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QUANTUM MONTE CARLO AND THE CASINO
PROGRAM
How to calculate the electronic structure and
properties of matter from first principles using random
numbers
Theory of Condensed Matter
Group Cavendish Laboratory, University of Cambridge,
UK
RESEARCH IN THE NEEDS AND TOWLER GROUPS
Richard
Needs, John Trail, Neil Drummond, Pablo Lopez Rios,
Zoltan Radnai, Alexander Badinski, Matthew Brown, Graham
Spink, Andrew Morris, Gareth Conduit.
The correlated motion of electrons
plays a crucial role in the aggregation of atoms into
molecules and solids, in electronic transport properties
and in many other important physical phenomena. Ab
initio electronic structure calculations in which
the properties of such correlated electron systems are
computed from first principles are a vital tool in
modern condensed matter physics and molecular quantum
chemistry. Currently the most popular way to include the
effects of electron correlation in these calculations is
density functional theory. This method is in
principle exact, in reality fast and often very
accurate, but does have a certain number of well-known
limitations. In particular, with only limited knowledge
available concerning the exact mathematical form of the
so-called exchange-correlation functional, the accuracy
of the approximate form of the theory is non-uniform and
non-universal, and there are important classes of
materials for which it gives qualitatively wrong
answers. An important and complementary alternative for
situations where accuracy is paramount is the quantum
Monte Carlo (QMC) method, which has many attractive
features for probing the electronic structure of real
systems. It is an explicitly many-body method which
takes electron correlation into account from the outset.
It gives consistent, highly accurate results while at
the same time exhibiting favourable scaling of
computational cost with system size. This is in sharp
contrast to the accurate methods used in mainstream
quantum chemistry such as configuration interaction or
coupled cluster theory which are impractical for
anything other than small molecules. The use of quantum
Monte Carlo has been greatly hampered over the last two
decades by a combination of insufficient computer power
and a lack of efficient computer programs of sufficient
generality available to the community. Fast parallel
computers are now widespread, and over the last few
years we have created a powerful and general QMC
computer program to carry out such calculations - the
first version of 'CASINO' was distributed in the summer
of 2000. The full power of the quantum Monte Carlo
method is now available!
The
development of new algorithms and methods useful in QMC
calculations, in particular : - the treatment
of forces -
the calculation of conductivities -
improved techniques for trial
wave function optimization - the treatment of non-collinear
spins - QMC description of magnetic
properties - pseudopotentials for many-electron wave
function calculations - orbital optimization -
relativistic effects - improved sampling
methods - implementation and evaluation of new
basis function types (e.g. splines etc..) -
development of QMC algorithms with improved scaling of
computational cost with system size (i.e. better than
N3) - creation of new
functionals for DFT calculations from studies of
pair-correlation functions and exchange-correlation
holes in real materials.
The
use of QMC to understand fundamental properties of
correlated electron systems : - dynamical
correlation functions in the homogeneous
electron gas - the phase diagram of the electron-hole
system
Cross-disciplinary
cooperation : - the promotion of interaction
and mutual comprehension between the traditionally
disparate yet in reality widely-overlapping theoretical
chemistry, computational condensed matter theory and
many-body theory communities.
Software development : - making
the 'CASINO' distribution as lovely
as possible.
How do I find
out more?
A very non-technical explanation of solid-state
quantum Monte Carlo (PDF) can be found online here.
For more technical questions, here is a review
article (PDF) by Matthew Foulkes, Lubos Mitas,
Richard Needs and Guna Rajagopal.
A more recent short review article (which had its origin as a Psi-k Newsletter "Scientific Highlight of the Month" - it says here) entitled The quantum Monte Carlo method by Mike Towler can be found here.
The freescience.info site has a large collection of material about quantum Monte Carlo here.
What are other
people in the field doing?
Laughably incomplete list
of references to Quantum Monte Carlo research around
the world.
Can I come and
do research in your group?
Yes! Particularly if you have your own
money, although this may not be necessary. Enquiries
with CV to Richard Needs or Mike Towler.
Workshops and
conferences
We organized a workshop entitled "The Diffusion Monte
Carlo Method" at CECAM, Lyon in France from 19th-21st
September 2002. Click here
for further details.
