exploring c-chem with numeric mm and ab-initio methods

Exploring C-Chem with numeric MM and Ab-Initio methods

Masood Malekghassemi

The Project

Comptuational Chemistry Methods Step 1: Molecular Mechanics

Step 2: Ab-initio quantum chemical methods

Analysis and translation of Ab-initio quantum chemical methods to molecular mechanics rules Step 3: AI

Concepts of Molecular Mechanics

Force field Defines how things interact

Simple particle mechanics, ball and spring model (basically what we did in AI mixed in with Parallel computing + making it look pretty)

Framework for Molecular Mechanics

Identities The different kinds of atoms and/or groups – may

be particular atoms in specific functional groups

Rules Governs the quantization of energy of particular

shapes and orientations of the molecule's constituents

Atoms and Atom Collections Atoms and/or groups governed by rules through

their identities

The Rules

The rules are the main difference between this program and other molecular mechanics programs Provides a generic interface to govern a system

through energetic interactions

Can be generated from arbitrary information

Will be made more generic by having types in themselves be data structures rather than hard-coded enumerations

Molecular Mechanics

Self-Consistent Field Method (SCF) Iterate over various orientations and shapes,

checking for lower energies.

Maximize energy or minimize energy Genetic Algorithms (more easily made parallel in the

future)

Display via dynamically updating 'Rule' view AtomsViewerRule utilizes a 'view' of an Atom Collection

to allow the GUI module to display the simulated system at any point in the simulation

Basics of Ab Initio methods

The underlying methods Schrodinger equation: H*Psi = E*Psi

Pseudo-eigenvalue/eigenfunction form H is a 'matrix' operator, Psi the wave'function', E the

energy 'eigenvalue'.

Solve either Ab Initio or semi-empirically Have finished neither – project may have been too

ambitious in terms of what was necessary to self-teach

*cough*graduate-level-math*cough*

Ab-initio Methods

Uses wavefunctions Represented by various functions

Slater Type Orbitals: N*exp(-a*r) Gaussian Type Orbitals: N*exp(-a*r^2)

General contraction: a linear combination c1*f1(x) + c2*f2(x) ... cn*fn(x)

Solves eqns via variational method Think differential equations, except more epic

Variational Method

The idea is to find minima: The energy of a system with wavefunctions is given

by <Psi|H|Psi> / <Psi|Psi> Psi is parameterized

Find stationary points w.r.t. the parameters

Identify minima

Boom – you have your minimum energy

Perturbation

The N-body problem is impossible to solve analytically Simplify the problem of atoms and electrons to

many 2-body problems

Add in the N-body elements later

Makes life a little bit easier with divide and conquer, essentially.

Artificial Intelligence

The lofty goal of the project (of course it's unaccomplished). Take the numeric values from all-periodic table

calculations and transform them into force field input for molecular mechanics applications.

Not even at the point where I'm thinking about it.

Previous incarnationImages:

Current Project

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More images

Left: 4p orbital, only partially through (note only 3 nodes)Up: 5f orbital – caught the image while it's refreshing, so you might see an artifact

What It Does So Far:

It used to display the MM portion as it ran Doesn't anymore – old version was lost in mad

Eclipse IDE rampage (no back-ups <_<)

It displays the wavefunctions (based on the spherical harmonic function and a general contraction of gaussian functions).

Can perform overlap and KE integration of wavefunction representations over all space Totally analytical (so much research...)

Mini-CAS

To do the integrations, basically made a partial CAS Represent multi-dimensional polynomials (the crux

of the work)

Integrate/Differentiate said polynomials

Cartesian Gaussian Functions (for GTOs)

Expand the polynomials, are general enough for the following kinds:

Legendre Laguerre Ricola ← my personal misnomer

Mini-CAS

Can perform Jacobi diagonalization of symmetric matrices By extension, gets the eigenvectors (requisite for

EHM + HF)

By extension, it can find the eigenvalues of square matrices (requisite for Ab Initio methods)

Math Library

As for actual programming techniques, there are a few I've employed SFINAE (C++ specific)

ScalarTraits ScalarTraits_Tools HalfInteger specializations

Class definition overloading

Variadic function argument iterators Makes life easier when dealing with tensors in general

Conclusions Overestimated my ability to understand complex

mathematics in the first quarter.

Restarted the molecular mechanics portion 5-6 times in the second and third quarters. Currently have nothing to show from that work – it was

all deleted after I'd screwed with my IDE too much...

Attempted to work on the Ab Initio portions fourth quarter – failed to make it in time for TJSTAR Also got food poisoning the night before <_<