## Publications by the Wheatley group

All papers published in AIP journals are copyright American Institute of Physics. These articles may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.### 2018

Active learning in Gaussian process interpolation of potential energy surfaces.

Three active learning schemes are used to generate training data for
Gaussian process interpolation of intermolecular potential energy surfaces.
These schemes aim to achieve the lowest predictive error using the
fewest points and therefore act as an alternative to the status quo methods
involving grid-based sampling or space-filling designs like Latin hypercubes
(LHC). Results are presented for three molecular systems: CO2–Ne, CO2–H2,
and Ar3. For each system, two of the active learning schemes proposed
notably outperform LHC designs of comparable size, and in two of the systems,
produce an error value an order of magnitude lower than the one produced by
the LHC method. The procedures can be used to select a subset of points
from a large pre-existing data set, to select points to generate data de novo,
or to supplement an existing data set to improve accuracy.

### 2017

Interpolation of intermolecular potentials using Gaussian processes.

An Editors Choice article. A procedure is proposed to produce intermolecular potential energy surfaces from limited data.
The procedure involves generation of geometrical configurations using a Latin hypercube design, with a maximin criterion, based on inverse internuclear distances.
Gaussian processes are used to interpolate the data, using over-specified inverse molecular distances as covariates, greatly improving the interpolation.
Symmetric covariance functions are specified so that the interpolation surface obeys all relevant symmetries, reducing prediction errors.

An empirical force field for the simulation of the vibrational spectroscopy of carbon nanomaterials.

### 2016

Yb^{3+} doping effects on thermal conductivity and thermal expansion of yttrium aluminium garnet.

Replacing the host cations with rare earth elements can cause a structure change which influences the thermal properties of YAG.
Because the octahedral holes in the lattice are relatively small, Yb^{3+} ions, which have the smallest ionic radial size in the lanthanide series,
have been selected and doped on dodecahedral and octahedral sites to investigate the effects on thermal conductivity and thermal expansion.

Reverse energy partitioning — An efficient algorithm for computing the density of states, partition functions, and free energy of solids.

The previously published energy partitioning method for calculating partition functions does not produce results for solids. This paper addresses the problem,
by starting with the equilibrium structure and partitioning in increasing, rather than decreasing, energy. The results can be used to calculate phase diagrams
involving the solid state.

Calculation of high-order virial coefficients for the square-well potential.

Our previously published method for fast calculation of the integrand of the virial coefficients is extended to the square well potential.
The method is extended to perform recursion on polynomial quantities, allowing results for all temperatures to be derived simultaneously,
and the calculation is further optimised using parallel processing to store lookup tables of the integrand for different overlap patterns.

### 2015

Investigation of La^{3+} doped Yb_{2}Sn_{2}O_{7} as new thermal barrier materials.

La ions were used to create doped ceramic materials for use as
high-temperature thermal barrier coatings.
The doped ceramics had high coefficients of thermal expansion and
low thermal conductivities. Experiment and theory showed good agreement.

### 2013

Calculation of high-order virial coefficients.

A new recursive method for calculating high-order virial coefficients
is introduced. Virial coefficients are calculated up to the twelfth
(for hard spheres) and tenth (for soft spheres). In both cases,
the calculations are two orders higher than was previously possible.

Density of states partitioning method for calculating the free energy of solids.

A cage model is introduced for solids and combined with the recently
developed energy partitioning implementation of the nested sampling method.
The method can be used to calculate accurate free energies and phase properties
of solids. It is applied to carbon dioxide in this work.

### 2012

Calculation of partition functions and free energies of a binary mixture.

The partition functions, free energies (relative to the ideal gas), chemical
potentials, critical point and phase diagram of the
CO_{2}-CH_{4} fluid mixture are
calculated using the energy partitioning method developed by us.

Covalent bond orders and atomic anisotropies from iterated stockholder atoms.

Iterated stockholder atoms are used to estimate covalent bond orders in
a number of different molecules. The results are in good agreement with
chemical intuition. A new definition of anisotropy is introduced and the
anisotropies of iterated stockholder atoms are also calculated.

### 2011

Rapid calculation of partition functions and free energies of fluids.

An Editor's Choice and highly downloaded JCP article.
We use an energy partitioning method
to calculate the canonical density of states,
partition functions and free energies of fluids.

Molecular simulation of the binary mixture of 1-1-1-2-tetrafluoroethane
and carbon dioxide.

We employ atomistic force fields and the configurational-bias Monte Carlo
technique to study the vapour-liquid equilibrium of this mixture.
We also characterize its microscopic structure.

Intermolecular potential energy surface and second virial coefficients
for the water-CO_{2} dimer.

A potential energy surface for the water - carbon dioxide interaction
is calculated.
The second virial coefficients are calculated and compared to experimental
data. The problems associated with using another potential with
incorrect long-range behaviour are emphasised.

First principles predictions of thermophysical properties
of refrigerant mixtures.

This paper includes calculations of pairwise and non-additive potentials,
second virial coefficients, and fluid-phase simulations, for mixtures
of carbon dioxide wih fluorinated methanes, as well as for the
pure components.

