Scientific report
Participants at the conference gave presentations on a very wide range of
topics which I shall attempt to summarize below. I have divided them very
roughly into two sections: (1) theoretical, algorithmic, and
computational developments (which of course may involve interesting applications), and (2) applications. Some of the talks could conceivably fit in either
of those categories; in such cases I have arbitrarily chosen one.
Theory
John Trail gave a very interesting report on his continuing efforts with
Richard Needs to develop 'correlated electron pseudopotentials' more
appropriate for use in explicitly manybody methods such as QMC than the
oneelectron DiracFock/HartreeFock/DFT pseudopotentials that have
traditionally been used. He showed that many of the difficulties
associated with doing this can be alleviated by generating the pseudopotentials
in very ionized atomic states, which are then very transferable to neutral
states. Explicitlycorrelated QMC results using these pseudopotentials were
shown to be significantly more accurate than with HartreeFock pseudopotentials
for a wide range of molecules and also for more difficult cases such
as stronglycorrelated and complex transition metal systems.
Multideterminant expansions are a tool often used in quantum chemistry to
construct very accurate wave functions. These can be used directly as trial
wave function input to a QMC program but lengthy expansions of this nature can
be very slow to evaluate. Pablo López Ríos presented a
compression method for significantly reducing the computational cost of such
expansions, whilst maintaining the desirable properties of leaving the existing
evaluation algorithm unchanged and the original expansion coefficients
optimizable. His implementation in the CASINO program showed compression ratios
of between 2 and 25 in tests, and these factors translated more or less
directly into an overall speedup of the calculation.
Csaba Daday presented work done in collaboration with the group of Claudia
Filippi on using an embedding method to combine different levels of theory to
describe ground and excited states of biomolecules. In particular, he showed
one way of describing the 'important' parts of molecules with highlevel wave
function theory (perturbation theory, coupled cluster, or even DMC) while
treating the rest of the system at the DFT level. Unfortunately, while this
scheme seems to work well for small solvated molecules, the excitation energies
obtained for green fluorescent protein were severely blueshifted compared to
experimental values. His conclusion was that classical embedding (point charges
and induced dipoles) is the way to go until better functionals become available
for DFT embedding. Clearly significant development work remains to be done.
In his presentation Bartomeu MonserratSanchez showed how to include the
effects of atomic vibrations in the calculation of total energies, electronic
band gaps, and NMR parameters in first principles calculations. He
demonstrated, for example, that static DMC and GW band gaps of diamond are in
error by about 0.5 eV due to the neglect of electronphonon coupling.
Prof. Sorella outlined his recently developed method for performing ab
initio molecular dynamics simulations with quantum Monte Carlo. In this
technique, ionic forces are computed using highly accurate variational wave
functions containing several parameters that are fully optimized on the fly. He
showed recent results obtained for hydrogen at high pressure and for liquid
water at ambient conditions. Though very preliminary the results were clearly
very interesting and promising for future applications.
PierreFrancois Loos of the National University of Australia gave an
unusual but very interesting presentation showing that finitesize uniform
electron gases can be used to create a generalised version of the localdensity
approximation. He observed that this new functional can be applied to
onedimensional inhomogeneous systems and that it yields accurate estimates of
the correlation energy. He also discussed atoms and molecules in one dimension
and demonstrated that, in distinct contrast to our world, onedimensional atoms
are bound by oneelectron bonds.
Gareth Conduit's talk was entitled "Pseudizing the Hamiltonian". He
began by describing the contact interaction often used in modelling ultracold
atomic gases, and how it leads to pathological behavior driven by the
divergence of the manybody wave function when two particles coalesce. He then
proposed a family of smooth pseudopotentials which reproduce the scattering
phase shifts of the contact interaction, resulting in significant improvements
in efficiency when used in numerical calculations. Finally, he showed how to
extend this formalism to generate a pseudopotential for the Coulomb
electronelectron interaction in such a way that calculations can be
accelerated by an order of magnitude.
Mike Towler's presentation focussed on 'highthroughput QMC'  motivated by the
remark made by Tim Mueller at last year's meeting: "By 2016ish, we should
be able to calculate QMC energies for every known inorganic material on a
single supercomputer in about a week (roughly)." Towler showed how it was
possible for QMC calculations to 'monitor themselves' so that (a) they know
when they have equilibrated and it is possible to begin accumulating
statistics, (b) they know when they have achieved a desired target for the
statistical error bar  which may be set in input  and then automatically
stop, and (c) they know when a desired target error bar is 'unreasonable' and
cannot be attained with a reasonable amount of computation. This can largely be
done in a statistically valid way using a 'distributionfree' technique which
does not rely on the validity of the central limit theorem. It is to be hoped
that techniques such as these can help to greatly improve the rate at which
calculations of large datasets can be done.
