# PyQuante: Python Quantum Chemistry

## Overview

PyQuante (Sourceforge Project Page) is an open-source suite of programs for developing quantum chemistry methods. The program is written in the Python programming language, but has many "rate-determining" modules also written in C for speed. The resulting code, though not as fast as Jaguar, NWChem, Gaussian, or MPQC, is much easier to understand and modify. The goal of this software is not necessarily to provide a working quantum chemistry program (although it will hopefully do that), but rather to provide a well-engineered set of tools so that scientists can construct their own quantum chemistry programs without going through the tedium of having to write every low-level routine.

### Current features

• Hartree-Fock: Restriced closed-shell HF and unrestricted open-shell HF;
• DFT: LDA (SVWN, Xalpha) and GGA (BLYP) functionals;
• Optimized-effective potential DFT;
• Two electron integrals computed using Huzinaga, Rys, or Head-Gordon/Pople techniques; C and Python interfaces to all of these programs;
• MINDO/3 semiempirical energies and forces;
• CI-Singles excited states;
• DIIS convergence acceleration;
• Second-order Moller-Plesset (MP2) perturbation theory.

### Getting Started

See the cookbook for short snippets to get started, and also see the tests subdirectory of the code distribution. Subscription to the pyquante-users mailing list is highly recommended for further nsupport. Additionally, people interested in day-to-day development issues in PyQuante are urged to subscribe to the pyquante-devel mailing list.

The software is released under the modified BSD license, which means that everyone is free to download, use, and modify the code without charge.

The program is available in tarball form from the PyQuante Sourceforge Project Page. The SVN archive for the program is also at Sourceforge, and is recommended for anyone wanting to stay current with the codebase; information on how to access the SVN archive is available here.

### Prerequisites

You will need to have a recent (2.3 or later) version of Python installed on your computer; this can be installed by following instructions on the Python Website, and binary packages exist for most platforms. Additionally, you need the multidimensional arrays and linear algebra libraries provided by either Numeric or numpy; both of these can be downloaded from the Numpy Website.

Given the choice between Numeric and Numpy, please use Numpy. The library is much newer, and future developments will center on this library. Although we will make every effort to continue supporting Numeric, Numpy is what we will use as the default, and should be much more stable with PyQuante.

Note: If you're installing on a Macintosh, I recommend the Framework binaries of Python and Numpy from the Pythonmac Packages Directory.

On Ubuntu and other Linux distros, several additional packages may be required, including python-dev, python-numpy, and possibly python-matplotlib.

### Building the Code

Much of the code is written in Python, and thus is platform independent. The rest of the code now uses the python distutils procedures for building the C modules:

% (sudo) python setup.py install


and the code should build and install properly. I've tested this on Linux, Windows/Cygwin, and Macintosh OS X. Installing the module like tsetxkbmap -option ctrl:nocaps # Make Caps Lock a Control key his will insure that the modules are installed where Python can find them.

However, the above assumes that you have write priviledges in the Python site-packages directory, possibly via the _sudo_ command. If you do not have access to these directories, create an install directory where you do have access and pass this directory to the install process:

% mkdir ~/pyquante_lib
% python setup.py install --install-lib=~/pyquante_lib
% export PYTHONPATH=~/pyquante_lib:\$PYTHONPATH


Email me (rmuller@sandia.gov) if you need additional help.