An informal workshop entitled "Quantum Monte Carlo in
the Apuan Alps" took place 24th-31st July 2005 at the
Towler Institute in Vallico Sotto, Tuscany, Italy. The
second of the conferences in this series and a QMC
summer school were held in July and August 2006. More
details available from the Institute
web page.. If you would like to participate in
future conferences at this venue or use the place for
your own conference, contact Mike Towler.
CASINO
The Cambridge quantum Monte Carlo
code
Our code that we use to perform quantum Monte Carlo
calculations is called 'CASINO'. The current program was
written by R.J.Needs,
M.D.Towler,
N.D.Drummond
and P.Lopez Rios. Important contributions to the initial
development of QMC in this group up to 1996 were made by
G.Rajagopal and A.J.Williamson. Additional contributions
to CASINO by the following people are gratefully
acknowledged: A.R.Porter, R.Q.Hood, A.J.Williamson,
W.K.Leung, G.J.Brown, D.Alfè, C.Pickard, R.Gaudoin,
B.Wood, A.Ma, R.Maezono, J.Trail, A.Badinski and
P.R.C.Kent.
The citation required in any publication quoting
results obtained with the current version of CASINO is
as follows: R.J. Needs, M.D. Towler, N.D.
Drummond and P. Lopez Rios, CASINO version 2.3 User
Manual, University of Cambridge, Cambridge (2008).
Note that in order not to offend Italian speakers we
prefer to stress the final syllable and write the name
of the program as CASINÒ, but clearly the user will be
the final judge of whether this modification is
justified.
Here is a list of some of the current capabilities of
the code.
current version : 2.3
(10.2008)
Variational Monte Carlo (including variance
minimization)
Fixed-node diffusion Monte Carlo (pure or
branching)
Applicable to finite systems such as atoms and
molecules but also to systems with periodic boundary
conditions in 1, 2 or 3 dimensions (polymers,
slabs/surfaces, crystalline solids) with any crystal
structure and in metallic or insulating phases. The
code is also capable of treating both fluid and
crystalline phases of the homogeneous electron gas
(2D, 2D slab, or 3D) and also systems containing both
electrons and 'holes' i.e. positively charged paricles
of variable mass (2D, 3D, and 2D bilayers with
separate layers of electrons and holes ; fluid,
crystalline, and excitonic insulator phases.).
The code may use a variety of basis sets to expand
the orbitals in the determinantal part of the
many-electron trial wave function: (1) s,
sp, p, d, f or g
Gaussian basis functions centred on atoms or elsewhere
(aperiodic or periodic systems) with cusp corrections
in the case of all-electron calculations. (2)
plane-waves (periodic systems) (3) atomic
calculations with numerical orbitals interpolated from
a radial grid. (4) blip functions i.e. cubic
splines on a regular grid (periodic systems)
Uses very flexible Slater-Jastrow many-electron
wave functions, where the Slater part may consist of
multiple determinants. Advanced scheme for handling
partial occupation of degenerate orbitals in building
each determinant.
It is linked to various one-electron packages via
a generic interface for each basis set type, which
allows us to use a variety of different software to
generate trial wave functions via density functional
theory or Hartree-Fock calculations. In certain cases
(e.g. excited states) it is also desirable to generate
multi-determinant trial wave functions via standard
quantum chemistry methods such as
CIS/CISD/TD-DFT/CASSCF methods. With Gaussian basis
sets we have used the following programs to calculate
trial wave functions: (1) CRYSTAL (95/98/03). DFT/HF for molecules and systems
periodic in 1,2 or 3 dimensions. (2) GAUSSIAN
(94/98/03). Huge quantum chemistry package for
molecules. (3) TURBOMOLE For
calculations with blip function or plane-wave basis
sets we use the PWSCF, ABINIT, CASTEP, k207 and GP
packages. The linear scaling code ONETEP is also
supported. Thus, any system that can be treated with
any of the above programs can now in principle also be
handled within QMC. Note that it is also planned at
some stage to look at implementing links to other
well-known DFT codes. If you wish to make a generous
offer to assist with such projects, then please email
Mike Towler, who will be pleased to hear from you.
Computation of excitation energies corresponding
to either promotion or addition/subtraction of
electrons.
Computation of distribution functions such as the
pair correlation function and density matrices.
Periodic Coulomb interactions computed either with
standard Ewald methods or with our MPC
(modified periodic Coulomb) interaction which is both
considerably faster than the Ewald method and exhibits
much smaller 'finite-size effects'.
Non-local pseudopotentials with s,
p, d non-locality, and core polarization
potentials.