Full configuration interaction QMC (FCIQMC) and related methods such as
semistochastic QMC have received a substantial amount of attention in recent
years, and we were treated to six separate talks on this topic. These
techniques arguably have a nontraditional focus compared to regular QMC
calculationss since they attempt to obtain the full configuration interaction
result, i.e., the exact result for a finite basis set, with reduced but still
nonpolynomial scaling. The utility of such results can typically be seen in
the benchmarking of other finite basis methods for small molecules and dimers,
but there have also been successes in applying FCIQMC directly to solids such
as nickel oxide chains. One can argue that FCIQMC has, in some sense, created a
bridge between the usual QMC community and the quantum chemistry
community and demonstrated the benefits of a stochastic approach to users of
wave functionbased methods. Amongst other developments, this has resulted in
a stochastic version of coupled cluster theory developed by Alex Thom and
collaborators.
Such developments are of course greatly assisted by the availability of
high quality standard software
and a particularly promising new opensource code is the
the 'highlyaccurate Ndeterminant' project : HANDE.
We heard five talks given by the developmental team of
HANDE, which is apparently nearing its public release. Will Vigor of Imperial
College, London and James Shepherd of Rice University, focussed on attempts to
understand the algorithmic detail of FCIQMC. They reported on errors related to
the stochastic algorithm and systematic issues arising from the sign problem.
Fionn Malone, also of Imperial College showed how FCIQMC can be parallelized
more efficiently using nonblocking asynchronous communication (apparently motivated by
Towler's similar developments in CASINO from several years earlier). Alex Thom
of Cambridge University discussed applications of FCIQMC and its coupled
cluster equivalent to finite electron gas systems. James Spencer from Imperial
gave the final talk as the lead developer in HANDE, and summed up how this work
and many others besides had been made possible by access to this new piece of
software.
A different but related technique known as semistochastic QMC was
reported by Prof. Cyrus Umrigar of Cornell University. He presented developments that
potentially offer routine efficiency gains of orders of magnitude over FCIQMC,
while apparently not compromising on the quality of the resulting full CI energies.
It seems clear that this community has much to do to make FCIQMC etc.
routinely useful such that a quantum chemist might consider using
it instead of their traditional techniques (it's bad enough trying to get them to use a nonGaussian basis set, after all). The exponential scaling with system size
remains a serious issue (the main advantage of DMC, for example, is the
favourable N^{3} scaling combined with the high accuracy; of course many techniques exist which can do just high accuracy).
Clearly much can be gained from observing similar problems that have been
solved in more traditional QMC techniques, and this was reflected in
the many and varied questions put to the speakers and the lively discussions
that followed both in the session and outside of them.
Applications
Jonathan LloydWilliams presented the results of a combined DFT and DMC
study of the phase diagram of solid hydrogen at pressures from 100 to 400 GPa.
He and his collaborators have performed highly accurate DMC calculations of the
static lattice energies of several candidate structures for the various
experimentally observed phases of solid molecular hydrogen. By combining the
DMC energies with anharmonic vibrational free energies  calculated using the
method described in the talk by MonserratSanchez  they found a phase
transition between two of the candidate structures at pressures and
temperatures in good agreement with those experimentally observed for the phase
III/IV transition in solid hydrogen.
Prof. Alfè began by demonstrating the serious deficiencies in the DFT description of water. By decomposing the energy of water
systems into a sum of onebody, twobody and manybody terms, and by
providing energy
benchmarks with CCSD(T) and QMC, he showed that different functionals have
different errors in these terms. For example, BLYP has serious twobody errors
but relatively small manybody errors. PBE has fairly small twobody errors
but larger manybody errors. Alfè then showed that BLYP
twobody errors
can be effectively eliminated using GAP technology, and the resulting BLYP+GAP potential energy
functional provides a good radial distribution function for water at ambient
conditions.
Prof. Guidoni gave a very colourful and wideranging talk entitled
'Geometries and properties of biomolecules by quantum Monte Carlo',
showing calculations of various molecules up to and including models for large
biological chromophores. He demonstrated  amongst other things  accurate QMC
energies for ground and excited states, geometries, polarizabilities, and
harmonic and ananharmonic frequencies. He also showed that geometry
optimizations involving more than 100 atoms are now feasible, and that the
called JAGP wave function ('Jastrow antisymmetrized geminal power')  a
highlyaccurate variational wave function based on Pauling's 'resonating
valence bonds' idea  is sufficiently flexible to do useful science at the VMC
level rather than the more expensive DMC.
