Final Report, GR/M91624/01
A Computational Chemistry Facility for Transition Metal Systems, Molecular Potential Energy Surfaces
and Molecular Dynamics
D.M. Hirst, R.J. Deeth and P.M. Rodger
The Beowulf computer cluster acquired under this grant has had a major impact on computational chemistry
research activity within the Department. It has enabled exciting developments to be made under each of the three
major headings identified in the original proposal. These are detailed below.
1
Structure & Reactivity of Transition Metal Systems
The substantial decrease in execution times afforded by the new hardware facilitated an enormous number of
calculations spanning four main areas of transition metal chemistry: organometallic chemistry; coordination
chemistry; development of new methodologies; and bioinorganic chemistry. Much of the research involved
geometry optimisation of medium to large metal complexes and the analysis of their geometric and electronic
structures. Several mechanistic studies were also undertaken which included transition state optimisation and the
calculation of reaction barriers. Most calculations were employed density functional theory (DFT) implemented
using the parallel version of the Amsterdam Density Functional (ADF) code.
Organometallic chemistry
Asymmetric catalysis: A strong collaboration has been developed with P. Scott’s group. Computer modelling
studies have made significant contributions to Ru-catalysed cyclopropanation1, Cu-catalysed aziridination2, and
the search for new chiral-at-metal Zr complexes.3
Figure 1: Optimised geometry for
103-atom Zr chiral-at-metal
complex. H atoms removed for
clarity
Each of these studies involved optimising many different conformations and binding modes. The computing
power of the cluster enabled modelling of the real synthetic systems rather than some cut-down model. The Zr
chiral-at-metal species (Figure 1) is, at 103 atoms, our current record and well beyond the capabilities of any
local hardware available prior to the award of this grant.
Aside from the ability to use ‘real’ chemical models, the beauty of fully-quantum DFT is that in both the
cyclopropanation and aziridination work, unsuspected secondary metal-ligand interactions appeared which
resolved hitherto unexplained phenomena. For example, the high regio- and enantioselectivity to aziridination of
cinnamate esters was traced to a secondary interaction between the ester carbonyl oxygen and the metal at about
2.2A which only occurs for one specific substrate binding mode of the four possibilities available.2
Heck reaction: Continued progress has been made on understanding the fundamentals of the Pd-catalysed Heck
reaction. Following earlier studies of the reaction paths for intermolecular C-C coupling between a vinyl group
and a monosubstituted alkene, transition states for phenyl-dihydrofuran couplings were located and the
subsequent H migration steps followed.4 The latest work involves establishing a simple selectivity index which
can predict the regiochemistry of Heck coupling under varying reaction conditions.5 This research involved a
preliminary but comprehensive analysis of the C-C coupling pathway for a variety of alkene substituents.
Although there are eight possible paths depending on substituent position, the TS energies cluster together as a
function of the regiochemistry. The significance of this observation is that the regiochemical fate of the reaction
is already implicit in the ground-state electronic structure. The selectivity index is based on both electrostatic and
orbital interactions derived from the ground state of the precursor.
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Other systems: Other studies supported by calculations on the cluster include oxidative addition to some Pd(0)6
and Rh(I) hydride 7 species, calculation of the structures for proposed intermediates in nitroaniline synthesis8 and
a study of the structures, vibrations and bond energies in some metal-dinitrogen complexes.9
Coordination chemistry
Modern DFT codes like ADF can access a range of spectroscopic properties including EPR g-values and excited
state energies although, for the latter, calculations on planar [PdCl4]2- 10 suggest there is still some way to go to
get an accurate description of multiplet states. For electronically simpler species like the d9 six-coordinate, JahnTeller distorted complex [Cu(dien)2]2+ (dien = diethylenetriamine) multiplets are not an issue but, although the
computed structure is in reasonably good agreement with experiment, the spectroscopic properties are still
poorly reproduced. 11 The excited states are too high leading to g-values which are too small. The source of
theses errors is the overestimation of Cu-N covalency. The cure is to modify the nuclear charge of the metal—a
possibility which, to my knowledge, is unique to ADF. Reducing Z from 29 to 28.2, brings the g-values and
excited state energies into much better agreement with experiment. This study highlights an apparently more
general trend that DFT overestimates covalency on the right of the transition series, probably because on an
increasing self-interaction error.
