR ITR Computational Workshop, UIUC, June, 2004.
Mallik A, Taylor C, Runge K, Dufty J. "An Evaluation of embedding of quantum domain (QM) within its classical (CM) environment". Sanibel Symposium, Feb 28 - Mar 3, 2004.
Mallik A, Runge K, Dufty J. "Characterization of QM/CM interface in multi-scale modeling". APS Annual March Meeting, 2004.
Mallik A, Runge K, Dufty J. "Developing a Classical Potential from ab initio Quantum Chemistry" REU Program, UF, Feb 12, 2004.
Mallik A, Runge K, Dufty J. "Multi-Scale Modeling of Solids", Seminar, Deptartment of Physics, IIT Kanpur, Jan 12, 2004.

Publications

Mallik A, Taylor C, Runge K, Dufty J. "An Application of Transfer Hamiltonian Quantum Mechanics to Multi-Scale Modeling".(Int. J. Quan. Chem. 100, 1019-1025, (2004))

Mallik A, Runge K, Cheng,H-P, Dufty J. "Constructing A Small Strain Potential for Multi-Scale Modeling".(physics/0501150, J.Molecular Simulations, 2005, 31(10), 695))

" Mallik. A, Runge K, Dufty J.W.,Cheng H.P." Multiscale modeling of materials based on force and charge density fidelity" (J Chem Phys 2007 Dec 14; 127(22):224707)

" Mallik. A, Taylor. DE, Runge K, Dufty J.W, Procedure for building a consistent embedding at the QM-CM interface (Journal of computer aided materials design, 13, 45, Oct 2006)

" Mallik. A, Runge K, Dufty J.W, (Journal of computer aided materials design, 13, 61, Oct 2006)

Abstracts

Choosing a Classical Potential in Multi-Scale Modeling

Multi-Scale modeling of materials assumes as a starting point a quantum mechanical description that is adequate to represent the properties of interest. Next, for practical purposes, the bulk of the material is represented classically with only a much smaller subsystem described by the chosen quantum description. For problems relating to fracture, a consistent embedding of a quantum (QM) domain in its classical (CM) environment requires that the classical potential chosen for the CM region should yield the same geometry and elastic properties as the QM domain. It is proposed that such a classical potential can be constructed using ab initio data on the equilibrium structure and weakly strained configurations calculated from the quantum description, rather than the more usual approach of fitting to a wide range of empirical data. This scheme is illustrated in detail for a model system, a silica nanorod that has the same stiochiometric ratio of Si:O as observed in real silica. The potential is chosen to have the same functional form as TTAM but the parameters are fitted using a genetic algorithm with force data obtained from a quantum calculation (Transfer Hamiltonian - NDDO). The Young's modulus (Y) obtained from this classical potential matches closely with that obtained from the QM method for strains up to 10%, unlike the standard TTAM which differs by almost 20%. Furthermore, the bond lengths and bond angles in the rod are an order of magnitude more accurate for the new potential in comparison to that from the current TTAM or BKS potential parameters. This potential provides a "seamless" coupling between the QM and CM regions in applications of QM/CM multi-scale modeling for this silica nanorod. The possible wider application of this potential can be found in glasses and silica nanorings.

A Comparison of Transfer Hamiltonian vs. DFT Methods in QM/CM Multi-Scale Modeling

A method for a consistent embedding of a quantum (QM) domain in its classical (CM) environment has been developed for application in QM/CM simulations for multi-scale modeling. A benchmark system is considered: a silica nanorod in which a part of the rod is treated quantum mechanically and the rest is treated classically. This system is chosen because a full ab initio quantum data can be obtained for the entire rod to assess the quality of the proposed embedding technique. However, even at the quantum level each possible choice for the ab initio method entails approximations used to optimize the accuracy and speed of the calculations. Each approximation has its own advantages and limitations, but the embedding scheme should be insensitive to these. In order to test how robust our proposed embedding scheme is, we have chosen two different methods for the underlying quantum mechanical description. The first method used is the Transfer Hamiltonian (TH) - Neglect of Diatomic Differential Overlap (NDDO) (Bartlett, 2003). The TH method uses a semi empirical Hamiltonian that has been parameterized to yield coupled cluster quality forces, thereby taking electron correlations into account like post-Hartree Fock methods. The second method used is the Born-Oppenheimer local spin density (Barnett and Landman, 1993) within density functional theory (DFT) and generalized gradient approximation (GGA). We use the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional. Here, the embedding method and resulting QM/CM composite rods using the two different ab initio methods are compared for the silica nanorod. It is found that the two quantum rods have noticeable differences, although the embedding method for the equilibrium composite rods is faithful to the underlying quantum method in each case. Nonequilibrium elastic properties are discussed briefly.

Characterization of Quantum Mechanical (QM) / Classical Mechanical (CM) Interface in Multi-Scale Modeling

For studying phenomena like crack propagation, surface corrosion and other chemomechanical processes in a macroscopic sample, it is divided into a small quantum domain (QM), where significant electronic changes are taking place and a classical region (CM), which plays the role of a static environment to influence the phenomenon in QM domain. Usually, the effect of CM region is ignored while studying the mechanism in the QM domain. Here, we present a method, in which the information of the state of the CM region is incorporated into the QM calculations. In this method, the atoms at the boundary of the QM and the CM regions are replaced by link-atoms1 or pseudo-atoms constructed to describe the nearest neighbor exchange interactions. Then, the remaining effect of the CM environment due to manybody coulombic interactions is modeled in terms of dielectrics or lower order multipoles. This partitioning scheme has been tested in a silica nanorod2, which is made up of stacked SiO2 rings in which one of the rings is treated quantum mechanically and the rest classically. Using the Transfer-Hamiltonian (TH) - NDDO method3, the forces and the charge densities for i) the entire rod and ii) the QM region with only nearest neighbor interactions are calculated. The TH-NDDO data for the whole system are taken as correct results, with respect to which the accuracy of the partitioning is examined. Comparing the results of forces and charge densities it is found that the pseudo-atom method is a better representation of the exchange interactions compared to the link-atom method. The rest of the rod is approximated by two dipoles, which are then included into the TH-NDDO calculations to incorporate the effects of polarization. It is found that the pseudo-atoms together with the dipoles in the TH-NDDO can effectively represent the CM region. The generality of the proposed scheme extends to systems such as strained rods and 3-M cyclic silica rings4 found abundantly on amorphous silica.

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