Spin-polarized calculations (e.g. of magnetic
solids).
Backflow corrections.
The code has been written entirely in Fortran90
using modern software design methods, and is supposed
to be easy to use, easy to install, and easy to read
and understand. It contains a self-documenting help
system and comes with a helpful manual and examples.
It is trivially transferable across a variety of
hardware (including workstations, weakly-linked
clusters, massively parallel supercomputers, laptops,
PCs, and probably Palm Pilots). It uses MPI to
function on parallel machines, but will work without
it on single processors.
The speed of the code scales essentially linearly
with the number of processors on a parallel computer.
In principle, the time taken to calculate the
total energy to within a specified error bar with a
QMC calculation scales (very roughly) as the third
power of the system size. Simply by using localized
orbitals and localized basis sets this scaling can be
improved. For problems where the total energy per
atom or per formula unit is to be computed
in a periodic system (e.g. for calculating cohesive
energies in solids) then CASINO can be made to scale
independently of system size. If the objective
is to calculate the total energy per simulation cell
or per molecule, then the code can be made to scale
quadratically with system size. Note that in
neither case is this "linear scaling" as might be
inferred from the literature.
How to get a
copy of the code
The code is normally made available on request
subject to certain conditions of use enforced by the
user signing an agreement.
No payment is requested from new academic users wishing
to use the code for non-profit making purposes (but of
course we appreciate any donations.). Profit-making
bodies (for whom the clause about profit-making purposes
in the CASINO agreement is deleted) should enquire for
current pricing. Due to the large volume of enquiries
and support requests, and a shortage of staff to deal
with them, it is appreciated if new users do not request
an extended email correspondence course when learning
how to use the code. Please be aware that we run CASINO
summer
schools in our monastery
in Tuscany every summer and we strongly recommend you
attend these.
Please email Mike Towler if you wish to obtain a copy
of the code, outlining briefy the nature of your
interest. As of July 2007, there are 152 registered users.
Computational
note
QMC calculations can be very computationally
demanding. The demand varies according to the system and
the statistical accuracy required: atomic calculations
typically require only a few minutes on a PC, whereas
calculating the excitonic properties of complex
crystalline solids may require a great many CPU hours of
supercomputer time.
QMC exhibits a high degree of scalability: demands on
memory and disk are low, compared with high-order
quantum chemistry methods. It is relatively easy to
obtain 99% parallel efficiency on a 512 node parallel
machine. CASINO has been mounted on many computers
including machines in the Cambridge-Cranfield
High-Performance Computing Centre and the UK
national parallel facilities at Daresbury and Manchester.
The code has been tested and run on the following
hardware :
Single-processor
machines :
DEC Alpha
SGI Octane
Linux PCs (with Intel ifc-ifort-iforte/Lahey
lf95/NAG f95/Portland pgf90/GNU g95 compilers. Beware
early buggy versions of ifort, and note that f95
produces slow executables and g95 incredibly slow
executables.
Macs with the g95 compiler
Parallel machines :
Cray T3E
Hitachi SR2201
SGI Origin 2000/3000
SGI Altix (Itanium2)
IBM SP3
IBM P-series
Fujitsu Primepower
SunFire Galaxy
Opteron clusters
Alpha multiprocessors
Linux multiprocessors and clusters (with above
compilers)
Mailing
list
We have an online
mailing list 'casino_users at tcm.phy.cam.ac.uk' which
is used both for occasional announcements of code
updates and new distributions and for general
discussions of quantum Monte Carlo and the use of
CASINO. If you wish to join this list then mail mdt26 at
cam.ac.uk .
Pseudopotential/Jastrow factor
library
CASINO has its very
own online library of pseudopotentials developed within
our group by John Trail, Yoonseok Lee, Mike Towler and
Richard Needs. Clicking on the desired element in the
graphical periodic table will reveal the pseudopotential
in KASINO grid format, and lots of associated
information (expansion of the pseudopotential in
Gaussians times power of r in both CRYSTAL9X/03
and GAUSSIAN98/03 format/atomic wavefunctions on a grid
for ground state and excited states/energy information
etc..). Use of this information is limited to CASINO
users at present - contact Mike Towler to find out the
URL.
More details concerning TCM quantum Monte Carlo
projects done off the back of the CRYSTAL electronic
structure package may be found online at Mike Towler's
CRYSTAL
resources page.