Prof. Cohen showed some applications of DFT, QMC and DFTDMFT to silicate
perovskite, cubic boron nitride, iron monoxide, and a number of other materials
at high pressures.
Elaheh Mostaani from the University of Lancaster gave a talk about DMC
results for the binding energy of bilayer graphene, demonstrating once more how
you can get any answer you like with density functional theory when dealing
with van der Waals or other weak interactions  with the sad exception of the
correct one [Mike ducks to avoid missiles..]. She also showed preliminary results for a DMC study of the ground
and excitedstate electronic properties of oligoynes (endcapped linear
carbon chains with alternating single and triple bonds).
Edgar Engel presented DFT PBE calculations of the anharmonic quantum
vibrational energies for hexagonal and cubic ice, showing that the
thermodynamic stability of hexagonal ice with respect to cubic ice has its
origin in the smaller anharmonicity of the nuclear vibrations.
Using the displacement patterns of the corresponding highenergy hydrogen
vibrational modes, this can be traced back to structural differences
between the hexagonal and cubic forms, or more specifically, to the fact
that hexagonal ice contains both boat and chairform hexamers of H_{2}O
molecules whilst cubic ice contains only chairform hexamers.
As has become traditional, Prof. Needs gave a talk about ab initio
random structure searching within DFT, this time with the aim of identifying
stable stoichiometries and structures of xenon oxides under pressure.
Kenta Hongo from Japan spoke about noncovalent interactions in
cyclohexasilane dimers (which are potentially important in 'liquid silicon
inks' used as a source material for Si thin films). He compared and
constrasted results for calculations done with various different DFT
functionals along with MP2, CCSD(T), and DMC methods. The latter two, as they
should, showed good agreement. He also showed preliminary results for a DMC
study of metallic hydrogen at high pressure.
Martin Korth presented research on molecular organic battery materials with
a focus on liquid electrolyte solvents. He used a variety of computational
methods from wave function theory to strongly empirical quantitative
structureproperty relationships with the aim of screening for advantageous
compounds. He was able to demonstrate that such an integrated approach is
already helping experimentalists to design better electrochemical energy
storage devices, and he also gave some insights into the complexity of an
accurate computational treatment of electrochemical processes at the atomic
scale.
Neil Drummond gave a talk in which he described density functional theory
calculations of the electronic band structures, cohesive energies, phonon
dispersions and optical absorption spectra of a new class of twodimensional
crystals: In_{2}X_{2}, where X is S, Se or Te. Two crystalline
phases (α and β) of monolayers of hexagonal
In_{2}X_{2} were identified, and it was shown that they are
characterized by different sets of Ramanactive phonon modes. Drummond's
calculations showed that these materials are indirectbandgap semiconductors
with a sombreroshaped dispersion of holes near the valenceband edge. The
latter feature results in a Lifshitz transition (a change in the Fermisurface
topology of holedoped In_{2}X_{2}) at experimentally
accessible hole concentrations. Quantum Monte Carlo calculations are clearly
required to describe the electronic structure of these materials with
quantitative accuracy.
Prof. Nic Harrison gave an interesting talk on a number of different
problems. First of all he investigated whether it was possible to perform
accurate compuations of the potential energy
surface for the scattering of He atoms off an MgO (100) surface. He showed
that it was possible to get close to the exact curve but only with
considerable effort (involving doing MP2 calculations of the periodic system
with the CRYSCOR code, with coupledcluster corrections computed using a
finite molecule). He also presented a very nice discussion comparing and
contrasting the effects of breaking
the symmetry in a linear polyacetylene chain using both dimerization
(Peierls distortion) and spinpolarization.
Mariapia Marchi showed how the workflow of computations involving both DFT
and QMC can be optimized using the commercial software modeFRONTIER
developed at the ESTECO S.p.A. company located in Trieste. The
modeFRONTIER (mF) code is described as 'an integration platform for
multiobjective and multidisciplinary optimisation, with an unlimited range of
applications, though mainly used in engineering design optimisation'. In her
talk, Marchi focussed on a system of sixteen hydrogen atoms in the molecular
liquid phase. DFT runs were used to fill in the Slaterdeterminant part of the
wave function, while one, two and threebody terms in the Jastrow factor were
optimised with VMC. This was followed by a molecular dynamics step using a
secondorder Langevin dynamics to sample the ionic configurations within the
BornOppenheimer approximation. For each new atomic position, the determinant
part was filled with new orbitals and the Jastrow factor reoptimised. DFT and
VMC energies can be monitored on the fly through mF's graphical user interface
during the run. Although results were shown only for a simple test system, it
is clear that this sort of thing can be very useful, for example, in
investigating the properties and phase diagram of larger systems in order to
avoid finitesize effects.
