Revision notes.

New material has been added to Chapter 2 and Chapter 4, including Figure 2.1. Current development work is mainly focusing on Section 4.4.4.

The third basis set choice, "3) To use 6-31G** type the number 3 (and see Revision Note 0.112)," has been commented out of the example program freeMQM-1.cpp, since a bug seems to have been introduced into the code involving the 6-31G** basis set. The option can still be used; the program just will not tell you that the option is available.

Equation punctuation, deliberately omitted until now, will be added gradually.

Olinking between documents is in the process of being implemented. This is anticipation of the need to link several tutorials together. Now, just the main tutorial, Topics in Molecular Quantum Mechanics, the revision notes, and the development notes are cross referenced using olinks. Thus, chapter numbers, figure numbers, equations numbers, etc., that appear as links, will kept current as the documents expand. On the other hand, references to chapter numbers, equations numbers, etc., that don't appear as links should be assumed to be outdated as the document expands [e.g., see the revision notes 0.100 - 0.115].

There have been several minor corrections.

Chapter 3 has been split into two chapters and a fair amount of material on the angular momentum properties of Slater determinants has been added to the new Chapter 4.

The discussion of the spin angular momentum properties of closed shell Slater determinants in Appendix B has been extended to include orbital angular momentum. Several typos have also been corrected in Appendix B.

The Chapter 1 from the last revision is in the process of being split into two chapters. After the discussion of hydrogen-like atoms has been completed, the development will focus on the basics of atomic and molecular spectroscopy.

Due to the large number of equations, the automatic numbering system of DocBook has been implemented. See the development notes for details.

A new appendix has been created in which example calculations and details on equations in the main text will be presented. Some material from this appendix may be moved to other chapters in the future.

Chapter 1 has undergone a fair amount of revising, and the equations involving the calculation of the matrix elements of one-electron operators has been moved to Chapter 2.

The search for typos has been postponed until the current development work on Chapter 1 and Appendix B has been completed.

In the example program freeMQM-1.cpp, the names of the basis set files H-6-31G*.dat, H-6-31G**.dat, He-6-31G*.dat, and He-6-31G**.dat have been changed to H-6-31Gx.txt, H-6-31Gxx.txt, He-6-31Gx.txt, and He-6-31Gxx.txt to allow them to be used on Windows systems. In addition, a platform dependent instability has been observed in the calculation of the molecular hydrogen ground state energy when one chooses to use the 6-31G** basis set (i.e., H-6-31Gxx.txt). The p-type polarization functions (L = 1) in the 6-31G** basis set appear to prevent the program from finding a solution on some platforms. The program, freeMQM-1, ran flawlessly when compiled with gcc on a Pentium II machine running Redhat Linux 8.0 for both the Hartree-Fock calculation and the density functional theory calculation. The program fails to find a solution for some values of the interatomic bond distance, such as the default value of 1.40 a.u., when compiled with gcc on a Mobile AMD64 machine running Fedora Core 3 x86_64. It also fails to find a solution for all values of the interatomic bond distance on a Mobile AMD64 machine using the cygwin gcc compiler on Windows XP. The program converges to an incorrect solution on some systems when the 6-31G** basis set is used in a Hartree-Fock calculation. Although the ground state of the hydrogen molecule is a  $\Sigma$ state, one would hope that the program would to be able to use a complete set of basis functions in the search for a solution, and let the program find that the expansion coefficients are zero for some functions as part of the solution, i.e., C[I]=0. This appeared to be the case on the Pentium II system running Redhat 8.0, since, in spite of intensive testing over a very broad range of input values, reasonable solutions were always produced and no anomalies observed. This system was used to produce the numbers discussed in the tutorial. Those numbers, however, were generated during the time between September 2003 and December 2003, and it is possible that a bug has been introduced since then. Although the problem only appears when the polarization functions in 6-31G** are used, it is, of course, unsatisfactory that the same program can appear to be completely robust on one system, and manifestly pathological on another. Since the original system is not currently available, and because demonstrating the use of polarization functions in the calculation of the ground state energy of two-electron systems, a conceptually trivial extension of the problem, is not a priority of this tutorial, the tracking of the bug in the program will not be pursued at this time.

Many typographical errors have been corrected in Chapter 2, along with other minor corrections and additions. During the next couple of weeks, more material will be added to the sections on angular momentum in many-electron atoms and molecules, in addition to correcting typographical errors in other chapters.

Many typographical errors have been corrected in Chapter 1, along with other minor corrections and additions.

Minor corrections and additions.

The development has been temporarily diverted to the basics of molecular spectroscopy with the intention of returning focus to exact-exchange methods and TDDFT immediately afterward. The Jmol applet has been updated and probably will be updated regularly. In addition, a substantial number of corrections and additions have been made.

Chapter 2.1, on the formalism of density-functional theory, has been expanded and split into two new Chapters 2.1 and 2.2; plus substantial corrections and additions. The development will now focus on exact-exchange methods.

Additional material regarding the Hartree-Fock theory has been added to Sections 1.1 and 1.2. Introduction to Kohn-Sham theory is in development; plus minor corrections and additions

Introduction to density-functional theory has begun development; plus minor corrections and additions.

Minor corrections and additions.

A few small changes to the example program freeMQM-1.cpp, including more useful output information.

Sections on exact-exchange methods and TDDFT have begun development; plus minor changes and corrections.

Perdew, Zunger correlation functional PZ81 and the Perdew, Burke, Ernzerhof exchange functional PBE have been added to the functional routine functionals.cpp to allow comparisons with various ab initio packages.

Minor corrections and additions.

Minor corrections and additions.

First draft.