COMPUTATIONAL CHEMISTRY – A TESTING GROUND

FOR HIGH PERFORMANCE COMPUTING

 

 

 

N Sathyamurthy

Department of Chemistry

IIT Kanpur 208 016

 

INTRODUCTION

 

Chemistry is an experimental science.  Auguste Comte wrote in his book, “Philosophie Positive”, in the year 1830, “Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry… If mathematical analysis should ever hold a prominent place in chemistry – an aberration which is happily almost impossible – it would occasion a rapid and widespread degeneration of that science”.

 However, by the early 20th century the situation changed so much that Henry Eyring wrote, “Insofar as we can accept quantum mechanics as exact, every problem of chemistry can be answered from direct calculation by a sufficiently skillful mathematician” [1].   In practice, however, no computation worth the effort could be carried out until electronic computers became available. Starting from ILIAC (the computer that was developed at the University of Illinois), every new generation of computers that became available subsequently was used to solve increasingly more complex problems in chemistry.  Each new computer excelled the previous in performance, both in terms of speed of computation and size of memory.  There has been no looking back. Whatever was the computer available on that day there was a chemist using it to determine the structure of a large molecule and/or studying the dynamics of the largest molecule or the largest collection of molecules possible.  With the advent of supercomputers like CRAY, the chemist let his computational dream grow big.  With the development of workstations and high resolution graphics, the chemist could visualize his favourite molecule, big or small, from the front as well as from the rear.  He could admire its beauty, watch it translate, rotate, vibrate and perform the molecular dance.   He could watch the chemical bonds break and/or form under the influence of another molecule or a photon.  He could examine the various sites available on a large receptor molecule and watch the drug molecule dock at the right place at the right angle. Designing drug molecules that have the requisite properties was a dream that has become a reality, thanks to the development of modern day electronic computers.  With the Moore’s law being operative, the computer power is improving every year and the chemist is able to study the structure and properties of larger and larger molecules, examine the dynamics of small molecules in greater detail and watch many molecular phenomena as they occur in space and time.  This capability has led to enormous insight into the nature of chemical bonding, nature of intermolecular forces and the various factors that govern the rates of chemical reactions.  Be it ozone depletion or atmospheric chemistry or combustion of a fuel inside an automobile engine or a drug–receptor interaction or protein folding, the computational chemist is able to study every one of them In Silico. 

The developments in the area of computational chemistry have been so much and so fast in the last two decades that some times people think that the job of a computational chemist is simple: buy a commercially available software, install it on your PC and with a click of a mouse you can study any chemical problem under the sun or beyond.  However, reality is far from that.

STRUCTURE: YES

Early on it was realized that the structure of molecules could be predicted easily with the help of an ab initio (from first principles) calculation that solves the time-independent Schrödinger equation using a set of Gaussian basis functions.  As a matter of fact, John A. Pople, who pioneered some of the electronic structure calculation softwares under the name of GAUSSIAN and went on to receive the Nobel Prize in chemistry for the year 1998, pointed out that it was possible to determine the structure of any reasonably large organic molecule or inorganic molecule (as long as it does not contain any metal atom) computationally with ease [2].  The structure of two water molecules trapped inside a fullerene cage, as obtained from an ab initio calculation from our lab is illustrated in Fig.1.

BONDING: NO

One of the simplest molecules that one could think of, hydrogen (H2), poses a challenge to computational chemistry, when it comes to the question of determining the strength of its covalent bond to experimental accuracy.  A rudimentary calculation would predict fluorine (F2) molecule to be unstable.   Determining the bond strength of a transition metal dimer accurately remains a formidable problem.

EXCITED STATES: IT IS A DIFFERENT BALL GAME

While it is straightforward to determine the structure and property of a reasonably sized molecule, the prediction of its excited state property cannot be taken for granted.  The excited state properties of fluorine molecule, for example, was studied to satisfaction only recently [3].  You can not predict the electronic spectrum of salicylic acid satisfactorily with the available computers at IIT Kanpur [4].  Predicting the fate of a double helical DNA when exposed to light requires much larger and faster computer than what is available anywhere in the world. 

INTERMOLECULAR FORCES

While it is nice to know the properties of individual molecules, there is hardly anything that you can do in chemistry without knowing the interaction between molecules.  The asymptotically accurate long range interaction is known analytically. The short range interaction, which is referred to as Pauli repulsion, is not difficult to determine.  Determining intermolecular forces at intermediate range continues to be a challenging task. Our recent work on He-F2 interaction is a case in point [5].  The interaction between F2 and He in its excited state(s) remains to be studied.

POTENTIAL-ENERGY SURFACES

One of the simplest exchange reactions in chemistry is that between a hydrogen atom and a hydrogen molecule. An approximate potential energy surface for this system in collinear geometry was proposed way back in 1928 by London [6].  Chemically accurate (± 1 kcal/mole) potential-energy surface for the system was determined in 1973 at IBM research lab! [7]. A spectroscopically accurate (± a few cm-1) potential-energy surface for the system has been determined recently [8].  The potential-energy surface for a slightly modified system, that is, an interaction of an H- ion with a hydrogen molecule has been computed at IIT Kanpur recently [9].  The number of accurate ab initio potential-energy surfaces that have been determined for any molecular system in the last two decades can be counted by the fingers in the two hands of an individual.