Another area of active research in DFT is its ability (or otherwise) to predict the correct spin state of metal
complexes. Our study on Co(II) aqua and ammine complexes12 concludes that B3LYP can do a reasonable job
for ionic species providing environmental effects like solvation are accounted for.
Finally, an ongoing study which has yet to generate any publications is to explore whether DFT can be used as
the basis for computing absolute metal-ligand binding energies. The work is focussed on Cu-carboxylate
interactions which are of interest to our industrial sponsor. Using reasonably large models embedded in a
COSMO description of the aqueous environment gives binding energies within a factor of two of experiment.
Further extensions and refinements are underway.
New theoretical methods
A parallel research project is the development of empirical schemes for modelling transition metal species. The
ligand field molecular mechanics (LFMM) method13 incorporates the d-electron stabilisation energy (and
gradients14) directly into the molecular mechanics (MM) calculation. Extensive DFT calculations are used to
provide a basis for LFMM parameters. Our study on the structures and relative spin state energies of Co(III)
complexes ultimately rested on a comparison between LFMM and DFT.15
Similarly, our attempts to model the regio- and enantioselectivities of the copper-catalysed two-point binding
Diels-Alder reaction16 involved using DFT calculations to characterise the energetics of twisting the substrate
relative to the plane of the bis-oxazoline ligand plus using the DFT-optimised TS structure as the basis for the
MM treatment.
Bioinorganic chemistry
Reaction pathways for the oxygen atom transfer reaction relevant to molydoenzymes have been computed for the
model system [MoO2(mnt)2]2- (mnt = SC(CN)C(CN)S). The calculations support the ‘normal’ pathway wherein
the incoming substrates abstract oxygen directly to leave the Mo(IV) monooxo species.17
A rather more complex system is the non-heme iron centre in extradiol catechol dioxygenase. In collaboration
with T.D.H. Bugg, the suggestion that this reaction is assisted by protons was verified theoretically.18 The
presence of an additional proton lowers the barrier to the initial epoxide from 17 to 3 kcal mol-1.
2
Potential Energy Surfaces for Molecular Ions and van der Waals Complexes
Computationally demanding calculations, with large basis sets and extensive treatment of electron correlation,
have been made for potential energy surfaces for the following four systems which are currently of interest to
experimentalists.
NO2+
Calculations on the NO2+ system have been made to elucidate two aspects of the chemistry of this system.19
There is extensive photoelectron spectroscopy for this species and potential energy surfaces for the NO2+ system
are needed for the interpretation of the observed reaction dynamics of the reaction of N+ (3P) with O2 (X 3Σg–).
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The lifetimes of the NO2+ ion are very state dependent. The experimental photoelectron spectrum shows that the
~
ground state X 1Σg+ is stable for most of the energy range populated by one-photon ionisation. The calculated
~
potential energy curve shows that there is a large barrier to dissociation for the X 1Σg+ state which correlates
~1
~1
1
+
1 +
3
~
with O ( D) + NO (X Σ ). The second ( a B2), fourth ( A A2) and fifth ( B B2) states have appreciable
lifetimes whereas the third state ( b~ 3A2) shows very little vibrational structure and has a very short lifetime of ~
~
10−13 s. Calculated potential energy curves show that the lowest 3A′ ( a~ 3B2) state and the 1 1A″ ( A 1A2) and 2
~1
1
3
~ 3
A′ ( B B2) states have local maxima in the range 0.8 – 1.0 eV whereas the 1 A″ ( b A2) state has a very
shallow quasi-bound minimum with a barrier of 0.1 eV. Thus we can understand qualitatively why the b~ state
~
~
~
has a very much shorter lifetime than the a~ , A and B states. The 1 1A″ ( A 1A2) surface crosses the 2 3A″
surface for a NO distance of about 1.5 Å and a non-adiabatic transition could give rise to dissociation to O (3P) +
NO+ (X 1Σ+).
