Accurate Semi-Empirical Quantum Chemistry via Evolutionary Algorithms
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Duane Johnson, Todd Martinez, and David Goldberg and Students: Kumara Sastry and Alexis Thompson
Sequence illustrates the light excitation of an ethylene molecule, the simplest photo-excitable molecule. Single photon approaches molecule (top left) and excites the twisted state (top right), then passes through a pyramidal state (bottom left) on it way back to groundstate (bottom right). All this occurs in about 160 femtoseconds! Ethylene is shown in polymer solution, represented by helical strands.
Similar photo-excitable materials include light-sensitive proteins in the retina that give rise to vision. Our new computational methods correctly predict molecular energy levels and structural configurations, up to 1000 times faster than other quantum chemistry methods. Faster computations enable quicker solutions to photochemistry problems in vision, solar energy, and photosynthesis research. [High-res image]
Objective
To accelerate Quantum Chemistry (QC) simulations of excited-state reactions by +1000 times by creating semi-empirical potentials with accuracy approaching that of high-level methods.
Approach
Use machine-learning methods based upon efficient, Competent Genetic Algorithms (eCGA) and multi-objective optimization (MO).
Why it matters
With fast but accurate semi-empirical potentials, we can search for new drugs or critical biological reactions 100 – 1000 times faster!
Strategy
Using well-known semiempirical (MP3) QC potential* we optimize two objectives (error in energy and energy-gradient) for ethylene (C2H4) using a few excited-state structures calculated from high-level QC (ab initio CASSCF learning set) to predict excited-states not in the learning set. *MP3 potential has 11 parameters just for carbon.
We get agreement with high-level QC methods:
- 160±40 fs (vs.180±50 fs) for excitation decay.
- D2d excitation energy 2.5 eV (vs 2.5 eV).
- Pyramidalization energy 0.9 eV (vs 0.9 eV).
- Potentials 1000x faster and “transferable” to other C-H based molecules.
Outlook
We are finalizing analysis for ethylene and benzene and details of why “non-dominate” Pareto front and eCGA are necessary to do well, as opposed to standard GA’s being used in chemistry.
We have:
- provided MO-GA code on Software Archive.
- proven the utility of MO-GA using eCGA.
- shown transferability of potentials for other C-H molecules that were not used in learning set.
- verified the cusp surfaces of the excited molecules are described well by semiempirical potentials.
- revealed the importance of “non-domininant Pareto fronts”, “crowding distances”, and “tournament selection” to obtain good MO-GA solutions.
RESULT: (left) An excitation of ethylene and example excited-state configurations. (right) Multi-objective Genetic Algorithms found the “best MP3 solutions” (circles) with ”on-the-fly” sensitivity analysis of solution sets. All optimal solution sets agree with our high-level QC calculations.
Publications 2006-2007
- Kumara Sastry, D.D. Johnson, Alexis L. Thompson, D.E. Goldberg, T.J. Martinez, "Optimization of Semiempirical Quantum Chemistry Methods via Multiobjective Genetic Algorithms: Accurate Photochemistry for Larger Molecules and Longer Time Scales" (invited) Materials and Manufacturing Processes 22 (2007) 553 - 561.
- Kumara. Sastry, D.D. Johnson, and D.E. Goldberg, "Scalability of a Hybrid Extended Compact Genetic Algorithm for Ground State Optimization of Clusters,” (invited) Materials and Manufacturing Processes 22 (2007) 570 - 576.
- Kumara Sastry, D.D. Johnson, Alexis L. Thompson, D.E. Goldberg, T.J. Martinez, J. Leiding, and Jane Owens, "Multiobjective Genetic Algorithms for Multiscaling Excited-State Dynamics in Photochemistry," GECCO 1745-1752 (2006)
* Silver Medal, Best Paper in real-world track.
Recognition and Industry
- At Genetic and Evolutionary Computation Conf. 2006.
- Awarded Silver “Hummie” Medal.
- Awarded “Best Paper” in Real-World Applications track.
- Student Kumara Sastry was finalist for the Lemelson-MIT innovation prize.
- US provisional patent application made.
- K. Sastry joining INTEL in fall 2007 to develop future-generation chip via optimization.