It is often said that fitting equations to data is simple.  Somebody remarked, “You can fit an elephant with two parameters.  With three you can make it wag its tail”!   Anybody who has tried to fit data would realize immediately that with two parameters you can only reproduce an ellipse.  The reproduction of the outline of a pachyderm requires far more than three parameters.   Fitting an analytic function to a potential energy surface is no mean task [10].  It requires all ingenuity, functional analysis and nonlinear least squares fitting ability and a good computer.  The success story of fitting the potential-energy surface for H3- from IIT Kanpur is described elsewhere [9].

NEWTON SHOWS THE WAY

If intermolecular forces are known, solving the dynamical equations is straightforward: solve the Newton’s (or Hamilton’s) equations numerically, treating atoms as classical particles.  Studying elementary chemical reactions has become routine (provided somebody has determined the potential-energy surface for you). Modelling the stretching, bending, twisting of an organic molecule is a child’s play.  This is often used by the salesman to impress the naïve buyer of computer hardware and software.  Protein folding is being studied, taking into account the motion of every individual atom under the influence of all other atoms in real time.  Watching a protein molecule undergo the molecular motion is like watching a huge giant trying to bend and touch his toe.  Nature does it in the case of protein molecules with ease, particularly in solution inside a cell. Including the ions and molecules that surround a protein inside a cell in a simulation is still not in the domain of today’s high speed computers (see the accompanying article by Sankararamakrishnan).  IBM’s Big Blue project is still in its infancy!

QUANTUM MECHANICS IS THE WAY TO GO

When it comes to predicting the experimental observables such as state-to-state differential and integral reaction cross sections that are measured by carefully monitoring the interaction of individual atoms and molecules under molecular beam conditions, with or without the influence of a laser beam, classical mechanics is not adequate.  One has to solve the quantum mechanical equations of motion that include time.  An example is the elementary ion-molecule reaction He + H2+ ® HeH+ + H    that has been studied for more than two decades in our lab.   Numerically solving the time-dependant Schrödinger equation in three dimensions requires a total of four independent variables.  In what is called the grid method, one starts with a wave packet (superposition of partial waves) localized in the reactant channel, watches it evolve with time and calculates the reaction probability for a given initial state of the reactants.  For an illustration of the dynamics of (H-, H2) collisions, see Fig. 2.  Also visit the website: www.iitk.ac.in  

If we include the total angular momentum (J) as an additional variable the problem becomes much more demanding computationally.   If we consider a 256 x 256 x 64 grid for the wave function as a function of two distances and one angle, for example, and we need to time evolve for about 5000-10,000 steps, you can estimate the memory requirement and the computer time required. We need to repeat such a calculation for several values of J.  Such a calculation was simply not possible with the available computers a few years ago!  Today that is not a problem.  Some researchers have carried out feasibility studies for 4-atom systems. However, the difficulty remains in that what is described above has to be repeated for several combinations of vibrational and rotational states of the reactants and one has to extract information about the product state and angular distribution for each initial state of the reactants.  When one considers the interaction between electronic states, one simply cannot manage all of what is said above with the available computers today.  Although several workers across the globe have tried to investigate polyatomic systems and molecule-surface interactions, most of the investigations till date have remained restricted in scope.

COLLECTION OF MOLECULES AND REAL LIFE CHEMISTRY

Water, water everywhere – it is definitely true in chemistry.  Most of the chemical reactions in and around us take place under aqueous  conditions.   Each atom, ion or molecule is surrounded by a large number of water molecules.  Be it protein folding or any other simple or complex reaction in real life, they all take place invariably under the influence of a large number of solvent molecules.  That is where one has to use statistical mechanical tools and carry out large scale molecular dynamical simulations if one has to solve real life problems in chemistry (see the accompanying article by A. Chandra).  Clearly any number of computers with any amount of memory and speed always becomes the limiting factor in deciding the choice of problems and the extent of solution.   Neither chemistry nor computer by itself   can solve all our problems.   But a combination of the two perhaps can.

 References

1.                  H. Eyring Trans. Faraday Soc.  34, 1 (1938).

2.                  J. A. Pople,  Nobel Lecture: Quantum Chemical Models, Rev. Mod. Phys. 71, 1267(1999).

3.                  U. Lourderaj, M.K. Harbola and N. Sathyamurthy Chem. Phys. Letters, 366, 88(2002).

4.                  S. Maheshwari, A. Chowdhury, N. Sathyamurthy, H. Mishra, H. B. Tripathi, M.Panda and J. Chandrasekhar, J. Phys. Chem. A103, 6257(1999).

5.                  U. Lourderaj and N. Sathyamurthy, Chem. Phys. –in press.

6.                  F. London, Probleme der Modernen Physik, Sommerfeld Festschrift, 104(1928); Z. Elektrochem. 35, 552(1929).

7.                  B. Liu, J. Chem. Phys. 58, 1925(1973).

8.                  Y. S. Mark Wu, A. Kuppermann and J. B. Anderson, Phys. Chem. Chem. Phys. 1, 929(1999).

9.                  A.N. Panda and N. Sathyamurthy.  J.Chem. Phys. – in press.

10.              N. Sathyamurthy, Compu. Phys. Rep. 3,  1(1985).

 

 

Figure Captions

 

1.      The structure of two water molecules trapped inside a fullerene cage.  While the dark green spheres represent carbon atoms, the red and white spheres represent oxygen and hydrogen atoms, respectively.

 

2.      Plots of probability density for (H-, H2) interaction in (R,r) and (R,Θ) spaces evolving with time, superimposed on the ab initio potential-energy surface. For convenience, contours of potential-energy and probability density are shown in the lower panel.

 

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