Experimental studies of the reaction of N+ (3P) with O2 (X 3Σg–) show that the main product (~70%) is O (1D) +
NO+ (X 1Σ+) with O (3P) + NO+ (X 1Σ+) being the minor channel. Neither of these two product channels correlate
adiabatically with the reactants N+ (3P) + O2 (X 3Σg–). The reactant asymptote lies 0.09 eV above the charge
exchange asymptote N (1D) + O2+ (X 2Πg) and the most reasonable interpretation of the dynamics is that a nonadiabatic transition from the 2 1Σ+ surface, correlating with N+ (3P) + O2 (X 3Σg–), to the 1 1Σ+ surface, which
correlates with N (1D) + O2+ (X 2Πg), takes place in the entrance channel. The calculations show that these two
surfaces are initially parallel. The coefficients of the CI vector and the dipole moment function indicate that there
is a change in configuration in the region of rNO = 2.75 Ă. The 1 1Σ+ surfaces correlates adiabatically with O (1D)
+ NO+ (X 1Σ+) so that following a transition to this surface, the singlet products can readily be formed.
H2 S +
~
~
~
Potential energy surfaces have been calculated for the X 2B1, A 2A1, B 2B2, 1 4A2 and 1 4B1 states with the
~
objective of locating intersections between surfaces which are relevant to the observed predissociation of the A
~
~
20
+
and B states. Previous experimental work has been shown that the A state dissociates to S + H2 whereas the
~
B state yields mainly HS+.
~
The dissociation of the A 2A1 state to S+ (4S) + H2 must involve a non-adiabatic transition from the doublet
4
surface to the 1 A2 surface On the basis of our calculations we suggest that vertical ionisation of H2S to the
~
A 2 A1 state of H2S+ yields an ion with sufficient energy to reach linearity where a non-adiabatic transition to
~
~
~
~
the X 2 B1 state could take place. At linearity the X and A states are degenerate. If the ion in the A state has
~
an initial vibrational energy of more than about 0.5 eV the resulting X ion will have sufficient energy to reach
~
the seam of intersection between the X 2 B1 and 1 4A2 states. At these geometries 1 4A2 state can interact with
~ 2
the X B1 state through one-electron spin-orbit coupling and a non-adiabatic transition to the repulsive 1 4A2
state would result in dissociation to S+ (4S) + H2 (X 1Σg+). 1 4Σ–
~
In order to understand the dissociation of the B 2 B 2 state to SH+ (3Σg−) + H (1S) we need to consider
asymmetric stretching. Consideration of the potential energy surfaces for C2v symmetry and Cs symmetry
~
indicates that on formation an ion in the B 2 B 2 state with the geometry of neutral H2S will initially undergo
both symmetric and asymmetric stretching rather than bending. In the symmetric stretching mode the ion will not
have sufficient energy to reach the intersection with the 1 4A2 state. However, for asymmetric stretching the 2
2
A′ and 1 4A″ surfaces intersect once the SH bond has stretched to a little over 1.8 Å and the energy along this
~
seam of intersection lies in the range of 0.2 to 0.4 eV above the energy of the B 2 B 2 ion on vertical ionisation.
~ 2
The band in the photoelectron spectrum corresponding to the B B 2 state extends over 2 eV so only a modest
vibrational excitation is needed to make the 1 4A″ surface accessible. In the region of the seam of intersection the
1 4A″ surface is dissociative with respect to SH+ (3Σg−) + H (1S).