### 2010

Microscopic structure of liquid 1-1-1-2-tetrafluoroethane (R134a) from
Monte Carlo simulation.

Vapour-liquid equilibrium properties and the liquid structure
of the refrigerant R134a are investigated using Monte Carlo
simulations with a flexible molecular model.

First principles models of the interaction of methane and carbon dioxide.

Additive and non-additive intermolecular potentials are calculated
from first principles for methane and carbon dioxide. Simulations of the
mixture show excellent agreement with experiment, requiring no fitting.

Simulations of mixtures of methane, difluoromethane and carbon dioxide.

Phase equilibria and microscopic structures of these industrially
important mixtures are investigated.

### 2009

Atomic charge densities generated using an iterative stockholder procedure.

A highly downloaded article from the Journal of Chemical Physics.
Our recently introduced ISA method is used to create and analyse
chemically reasonable atoms from different molecules and molecular dimers.

Potential energy surface and virial coefficients for the water-CO dimer.

The CO molecule has a small dipole which depends strongly on the
C-O bond length. This makes its interaction with the water molecule
quite complicated and difficult to calculate. This study considers the
intramolecular and intermolecular effects on the interaction energy
and the second virial coefficient of the mixture.

Additive and nonadditive models of vapor-liquid equilibrium in
CO_{2} from first principles.

By calculating the three-body potential as well as the usual pair interactions,
we can model the vapour-liquid phase behaviour of carbon dioxide without
empiricism, roughly as well as an effective pair potential that is fitted to
the phase behaviour!

Intermolecular potential and ab initio spectroscopy of the Ne-HF complex.

A paper produced by my former PhD student, now in Kazakhstan.

### 2008

Redefining the atom: atomic charge densities produced by an iterative stockholder approach.

Given a molecular charge density, Iterated Stockholder Atoms (ISAs or
"Wheatley Atoms") can be calculated using a very simple algorithm.
I think that they look and behave as chemists would expect for atoms
within a molecule. If you need any atomic properties, you should try ISAs!

Local polarizabilities and dispersion energy coefficients.

First-principles calculation of local atomic polarizabilities.

Defining the properties of individual atoms within molecules
is an important unsolved problem in Chemistry. The polarization
of atoms by an electric field, such as in hydrogen bonds, is particularly
difficult to calculate. This new method, developed recently by us,
allows atomic polarizabilities and dispersion energy coefficients
to be calculated directly without any fitting or other assumptions.

### 2007

Time-dependent coupled-cluster calculations of polarizabilities and dispersion energy coefficients. Accurate calculation of dispersion energy coefficients (C6, C8 etc.) is crucial for weak intermolecular interactions. My new benchmark calculation method is based on coupled-cluster theory and includes full treatment of orbital rotations and of open-shell electronic states.

The water-oxygen dimer: First-principles calculation of an
extrapolated potential energy surface and second virial coefficients.

The water-oxygen interaction is one of the most important in the Earth's
atmosphere, in rivers and oceans, and in fires. The structure of the weakly
bound H_{2}O–O_{2} molecular pair had been controversial until recently, and this
paper describes a complete calculation of the potential energy surface,
and related thermodynamic properties of water/oxygen gas mixtures.

Intermolecular potential and second virial coefficient of the
water-nitrogen complex.

The SIMPER method is used to calculate a new water-nitrogen potential
energy surface, and to predict that the equilibrium geometry
is "hydrogen bonded". Thermodynamics of air-water mixtures can now
be calculated from this work and related water-oxygen work.

### Selected earlier papers

Inverse Power Potentials: Virial Coefficients and a General Equation of State.

Soft-sphere potentials are widely used for modelling substances like
colloids. This paper is the first complete investigation of the
thermodynamics of soft-sphere systems as a function of their hardness.

Intermolecular potential energy extrapolation method for weakly bound systems: Ar_{2}, Ar-H_{2} and Ar-HF dimers.

This is the first full description of the SIMPER methods (SIMPER-K and
SIMPER-P) which were developed in our group to calculate
intermolecular potentials using the 'best' features of perturbation
theory and supermolecule calculations.

Intermolecular potential and second virial coefficient of the water-hydrogen complex.

The water-hydrogen interaction is difficult to calculate because it is
so weak. This work showed that previous calculations of the binding
energy were a severe underestimate (about 40%). More recent experimental
work has confirmed the correctness of our prediction.

Application of the overlap model to calculating correlated exchange energies.

An overlap model for exchange-induction: application to alkali halides.

Structure and vibrational spectra of methanol clusters from a new potential model.

### Reviews

Richard J. Wheatley; Timothy C. Lillestolen; International Reviews in Physical Chemistry, Volume 26, 2007, pp. 449–485.

Intermolecular potentials from supermolecule and monomer calculations.

Richard J. Wheatley; Akyl S. Tulegenov; Elena Bichoutskaia;
International Reviews in Physical Chemistry, Volume 23, 2004, pp. 151–185.