## Using the Code

### Cookbook

#### Specifying a molecule

You can specify a molecule using the following code:

>>> from PyQuante.Molecule import Molecule
>>> h2 = Molecule('h2',[(1,(0,0,0)),(1,(1.4,0,0))])


#### Simple HF calculation

Using the above definition, you can run a simple HF calculation via:

>>> from PyQuante.hartree_fock import rhf
>>> en,orbe,orbs = rhf(h2)
>>> print "HF Energy = ",en


We're also working on a more object-oriented interface (called PyQuante 2) that will hopefully decrease the amount of duplicated code in the project. You can run the same calculation as above using:

>>> from PyQuante import SCF
>>> solver = SCF(h2,method="HF")
>>> solver.iterate()
>>> print "HF Result = ",solver.energy


With the new solvers, you can run with an alternate basis set (say, STO-3G), via:

>>> solver = SCF(h2,method="HF",basis="sto-3g")
>>> solver.iterate()
>>> print "HF Result = ",solver.energy


At this geometry (R=1.4 bohr) this should produce an energy of -1.1313 hartrees. Note that you may also import Molecule and SCF directly from the PyQuante namespace now.

#### Simple DFT calculation

We can run a DFT calculation on the same molecule by running the commands:

>>> from PyQuante.dft import dft
>>> en,orbe,orbs = dft(h2)


This will produce an energy of -1.1353 hartrees. Again, the 6-31G** basis set is used by default. In DFT calculations, the functional defaults to SVWN (LDA). To use a different functional, you can type:

>>> en,orbe,orbs = dft(h2,functional='BLYP')


which will produce an energy of -1.1665 hartrees.

With the new solvers this calculation could be run via:

>>> from PyQuante import SCF
>>> lda = SCF(h2,method="DFT")
>>> lda.iterate()
>>> blyp = SCF(h2,method="DFT",functional="BLYP")
>>> blyp.iterate()
>>> print "DFT Results: LDA = %f  BLYP = %f" % (lda.energy,blyp.energy)


### Users Guide

Here we provide a bit more detail about the PyQuante functions.

#### Molecules

PyQuante programs use the Molecule object to contain the information about the molecule - the atoms, the charge, and the multiplicity. The syntax for Molecule is:

>>> Molecule(name,atomlist,**opts)


The atomlist is a list of atomic numbers and a tuple with the x,y,z coordinates. Here's an example for constructing a molecule object for water:

>>> h2o=Molecule('h2o',[(8,(0,0,0)),(1,(1.0,0,0)),(1,(0,1.0,0))],units = 'Angstrom')


(of course the bond-angle is 90 degrees here, and is thus completely wrong, but this is only an example). Here's an example for the hydroxide ion that shows the use of the charge field:

>>> oh = Molecule('OH-',[(8,(0,0,0)),(1,(0.96,0,0))], units = 'Angstrom', charge=-1)


Here's an example for the NO molecule that shows the use of the multiplicity field:

>>> no = Molecule('NO', [(7,(0,0,0)),(8,(2.12955,0,0))],multiplicity=2)


As of version 1.5.1, you may construct molecules using the atomic symbol instead of the atomic number, e.g.:

>>> h2o=Molecule('h2o',[('O',(0,0,0)), ('H',(1.0,0,0)),('H',(0,1.0,0))],units = 'Angstrom')


Currently, the semiempirical code uses an extended verion of the Molecule object that adds a variety of additional features. Upcoming releases will hopefully unify the use of the Molecule between the HF, DFT, and semiempirical codes.

As of version 1.6, you can directly import Molecule from the PyQuante module:

>>> from PyQuante import Molecule


#### Basis Sets

Basis functions are constructed using the CGBF (contracted Gaussian basis function) object, which, in turn, uses the PGBF (primitive Gaussian basis function) object. Basis sets are simply lists of CGBF's. In the Ints module there is a convenience function getbasis that constructs basis sets for different molecules. The syntax for the getbasis function is:

>>> bfs = getbasis(molecule,basis_data=None)


The basis data can be input from a number of data files in the PyQuante suite. Here are some of the more commonly used basis sets:

• basis_631ss The Pople 6-31G** basis set
• basis_sto3g The Pople STO-3G basis set
• basis_321 The Pople 3-21G basis set
• basis_ccpvtz The Dunning cc-pVTZ basis set
• basis_ccpvtzmf The Dunning cc-pVTZ(-f) basis set (cc-pVTZ without f-functions)