The TCM quantum
Monte Carlo online reference library
Phase diagram of the low-density two-dimensional homogeneous electron gas
N.D. Drummond and R.J. Needs
Phys. Rev. Lett. 102, 126402 (2009)
[PDF] (paper)
[PDF] (auxiliary material)
Quantum Monte Carlo studies of covalent and metallic clusters: accuracy of density functional approximations
C.R. Hsing, C.M. Wei, N.D. Drummond and R.J. Needs
Phys. Rev. B 79, 245401 (2009)
[download]
Quantum Monte Carlo study of the ground state of the
two-dimensional Fermi fluid
N.D. Drummond and R.J. Needs
Phys. Rev. B 79, 085414 (2009)
[PDF]
Energy derivatives in quantum Monte Carlo involving the zero-variance property
A. Badinski, J.R. Trail, and R.J. Needs
J. Chem. Phys 129, 224101 (2008)
[download]
Diffusion Monte Carlo study of a valley degenerate electron gas and application to quantum dots
G.J. Conduit and P.D. Haynes
Phys. Rev. B 78, 195310 (2008)
[PDF]
Finite-size errors in continuum quantum Monte Carlo calculations
N.D. Drummond, R.J. Needs, A. Sorouri and W.M.C. Foulkes
Phys. Rev. B 78, 125106 (2008)
[PDF]
Quantum Monte Carlo study of porphyrin transition metal complexes
J. Koseki, R. Maezono, M. Tachikawa, M.D. Towler and R.J. Needs
J. Chem. Phys. 129, 085103 (2008)
[PDF]
Spectroscopic data for the LiH molecule from pseudopotential quantum Monte Carlo calculations
J.R. Trail and R.J. Needs
J. Chem. Phys. 128, 204103 (2008)
[download]
Heavy-tailed random error in quantum Monte Carlo
J.R. Trail
Phys. Rev. E 77, 016703 (2008).
[download]
Alternative sampling for variational quantum Monte Carlo
J.R. Trail
Phys. Rev. E 77, 016704 (2008).
[download]
Nodal Pulay terms for accurate diffusion quantum Monte Carlo forces
A. Badinski, P.D. Haynes and R.J. Needs
Phys. Rev. B 77 085111 (2008).
[download]
Accurate forces in quantum Monte Carlo calculations with non-local pseudopotentials
A. Badinski and R.J. Needs
Phys. Rev. E 76, 036707 (2007).
[download]
Dissociation energy of the water dimer from quantum Monte Carlo calculations
I.G. Gurtubay and R.J. Needs
J. Chem. Phys 127, 124306 (2007).
[download]
Van der Waals interactions between thin metallic wires and layers
N.D. Drummond and R.J. Needs
Phys. Rev. Lett. 99, 166401 (2007).
[PDF]
Accurate forces in quantum Monte Carlo calculations with non-local pseudopotentials
A. Badinski and R.J. Needs
Phys. Rev. E 76, 036707 (2007).
Energies of the first-row atoms from quantum Monte Carlo
M.D. Brown, J.R. Trail, P. Lopez Rios and R.J. Needs
J. Chem. Phys. 126, 224110 (2007).
[download]
Fragmentation method combined with quantum Monte Carlo calculations
R. Maezono, H. Watanabe, S. Tanaka, M.D. Towler, and R.J. Needs
J. Phys. Soc. Jpn., 76 064301 (2007).
[download]
Equation of state and Raman
frequency of diamond from quantum Monte Carlo
R. Maezono, A. Ma, M.D.
Towler, and R.J. Needs
Phys. Rev. Lett., 98, 025701 (2007) [PDF]
Inhomogeneous backflow
transformations in quantum Monte Carlo
P. Lopez Rios, A. Ma,
N.D. Drummond, M.D. Towler and R.J. Needs
Phys. Rev. E ,74, 066701 (2006) [PDF]
The Quantum Monte Carlo method
M.D.
Towler Phys. Stat. Solidi,243,
2573 (2006) [PDF]
Quantum Monte Carlo calculations
of the dissociation energy of the water dimer
N.A. Benedek, I.K. Snook,
M.D. Towler, and R.J. Needs J. Chem.
Phys., 125, 104302 (2006)
Quantum Monte Carlo study of the
Ne atom and the Ne+ ion N.D. Drummond, P. Lopez Rios, A. Ma, J.R.