OCS+
There have been many studies of the photoelectron spectrum of OCS but there are relatively few ab initio studies
~
~
of the potential energy surfaces of OCS+. We have made comprehensive calculations for the X 2 Π , A 2 Π ,
~2 + ~2 +
2 –
2
4 –
+
B Σ , C Σ , 1 Σ , 1 ∆ and 1 Σ states of OCS in order to locate intersections between the potential
surfaces.21 The objective of these calculations was to elucidate the dissociation mechanisms for the lower states
~
observed in the photoelectron spectrum. The surface for the X 2 Π state is a straightforward bound potential
+ 2
energy surface which correlates adiabatically with S ( D) + CO (X 1Σ+). Excitation of about 1.8 eV is needed to
~
~
reach the dissociative 1 4Σ– surface, which correlates with S (4S) + CO (X 1Σ+). The A 2 Π and B 2 Σ + surfaces
2
1 +
4
1 +
both correlate with S ( P) + CO (X Σ ) but also dissociate to S ( S) + CO (X Σ ) although formation of S (2D) +
~
CO (X 1Σ+) is a minor channel for the B state. Both surfaces are quasi-bound with well depths of 3.1 and 0.9 eV
respectively. The potential wells of these surfaces intersect the dissociative 1 4Σ–, 1 2Σ– and 1 2∆ surfaces and
dissociation may occur via non-adiabatic transitions to these surfaces.
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Ar···HS
~
There is currently a lot of interest in the spectroscopy of rare-gas complexes with SH. The A 2 Σ + –
~
~2
X Π transition for Ar···HS has been extensively investigated and an empirical surface derived for the A 2 Σ +
state. This surface was not optimised for Ar···SH geometries. However, there is no ab initio potential energy
surface for this state in the literature. To complement experimental studies in this laboratory and to generate ab
initio surfaces which can be used to simulate the spectra and the formation of Ar···HS from Ar···H2S we have
~
~
calculated surfaces for A 2 Σ + and X 2 Π states by the RCCSD(T) method with the aug-cc-pV5Z basis set (342
~
basis functions).22 We considered the full range of geometries. The surface for the X 2 Π state is comparable
~
with that obtained by Sumiyoshi et al. with the aug-cc-pVQZ basis set. The calculated A 2 Σ + surface has two
mimima for the collinear geometries Ar···HS and Ar···SH. The global minimum is for Ar···HS (rArH = 2.017 Ǻ
with a well depth of 741.8 cm–1. The Ar···SH well is a little shallower (673.8 cm–1) with rArS = 2.770 Ǻ. We have
~
used our calculated potential surface for the A 2 Σ + state in a discrete variable representation (DVR)2 calculation
for the energy levels and rotational constants for the Ar···HS complex. Good agreement with experiment was
obtained for the rotational constants. However, the calculated energy level separations were about 5% smaller
than the experimental values. We also obtained rotational constants for some levels of the Ar···SH well for
which there are currently no experimental data
3
Condensed Phase Simulations
Clathrate Hydrates
Simulations with the hardware provided by this grant have enabled at least three major developments in the
modelling and understanding of clathrate hydrates. In the first place, computational screening methods have
enabled us to identify a completely new class of low dosage inhibitor for clathrate hydrate formation23;
subsequent development of the new lead compound has lead to the development of compounds that are about 10
times more active than existing commercial inhibitor blends.24. Patent applications are being prepared for these
compounds.
Long timescale simulations using the cluster have enabled us to produce both the first simulation of primary
nucleation of methane hydrate crystals (see Figure 2).25, and the first direct simulation of low dosage inhibition:26
the latter was achieved using polyvinylpyrrolidone (PVP), which is often taken as the archetype for low dosage
hydrate inhibitors. These simulations have been instrumental in revising our understanding of the mechanism for
nucleation. In particular, they have identified shortcomings in the current understanding of the molecular
mechanism for both nucleation and low dosage inhibition. Most strikingly, they have shown that a strict
understanding of surface adsorption is not essential for low-dosage anti-freeze activity in hydrate inhibitors.
These simulations have enabled us to develop a new mechanistic understanding of both the formation and
inhibition processes that is consistent with both recent experiments and with the new simulation data.27
Figure 2: growth of
methane hydrate crystal in
molecular dynamics
simulations
0.6 ns
10.5 ns
40.2 ns
Surfaces & Interfaces
Detailed atomistic simulations have been undertaken on a number of complex interfaces of practical importance.