Andrea Droghetti reported extensive calculations
assessing the performances of DMC for 'spin crossover' molecules containing
Fe(II) ions. Looking at the spin
crossover transition he showed that, independently of the choice of the
trial wave function, DMC gave an energy difference between the high
spin (spin=2) and low spin (spin=0) states which was almost an order of
magnitude larger than that computed with stateofart CASPT. As he pointed out, the quantum chemists normally
tell us to trust CASPT2 as a reference so this is a little puzzling, to say the least. Of
course we expect DMC to be even better, since with CASPT2 the shortrange
correlations are treated only perturbatively in contrast to the essentially
exact QMC treatment. Andrea says 'this calls for new studies aimed at
unrevealing the shortcomings
of both DMC and CASPT for transition metal complexes, which confirm
themselves as very challenging systems even for the most advanced electronic
structure methods available'. Me, I'm sensing a cockup somewhere, but what do
I know? ;)
Prof. ChingMing Wei from Taiwan presented various materials simulation applications of
QMC
including CO adsorption on late transition metal (111) surfaces and the
binding energies of 2D layers such as graphene, BN films, and silicene. Though
limited computer resources meant that there some issues with DMC error bar convergence he showed a large number of interesting results in systems
where DFT is known to fail.
Carlo Pierleoni gave a presentation in which he outlined the established
Coupled Electron Ion Monte Carlo (CEIMC) method, and showed an application to
the liquidliquid phase transition in high pressure hydrogen. The region of the
phase diagram where molecular hydrogen  stable at low pressure and
temperature  transforms into a monoatomic or plasma state with increasing
pressure and/or temperature is both interesting and challenging, in particular
since molecular dissociation under pressure is also accompanied by a metalinsulator
transition. Traditional QMC methods are largely used to study ground states
and miss the important temperature dependence, and the usual Path
Integral MC method for fermions is limited to the
temperature range above 1015K. CEIMC is a QMC method, based on the
BornOppenheimer approximation, in which nuclear degrees of freedom,
either classical or quantum, are sampled by standard MC methods, while the
electronic energy is obtained by highly accurate ground state QMC method for
the electrons. The use of BornOppenheimer means CEIMC is capable of
investigating the temperature range below which electronic thermal excitation
can be safely neglected in the system, and allows one to apply QMC methods to
high pressure hydrogen in the most interesting region of the phase diagram
where molecular dissociation and metalization under pressure occur.
Prof. Pierleoni showed the results of calculations of the molecular
dissociation under pressure both with CEIMC and BornOppenheimer MD employing several XC
functionals, both for classical and quantum nuclei. All the theories
(except PBE with quantum nuclei) led to the same qualitative picture of
the existence of a weakly firstorder liquidliquid phase transition below
some temperature. The
precise location of the transition line and of the critical point strongly
depended on the theory with the CEIMC line lying in between the GGAPBE line
(at lower pressure) and the vdWDF2 line (at higher pressure). Note that the
pressure difference with different DFT functionals was up to several
hundred GPa.
The quantitative prediction for the location of the transition line depended
crucially on the relative accuracy with which a specific theory can treat both
molecular and atomic (or plasma) states, and both insulating and metallic
states. He showed that their trial wave function is very accurate even across
this crossover and therefore the CEIMC line is expected to to be very accurate.
An experimental validation of these theoretical predictions would clearly
be immensely valuable.
Tack Uyeda and Tom
Poole also gave talks which I will summarize when I manage to
find a copy of their slides.
In summary, while "Quantum Monte Carlo in the Apuan Alps IX" was a
fascinating meeting which demonstrated many interesting theoretical advances
and a very considerable range of applications that QMC is being used to study,
my own personal opinion  and this really isn't meant as any sort of criticism  is that overall it all felt a bit flat with no real killer
advances or much that was really new. Perhaps this was because I was simultaneously
attempting to write about a dozen separate presentations, both for the
workshop and for the summer school the following week, and so in some cases I was able to listen with only half an ear. However, that was the impression I got. I did note that quite a
few of the major QMC players attending chose not to give a talk at all, or to give
a talk only about DFT, or to disagree with each other about stuff  which didn't really help  and I felt
it was a pity that most of the people whose work I selected to highlight as particularly groundbreaking for a
recent review talk entitled "QMC
at the research frontier: useful calculations for big complicated systems"
were unable to attend this year. I'm thinking of regular visitors like Lucas Wagner, Elif
Ertekin, Richard Hennig, Tim Mueller, Luke Shulenburger, Jeff Grossman.. at
least two of whom couldn't come because they're setting up home together and
were installing solar panels on their new roof.
I'm sure you'll all join me in wishing Lucas and Jeff every future
happiness.
Oh, wait..
MDT