Trail, G. Spink, M.D. Towler and R.J. Needs
J. Chem. Phys. 124, 224104
(2006). [PDF]
Quantum Monte Carlo calculations
of the disociation energies of three-electron
hemibonded radical cationic dimers I.G. Gurtubay, N.D. Drummond, M.D. Towler
and R.J. Needs J. Chem. Phys. 124,
024318 (2006). [PDF]
Quantum Monte Carlo, density
functional theory, and pair-potential studies of solid
neon N.D. Drummond and R.J. Needs
Submitted to Phys. Rev. B [PDF]
A variance-minimization scheme for
optimizing Jastrow factors N.D. Drummond
and R.J. Needs Phys. Rev. B 72, 085124
(2005) [PDF]
Electron emission from diamondoids
: a diffusion quantum Monte Carlo study
N.D. Drummond, A.J. Williamson, R.J. Needs
and G. Galli Phys. Rev. Lett 95, 096801
(2005) [PDF]
Quantum Monte Carlo calculation of
the structural properties and the B1-B2 phase
transition of MgO D. Alfè, M. Alfredsson,
J. Brodholt, M.J. Gillan, M.D. Towler and R.J. Needs
Phys. Rev. B 72, 014114 (2005)
[PDF]
Scheme for adding electron-nucleus
cusps to Gaussian orbitals A.Ma, N.D.
Drummond, M.D. Towler and R.J. Needs J. Chem.
Phys. 122, 224322 (2005). [PDF]
All-electron diffusion quantum
Monte Carlo calculations for the noble gas atoms He to
Xe A. Ma, N.D. Drummond, M.D. Towler and
R.J. Needs Phys. Rev. E, 71, 066704
(2005) [PDF]
Diamond and betatin structures of
Si studied with quantum Monte Carlo calculations
D. Alfè, M.J. Gillan, M.D. Towler and R.J.
Needs Phys. Rev. B, 70 214102 (2004).
[PDF]
Smooth relativistic Hartree-Fock
pseudopotentials for H to Ba and Lu to Hg
J.R. Trail and R.J. Needs J. Chem.
Phys. 122, 174109 (2005). [PDF]
Norm-conserving Hartree-Fock
pseudopotentials and their asymptotic behaviour
J.R. Trail and R.J. Needs J. Chem.
Phys. 122, 014112 (2005). [PDF]
Exciton and biexciton energies in
bilayer systems M.Y.J. Tan, N.D. Drummond
and R.J. Needs Phys. Rev. B 71, 033303
(2005). [PDF]
Interpretation of Hund's
multiplicity rule for the carbon atom K.
Hongo, R. Maezono, Y. Kawazoe, H. Yasuhara, M.D.
Towler and R.J. Needs J. Chem. Phys.,
121, 7144 (2004) [PDF]
Jastrow correlation factor for
atoms, molecules, and solids N.D. Drummond,
M.D. Towler and R.J. Needs Phys. Rev. B
70, 235119 (2004) [PDF]
Coulomb finite-size effects in
quasi-2d systems B. Wood, W.M.C. Foulkes,
M.D. Towler and N.D. Drummond J. Phys.: Cond.
Mat. 16, 891 (2004) [PDF]
Diffusion quantum Monte Carlo
study of three-dimensional Wigner crystals
N.D. Drummond, Z. Radnai, J.R. Trail, M. D.
Towler, and R.J. Needs Phys. Rev. B 69,
085116 (2004) [PDF]
Quantum Monte Carlo and the CASINO
program : highly accurate total energy calculations
for finite and periodic systems M.D.
Towler Psi-k Newsletter "Scientific Highlight of
the Month" December 2003 [PDF]
Quantum Monte Carlo study of the
optical and diffusive properties of the vacancy defect
in diamond R. Q. Hood, P. R. C. Kent, R. J.
Needs, and P. R. Briddon Phys. Rev. Lett.91, 076403 (2003) [PDF]
Stability and aromaticity of
BiNi rings and fullerenes
Jon M. Matxain, Jesus M. Ugalde, M.D.
Towler and R.J. Needs J. Phys. Chem A107, 10004 (2003) [PDF]
Quantum Monte Carlo studies of
density functional theory M. Nekovee,
W.M.C. Foulkes, and R.J. Needs Mathematics and
Computers in Simulation62, 463
(2003) [PDF]
Quantum Monte Carlo study of
sodium Ryo Maezono, M.D. Towler, Y. Lee and
R.J. Needs Phys. Rev. B68, 165103
(2003) [PDF]
Unrestricted Hartree-Fock theory
of Wigner crystals J.R. Trail, M.D. Towler
and R.J. Needs Phys. Rev. B68,
045107 (2003) [PDF]
.