Simulations of wax inhibition have lead to a considerably greater understanding to the molecular properties
required for an effective wax inhibitor. By simulating the adsorption of potential inhibitors on various alkane
crystalline surfaces — both under vacuum28 and in the presence of liquid n-heptane29,30 — and then examining
the subsequent growth of wax on the inhibited surface30,31 we have been able to show how the inhibitors favour a
continued growth that is incommensurate with the underlying wax structure. The molecular dynamics
simulations have then been used to parameterise mesoscale kinetic Monte Carlo simulations that show good
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correlation with the observed behaviour. In the process we have been able to answer a long-standing issue about
low dosage wax inhibitors by proving that there is a thermodynamic limit to the sub-cooling they can provide.
The mechanistic understanding of inhibition gleaned from the MD simulations have also enabled us to develop a
simple predictive scheme based on alkane adsorption energies that shows remarkably good correlation with
experimental activity within a consistent class of inhibitors32.
Simulations of corrosion inhibition have been used to address the question of whether corrosion inhibition films
may induce wax deposition in oil pipelines. MD simulations were performed of wax growth on hematite
surfaces33 on the adsorption of corrosions inhibitors (oleic imidazolines) on the hametite34 and the subsequent
effect this has on alkane liquids (both C7 and C28)35. These simulations have shown that wax deposition is
inhibited by the hematite surface, but can be promoted on the inhibited surfaces when the concentration of
heavier alkanes is sufficiently high.
Complex surface dynamics are also at the heart of molecular recognition in phenomena such as liquid
chromatography. Based on both molecular dynamics and Monte Carlo atomistic simulations, we have developed
new ensemble-sampling methods for predicting the free energy differences (∆∆G) that lead to differential
permeation of analytes in a chromatography column. The methods have been applied to chiral HPLC, and have
shown that the chiral recognition arises from an ensemble of recognition motifs—of both handednesses—and
cannot be understood in terms of any simple 3-point interaction model36
Biomolecules
Molecular dynamics simulations with explicit solvent have been used to study the binding of novel synthetic
metallo-cylinders to DNA, and to understand the dramatic effect these compounds have in controlling the
secondary structure of DNA.37 Simulations with different enantiomers have enabled interpretation and
verification of NMR and spectroscopic experiments to show that the two enantiomers of the parent compound
have very different binding sites, with one enantiomer binding in the major groove and inducing coiling, while
the other can bind in both major and minor grooves, with a weak preference for the minor grove. The simulations
have also shown that the response of the DNA arises from specific molecular shape interactions (largely
associated with van der Waals forces) and not from electrostatic interactions due to the large positive charge of
the metallocylinders.
Another project enabled by the acquisition of this compute cluster has been an MD study of a TAT signal
peptide. Twin argenine translocation (TAT) is a mechanism by which proteins can migrate across a membrane
without first unfolding then refolding. A number of signal peptide sequences have been identified, all of which
contain certain conserved elements—particularly adjacent argenines with nearby bulky hydrophobic residues. By
comparing the molecular dynamics simulations of wild-type sequence with specific mutations that remove the
TAT motif in both water and trifluorethanol with analogous circular dichroism experiments, we have been able
to show that the twin argenine motif has the effect of promoting the rate at which an α-helix both forms and
decomposes in the signal peptide.38
Other Systems
Various other simulation projects have commenced in collaboration with various industrial partners. Two
examples are cited here. We have commenced a simlation study of the crystallisation of caesium formate from
concentrated aqueous solution (with Cabot Specialty fluids, USA). Caesium formate has recently emerged as an
extremely effective base for drilling fluids in the oil industry, but can be affected by crystallisation at low
temperatures. We are currently simulating the effect of various possible inhibitors on the crystal / liquid interface
to identify new additives that will inhibit crystallisation without disrupting the desirable liquid properties (high
density and low viscosity). The second emerging application is a study of the rheology of fluids for continuously
variable transmission engines (Lubrizol). Complex alkanes are being simulated under both planar and
elongational shear flow to identify the molecular properties that lead to the rapid increase in viscosity with
pressure that is required for such applications. Extensive calculations have also been performed on amorphous
phases of ice, pioneering a combined MD / Lattice Dynamics methods; these have clarified the existence of a
phase transition from low density amorphous ice at ca. 150 K and helped resolve questions about the possible
existence of supercooled “liquid” phases.39
References
1
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2
K. M. Gillespie, E. J. Crust, R. J. Deeth and P. Scott, Chem. Commun., 2001, 785-786
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I. J. Munslow, A. J. Clarke, R. J. Deeth, I. Westmoreland and P. Scott, Chem. Commun, 2002, 1868-1869
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A Computational Chemistry Facility
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K. K. (Mimi) Hii, T. D. W. Claridge, J. M. Brown, A. Smith and R. J. Deeth, Helv. Chim. Acta, 2001, 84,
3043-3056
A. Smith, J. M. Brown and R. J. Deeth, J. Am. Chem. Soc., submitted
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57, 5061-5066
J. P. Rourke, G. Stringer, P.Chow, R. J. Deeth, D. S. Yufit, J. A. K. Howard and T. B. Marder,
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I. W. Davies, J. F. Marcoux, J. D. O. Taylor, P. G. Dormer, R. J. Deeth, F. A. Marcotte, D. L. Hughes, P. J.
