(1) Deciphering the code. The language of computational chemistry
is littered with acronyms what do these abbreviations stand for in terms
of underlying assumptions and approximations?
(2) Technical problems. How does one actually run the program and what
does one look for in the output?
(3) Quality assessment. How good is the number that has been calculated?
Point (1) is part of every new field, there is not much you can do about it. If you want to live in another country, you have to learn the language. If you want to use computational chemistry methods, you need to learn the acronyms. I have tried in the present book to include a good fraction of the most commonly used abbreviations and standard procedures.
Point (2) is both hardware and software specific. It is not well suited to a text book, as the information rapidly becomes out of date. The average lifetime of computer hardware is a few years, the time between new versions of software is even less. Problems of type (2) need to be solved "on location".
As computer programs evolve they become easier to use. Modern programs often communicate with the user in terms of a graphical interface, and many methods have become essential "black box" procedures: if you can draw the molecule, you can also do the calculation. This effectively means that you no longer have to be a highly trained theoretician to run even quite sophisticated calculations.
The ease by which calculations can be performed means that point (3) has become the central theme in computational chemistry. It is quite easy to run a series of calculations which produce results that are absolutely meaningless. The program will not tell you whether the chosen method is valid for the problem you are studying. Quality assessment is thus an absolute requirement. This, however, requires much more experience and insight than just running the program. Basic understanding of the theory behind the method is needed, and knowledge of the performance of the method for other systems. If you are breaking new ground, where there is no previous experience, you need a way of calibrating the results.
The lack of quality assessment is probably one of the reasons why computational chemistry has (had) a somewhat bleak reputation. "If five different computational methods give five widely different results, what has computational chemistry contributed? You just pick the number closest to experiments and claim that you can reproduce experimental data accurately." One commonly see statements of the type "The theoretical results for property X are in disagreement. Calculation at the CCSD(T)/6-31G(d,p) level predicts that ...., while the MINDO/3 method give opposing results. There is thus no clear consent from theory." This is clearly a lack of understanding of the quality of the calculations. If the results disagree, there is a very high probability that the CCSD(T) results are basically correct, and the MINDO/3 results are wrong. If you want to make predictions, and not merely reproduce known results, you need to be able to judge the quality of your results. This is by far the most difficult task in computational chemistry. I hope the present book will give some idea of the limitations of different methods.
Computers don't solve problems, people do. Computers just generate numbers. Although computational chemistry has evolved to the stage where it often can be competitive with experimental methods for generating a value for a given property of a given molecule, the number of possible molecules (there are an estimated 10200 molecules with a molecular weight less than 850) and their associated properties is so huge that only a very tiny fraction will ever be amenable to calculations (or experiments). Furthermore, with the constant increase in computational power, a calculation which barely can be done today, will be possible on medium sized machines in 5-10 years. Prediction of properties with methods which do not provide converged results (with respect to theoretical level), will typically only have a lifetime of a few years before being surpassed by predictions using more accurate calculations.
The real strength of computational chemistry is the ability to generate data (for example by analyzing the wave function) from which a human may gain insight, and thereby rationalize the behavior of a large class of molecules. Such insights and rationalizations are much more likely to be useful over a longer period of time, than the raw results themselves. A good example is the concept used by organic chemists with molecules composed of functional groups, and representing reactions by "pushing electrons". This may not be particular accurate from a quantum mechanical point of view, but it is very effective in rationalizing a large body of experimental results, and has good predictive power.
Just as computers do not solve problems, mathematics by itself do not provide insight. It merely provides formulas, a framework for organizing thoughts. It is in this spirit that I have tried to write this book. Only the necessary (obviously a subjective criterion) mathematical background has been provided, the aim being that the reader should be able to understand the premises and limitations of different methods, and follow the main steps in running a calculation. This means that in many cases I have omitted to tell the reader of some of the finer details, which may annoy the purists. However, I believe the large overview is necessary before embarking on a more stringent and detailed derivation of the mathematics. The goal of this book is to provide an overview over commonly used methods, giving enough theoretical background to understand why for example the AMBER force field is used for modeling proteins but MM2 is used for small organic molecules. Or why Coupled Cluster inherently is an iterative method, while Perturbation Theory and Configuration Interaction inherently are non-iterative methods, although the CI problem in practice is solved by iterative techniques.
The prime focus of this book is on calculating molecular structures and (relative) energies, and less on molecular properties or dynamical aspects. In my experience, predicting structures and energetics are the main uses of computational chemistry today, although this may well change in the coming years. I have tried to include most methods which already are extensively used, together with some that I expect to become generally available in the near future. The amount of detailing in the description of the methods depends partly on how practical and commonly used the methods are (both in terms of computational resources and software), and partly reflects my own limitations in terms of understanding. Although simulations (e.g. molecular dynamics) are becoming increasingly powerful tools, only a very rudimentary introduction is provided in Chapter 16. This area is outside my expertise and several excellent textbooks are already available.
Computational chemistry contains a strong practical element. Theoretical methods must be translated into working computer programs in order to produce results. Different algorithms, however, may have different behaviors in practice, and it becomes necessary to be able to evaluate whether a certain type of calculation can be carried out with the available computers. The book thus contains some guidelines for evaluating what type of resources that are necessarily for carrying out a given calculation.
I have assumed that the reader has no prior knowledge of concepts specific to computational chemistry, but has a working understanding of introductory quantum mechanics and elementary mathematics, especially linear algebra, vector, differential and integral calculus. The following features specific to chemistry are used in the present book without further introduction.
(1) The Schrödinger equation, with the consequences of quantized
solutions and quantum numbers.
(2) The interpretation of the square of the wave function as a probability
distribution, Heisenbergs uncertain principle and the possibility of tunneling.
(3) The solutions for the hydrogen atom, atomic orbitals.
(4) The solutions for the harmonic oscillator and rigid rotor.
(5) The molecular orbitals for the H2 molecule generated
as a linear combination of two s-functions, one on each nuclear
center.
(6) Point group symmetry, notation and representations, and the group
theoretical condition for when an integral is zero.
I have elected to include a discussion of the variational principle and perturbational methods, although these often are covered in courses in elementary quantum mechanics. The properties of angular momentum coupling are used at the level of knowing the difference between a singlet and triplet state. I do not believe that it is necessary to understand the details of vector coupling to understand the implications.