Core-polarization potentials
for Si and Ti Y. Lee and R.J. Needs
Phys. Rev. B67, 035121
(2003) [PDF]
The diffusion quantum Monte Carlo
method: designing trial wave functions for NiO
R.J. Needs and M.D. Towler "Proceedings
of the 11th International Conference on Recent Progess
in Many-Body Theories", Eds. R.F. Bishop and N.R.
Walet, pp.435-444 (World Scientific, 2002).
Quantum Monte Carlo
calculations for excited electronic states
R.J. Needs, A.R. Porter and M.D.
Towler Recent Advances in Quantum Monte Carlo
Methods, II, eds. W.A. Lester, S.M. Rothstein and
S. Tanaka, pp.143-155 (World Scientific, 2002).
Quantum Monte Carlo in molecular
quantum chemistry and condensed matter physics
M.D. Towler and R.J. Needs "Quantum
Monte Carlo: Recent Advances and Common Problems in
Condensed Matter and Field Theory" (ETS, Pisa,
2001).
Quantum Monte Carlo
calculations for ground and excited states
R.J. Needs, P.R.C. Kent, A.R. Porter, M.D.
Towler and G. Rajagopal Int. J. Quant. Chem.86, 218 (2001) [PDF]
Quantum Monte Carlo analysis
of exchange and correlation in the strongly
inhomogeneous electron gas M. Nekovee,
W.M.C. Foulkes, and R.J. Needs Phys. Rev.
Lett.87, 036401 (2001). [PDF]
Excitons in small hydrogenated
silicon clusters. A.R. Porter, M.D. Towler
and R.J. Needs Phys. Rev. B64,
035320 (2001). [PDF]
Electronic excited-state wave
functions for quantum Monte Carlo: application to
silane and methane A.R. Porter, O.K.
Al-Mushadani, M.D. Towler and R.J. Needs J.
Chem. Phys.114, 7795 (2001) [PDF]
The inhomogeneous RPA and
many-electron trial functions R. Gaudoin, M.
Nekovee, W. M. C. Foulkes, R. J. Needs and G.
Rajagopal Phys. Rev. B63, 115115
(2001) [PDF]
Quantum Monte Carlo
simulations of solids (Review article)
W.M.C. Foulkes, L. Mitas, R.J. Needs and G.
Rajagopal Rev. Mod. Phys.73, 33
(2001) [PDF]
Pseudopotentials for
correlated electron calculations Y. Lee,
M.D. Towler, P.R.C. Kent, R.J. Needs and G.
Rajagopal Phys. Rev. B.62, 13347
(2000) [PDF]
Carbon clusters near the
crossover to fullerene stability P.R.C.
Kent, M.D. Towler, R.J. Needs and G.
Rajagopal Phys. Rev. B62, 15394
(2000) [PDF]
Minimum principles and level
splitting in quantum Monte Carlo excitation spectra:
application to diamond M.D. Towler, R.Q.
Hood and R.J. Needs Phys. Rev. B62,
2330-2337 (2000) [PDF]
Comment on "Quantum Monte
Carlo study of the dipole moment of CO"
K.C. Huang, R.J. Needs and G.
Rajagopal J. Chem. Phys.112, 4418
(2000) [PDF]
Calculations of silicon
self-interstitial defects W.K. Leung, R.J.
Needs, G. Rajagopal, S. Itoh and S. Ihara Phys.
Rev. Lett.83, 2351 (1999) [PDF]
Symmetry constraints and
variational principles in diffusion quantum Monte
Carlo calculations of excited-state
energies W.M.C. Foulkes, R.Q. Hood and R.J.
Needs Phys. Rev. B60, 4558
(1999) [PDF]
Monte Carlo energy and
variance minimization techniques for optimizing
many-body wave functions P.R.C. Kent, R.J.
Needs and G. Rajagopal Phys. Rev. B59, 12344 (1999) [PDF]
Finite size errors in quantum
many-body simulations of extended
systems P.R.C. Kent, R.Q. Hood, A.J.
Williamson, R.J. Needs, W.M.C. Foulkes and G.