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R. J. Deeth and N. Fey, Organometallics, in the press
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Hirst, D.M. manuscript in preparation
Hirst, D.M.; Doyle, R.; Mackenzie, S.R. manuscript in preparation
Storr, M. T.; Taylor, P. C.; Monfort, J.-P.; Rodger, P. M. J.Am.Chem.Soc. 2004, 126, 1569-1576
Duffy, D. M., Moon, C., Irwin, J. L., Di Salvo, A. F., Taylor, P. C., Arjmandi, M., Danesh, A., Ren, S. R.,
Tohidi, B., Todd, A., Storr, M. T., Jussaume, L., Monfort, J.-P., Rodger, P. M., Proc., Chemistry in the Oil
Industry Symposium, VIII., 46-58. 2003. 2003; Di Salvo, A. F., Taylor, P. C., Arjmandi, M., Ren, S. R.,
Tohidi, B., and Rodger, P. M., manuscript in preparation
Moon, C., Taylor, P. C., and Rodger, P. M. Proc. 4th Int. Conf. Natural Gas Hydrates, 2002, 2, 665-668;
Moon, C.; Taylor, P. C.; Rodger, P. M. J.Am.Chem.Soc. 2003, 125, 4706-4707
Moon, C.; Taylor, P. C.; Rodger, P. M. Can.J.Phys. 2003, 81, 451-457
Rodger, P. M. Chem.Phys.Chem., 2004, invited article
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Duffy, D. M.; Rodger, P. M. Phys.Chem.Chem.Phys. 2001, 3, 3580-3585
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P. M., manuscript in preparation
San Miguel, M. A. and Rodger, P. M., manuscript in preparation
Lukac, R.; Clark, A. J.; San Miguel, M. A.; Rodger, A.; Rodger, P. M. J.Mol.Liq. 2002, 101, 261-272;
Lukac, R.; Clark, A. J.; Khalid, S.; Rodger, A.; Snedden, A.; Rodger, P. M. J.Mol.Liq. 2002, 98-9, 411-423
Meistermann, I.; Moreno, V.; Prieto, M. J.; Moldrheim, E.; Sletten, E.; Khalid, S.; Rodger, P. M.; Peberdy,
J. C.; Isaac, C. J.; Rodger, A.; Hannon, M. J. Proc.Natl.Acad.Sci.U.S.A. 2002, 99, 5069-5074; Khalid, S.,
PhD Thesis, University of Warwick, 2004
San Miguel, M. A.; Marrington, R.; Rodger, P. M.; Rodger, A.; Robinson, C. Eur.J.Biochem. 2003, 270,
3345-3352; San Miguel, M. A.; Rodger, P. M, manuscript in preparation
Shpakov, V. P.; Rodger, P. M.; Tse, J. S.; Klug, D. D.; Belosludov, V. R. Phys.Rev.Lett. 2002, 88, 155502155505