For, example, to construct a basis set for the h2o object for water created above, we would call:

>>> from basis_631ss import basis_data
>>> bfs = getbasis(h2o,basis_data)


If the basis_data argument is omitted, the program will default to 6-31G**. As of version 1.6, you may now specify a string for the basis_data argument, e.g. "6-31G**" so you may do things like:

>>> bfs = getbasis(h2o,'6-31G**')
>>> bfs2 = getbasis(h2o,'sto-3g')


and so on. Use PyQuante.Basis.Tools.basis_map.keys() for a list of the supported basis strings.

#### Output

If you want to check the output of PyQuante and to have a feedback of what's happening, you can use the configure_output routine before launching the calculation:

>>> from PyQuante import configure_output
>>> configure_output()


This will display to the standar output the log of PyQuante. You can also specify other ways to handle the output:

>>> configure_output("calc.log") # save also in a log file and display on stdout
>>> configure_output(stream=sys.stderr) # Redirect the output on a generic stream
>>> configure_output(filename="h2.log", stream=None) # Suppress stream output


Internally, the output is handled using the logging module (available in the standard library), you can access the logger used by PyQuante in this way:

>>> import logging
>>> logger = logging.getLogger("pyquante")


Further information about using Loggers: http://docs.python.org/library/logging.html

#### Integrals

##### One-electron integrals

The one-electron integrals consist of the overlap matrix S, the kinetic energy matrix T, and the nuclear attraction matrix V. The latter two are often combined into the one-electron Hamiltonian h.

There are a number of helper functions in the Ints module:

• getT: Form the kinetic energy matrix T
• getS: Form the overlap matrix S
• getV: Form the nuclear attraction matrix V
• get1ints: Form and return S,h
• getints: Form and return S,h,Ints, where Ints are the two-electron integrals (see below).

These functions actually call instance functions of the CGBF objects, which can themselves be used individually. Some of the instance functions in the CGBF module use functions in the pyints and cints modules.

##### Two-electron integrals

The two-electron integrals consist of the electron-electron Coulomb repulsion interactions. The easiest way to construct these is to use the functions in the Ints module

• get2ints: Form and return Ints, where Ints are the two-electron integrals (see below).
• getints: Form and return S,h,Ints, where Ints are the two-electron integrals.

The Ints object (not to be confused with the Ints module, which is just a collection of helper functions) consists of a list of the two-electron integrals.

There are actually three different methods to computing the two-electron integrals, and the helper functions in the Ints module default to one of these functions.

• Huzinaga's original method for computing integrals over Gaussians.
• Head-Gordon and Pople's recurrance relations.

There are python versions of these methods implemented in the modules pyints, rys, and hgp, respectively. For speed, there are also C-versions of these modules in cints, crys, and chgp. The program defaults to the Coulomb repulsion routines in crys, since these are the fastest (although recent improvements to chgp make it not much slower).

The coulomb_repulsion function is the same in all six modules:

>>> integral = coulomb_repulsion((xa,ya,za),norma,(la,ma,na),alphaa,
(xb,yb,zb),normb,(lb,mb,nb),alphab,
(xc,yc,zc),normc,(lc,mc,nc),alphac,


This routine computes the Coulomb repulsion integral between four basis functions. The terms xi, yi, zi are the origins of the different basis functions. The terms normi are the normalization constants for the basis function. The terms li, mi, ni are the exponents of the Cartesian powers for the basis function. And the terms alphai are the Gaussian exponents.

#### Hartree-Fock Calculations

This section is under construction. In the meantime, see the PyQuante Cookbook recipe Simple HF calculation for an example of a HF calculation using PyQuante.

#### Density Functional Theory Calculations

This section is under construction. In the meantime, see the PyQuante Cookbook recipe Simple DFT calculation for an example of a DFT calculation using PyQuante.

#### Semiempirical Calculations

This section is under construction.