CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
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2 The quantum Monte Carlo method<br />
The correlated motion <strong>of</strong> electrons plays a crucial role in the aggregation <strong>of</strong> atoms into molecules<br />
and solids, in electronic transport properties and in many other important physical phenomena. Ab<br />
initio electronic structure calculations, in which the properties <strong>of</strong> such correlated electron systems are<br />
computed from first principles, are a vital tool in modern condensed matter physics and molecular<br />
quantum chemistry. Currently the most popular way to include the effects <strong>of</strong> electron correlation in<br />
these calculations is density functional theory (DFT). This method is in principle exact, in reality fast<br />
and <strong>of</strong>ten very accurate, but does have a certain number <strong>of</strong> well-known limitations. In particular, with<br />
only limited knowledge available concerning the exact mathematical form <strong>of</strong> the so-called exchange–<br />
correlation (XC) functional, the accuracy <strong>of</strong> the approximate form <strong>of</strong> the theory is nonuniform and<br />
nonuniversal, and there are important classes <strong>of</strong> materials for which it gives qualitatively wrong<br />
answers.<br />
An important and complementary alternative for situations where accuracy is paramount is the quantum<br />
Monte Carlo (QMC) method, which has many attractive features for probing the electronic<br />
structure <strong>of</strong> real systems. It is an explicitly many-body method, applicable to both finite and periodic<br />
systems, which takes electron correlation into account from the outset. It gives consistent, highly accurate<br />
results while at the same time exhibiting favourable scaling <strong>of</strong> computational cost with system<br />
size. This is in sharp contrast to the accurate methods used in mainstream quantum chemistry, such<br />
as configuration interaction or coupled-cluster theory, which are impractical for anything other than<br />
small molecules, and cannot generally be applied to condensed matter problems.<br />
The use <strong>of</strong> QMC was greatly hampered over its first two decades <strong>of</strong> existence by a combination<br />
<strong>of</strong> insufficient computer power and a lack <strong>of</strong> available, efficient QMC computer programs general<br />
enough to treat a similar range <strong>of</strong> problems to regular DFT codes. Fast parallel computers are now<br />
widespread, and you are now in possession <strong>of</strong> just such a computer program, which is capable <strong>of</strong><br />
carrying out QMC calculations for a wide range <strong>of</strong> interesting chemical and physical problems on a<br />
variety <strong>of</strong> computational hardware. As a bonus, casino is capable <strong>of</strong> exploiting with essentially perfect<br />
parallel efficiency as many processors as you like—a great asset in this era <strong>of</strong> petascale computing<br />
where machines with hundreds <strong>of</strong> thousands or even millions <strong>of</strong> cores are beginning to appear. casino<br />
has been designed to make the power <strong>of</strong> the QMC method available to everyone and we hope you<br />
enjoy using it.<br />
3 Miscellaneous issues<br />
3.1 Support<br />
casino has documentation and examples, etc., but it is a research code, and learning how to use it<br />
is a significant task. This is particularly the case if the user does not have relevant experience, such<br />
as familiarity with the theory <strong>of</strong> variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC)<br />
calculations and knowledge <strong>of</strong> DFT or Hartree–Fock (HF) methods for atoms, molecules and solids.<br />
We have found that supporting users can take up a large amount <strong>of</strong> our time and so we have to<br />
limit the number <strong>of</strong> groups that we work with directly. Most users need quite a lot <strong>of</strong> help and their<br />
projects turn into collaborations, but <strong>of</strong> course we cannot enter into too many projects <strong>of</strong> this type<br />
as our time is limited. We <strong>of</strong>ten have people visiting Cambridge to learn about the codes and how to<br />
do calculations, and this seems to work well.<br />
Beginning in 2006 we also organize annual summer schools at MDT’s Tuscan monastery (see vallico.<br />
net/tti/tti.html). The scientific side <strong>of</strong> these week-long events involves over 20 hours <strong>of</strong> lectures<br />
from the main authors <strong>of</strong> the code with plenty <strong>of</strong> hands-on tuition, and people who have attended<br />
these events have generally found them to be beneficial.<br />
Since June 2013, the best place for having your questions about casino answered is over at the<br />
casino discussion forum vallico.net/casino-forum. Unless you have a good reason for thinking<br />
some particular individual can help you, this forum should be the first place you ask for help. This<br />
supersedes the earlier mailing list casino-users ‘at’ tcm.phy.cam.ac.uk which still exists but is<br />
now only used by the casino administrators for announcements <strong>of</strong>, e.g., events and new versions <strong>of</strong><br />
the code.<br />
2