Rajagopal Phys. Rev. B59, 1917
(1999) [PDF]
A quantum Monte Carlo approach
to the adiabatic connection method M.
Nekovee, W.M.C. Foulkes, A.J. Williamson, G. Rajagopal
and R.J. Needs Advances in Quantum
Chemistry, 343, 189 (1999) [PDF]
Quantum Monte Carlo
calculations of the one-body density matrix and
excitation energies of silicon P.R.C. Kent,
R.Q. Hood, M.D. Towler, R.J. Needs and G.
Rajagopal Phys. Rev. B, 57, 15293
(1998) [PDF]
Quantum Monte Carlo
simulations of real solids W.M.C. Foulkes,
M. Nekovee, R.L. Gaudoin, M.L. Stedman, R.J. Needs,
R.Q. Hood, G. Rajagopal, M.D. Towler, P.R.C. Kent, Y.
Lee, W.-K. Leung, A.R. Porter and S.J.
Breuer. High Performance Computing, edited
by R.J. Allan, M.F. Guest, A.D. Simpson, D.S. Henty,
and D.A. Nicole (Plenum) 1998. [PDF]
Diffusion quantum Monte Carlo
calculations of excitation energies in
silicon A.J. Williamson, R.Q. Hood, R.J.
Needs and G. Rajagopal Phys. Rev. B,
57, 12140 (1998) [PDF
]
Exchange and correlation in
silicon R.Q. Hood, M.-Y. Chou, A.J.
Williamson, G. Rajagopal and R.J. Needs Phys.
Rev. B57, 8972 (1998) [PDF]
Elimination of Coulomb finite
size effects in quantum many-body
simulations A.J. Williamson, G. Rajagopal,
R.J. Needs, L.M. Fraser, W.M.C. Foulkes, Y. Wang and
M.-Y. Chou Phys. Rev. B55,
R4851-R4854 (1997) [PDF
]
Quantum Monte Carlo
investigation of exchange and correlation in
silicon R.Q. Hood, M.-Y. Chou, A.J.
Williamson, G. Rajagopal, R.J. Needs and W.M.C.
Foulkes Phys. Rev. Lett.78, 3350
(1997) [PDF]
Finite size effects and
Coulomb interactions in quantum Monte Carlo
calculations for homogeneous systems with periodic
boundary conditions L.M. Fraser, W.M.C.
Foulkes, G. Rajagopal, R.J. Needs, S.D. Kenny and A.J.
Williamson Phys. Rev. B53, 1814
(1996) [PDF
]
Quantum Monte Carlo studies of
electronic systems R.J. Needs, G. Rajagopal,
A.J. Williamson, L.M. Fraser, S.D. Kenny, W.M.C.
Foulkes, A.J. James and P. Maccallum Journal of
Korean Physical Society29, S116-S120
(1996) [PDF
]
Quantum Monte Carlo
calculations of the energy of the relativistic
homogeneous electron gas S.D. Kenny, G.
Rajagopal, R.J. Needs, W.-K. Leung, M.J. Godfrey, A.J.
Williamson and W.M.C. Foulkes Phys. Rev.
Lett.77, 1099-1103 (1996) [PDF
]
Optimized wave functions for
quantum Monte Carlo studies of atoms and
solids A.J. Williamson, S.D. Kenny, G.
Rajagopal, A.J. James, R.J. Needs, L.M. Fraser, W.M.C.
Foulkes and P. Maccallum Phys. Rev. B53, 9640 (1996) [PDF]
Variational and diffusion
quantum Monte Carlo calculations at non-zero wave
vectors: theory and application to diamond-structure
germanium G. Rajagopal, R.J. Needs, A.J.
James, S.D. Kenny and W.M.C. Foulkes Phys. Rev.
B51, 10591 (1995) [PDF
]
Relativistic corrections to
atomic energies from quantum Monte Carlo
calculations S.D. Kenny, G. Rajagopal, and
R.J. Needs Phys. Rev. A51, 1898
(1995) [PDF]
Quantum Monte Carlo
calculations for solids using special k-points
methods G. Rajagopal, R.J. Needs, S.D.
Kenny, W.M.C. Foulkes and A.J. James Phys. Rev.
Lett.73, 1959 (1994) [PDF]
An optimised Ewald method for
long-ranged potentials G. Rajagopal and R.J.
Needs J. Comput. Phys.115, 399
(1994)
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