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the importance of water in many areas of science has motivated a large number of experimental and theoretical investigations of the liquid .
however , it is only recently that x - ray and neutron diffraction measurements have come to an overall agreement for properties such as the structure of water at ambient conditions @xcite .
in addition , several details of the water structure remain the subject of debate , and many dynamical properties of the liquid are not yet well understood .
theoretical models have played an important role in the interpretation of experimental measurements and in understanding the physical properties of water @xcite . over the last thirty years , rather accurate empirical force fields
have been developed , which can reproduce not only the structure but also many dynamical properties of the liquid @xcite .
although empirical models work well for pure water under ambient conditions , they are usually difficult to generalize to complex solutions or thermodynamic states far from ambient conditions . for example , the majority of empirical water models that are in current use employ potentials that do not change depending on the environment .    in recent years , it has become possible to simulate the properties of a liquid entirely from first principles , without having to resort to fitted potentials .
this is due in large part to the development of the car - parrinello ( cp ) method @xcite along with the continual increase in high performance computing resources .
although rather accurate and with the potential of being a truly predictive tool , cp simulations are much more computationally intensive than classical simulations .
the case of water is particularly demanding for cp simulations .
the ionic vibrational spectrum of the liquid exhibits high frequency modes , i.e. o - h stretch ( 3200 to 3600 @xmath0 ) and h - o - h bending modes ( @xmath11600 @xmath0 ) .
therefore , in order to avoid a coupling between the ionic and electronic degrees of freedom , which could cause severe inaccuracies in a cp simulation , a relatively small fictitious electronic mass ( @xmath2 400 a.u . for protonated water ) needs to be used @xcite . in turn , the use of small values of @xmath3 , together with the high kinetic energy cutoff required to describe the oxygen pseudopotential in a plane wave description , necessitates the use of small integration time steps . the time step may need to be as small as 0.08 fs , which is approximately ten times smaller than what is often used in classical md simulations with empirical inter - atomic potentials .
this poses a severe restriction on the time scales that can be accessed in cp simulations of water .
we note that when using born - oppenheimer ( bo ) dynamics ( where the total energy of the system is minimized at each ionic step ) , one can use larger time steps than in cp simulations , since electronic degrees of freedom are not propagated at the same time as ionic coordinates .
however , the accuracy required to reduce systematic errors on the ionic forces so as to have conservative dynamics is such that large number of iterations are usually necessary to minimize the kohn - sham energy at each ionic step .
therefore , the gain in efficiency obtained with a large time step is more than counter - balanced by the computational time requirement for total energy minimizations .
it is interesting to note that the problem of integrating fast vibrational modes in simulations of liquid water has also been encountered in classical md simulations , where the most common approach has been to completely eliminate the high - frequency intra - molecular motion by using bond length and angle constraints @xcite .
based on this approach , a variety of classical water potentials , e.g. the tip series @xcite , are capable of accurately reproducing many of the interesting properties of water . in particular , results obtained with the rigid water tip5p potential are in very good agreement with a variety of experimental measurements such as the structure , the temperature of maximum density , diffusion , as well as dielectric properties @xcite .    with the aim of investigating how to increase the integration time step in cp simulations of water and thus access larger time scales , we have carried out calculations using a rigid water approximation . in this paper , we present the results of these simulations and compare them to those obtained with flexible water molecules ( i.e. without imposing any constraints on the geometry of the molecules in the liquid ) , and we discuss the effect of a rigid model on the structural properties of water at ambient and high pressure conditions .
our results show that an _ ab initio _ rigid water model yields faster diffusion and radial distribution functions which are less structured than those found with a flexible model .
overall , the properties computed with the rigid model are in better agreement with experiment than those determined with a flexible model . possible reasons for this improved agreement are discussed .
in addition , we present a localized orbital analysis of the trajectories obtained with both a rigid and flexible water model , and we demonstrate that the large dipole moment changes in going from the gas to the liquid phase are not significantly altered by the rigid water approximation .
the use of a rigid water model in _ ab initio _ simulations opens the way to much longer simulations of solutions where chemical reactions and dissociation effects do not occur .
in order to examine how the structural and dynamical properties of water are altered by a rigid water approximation , we have performed a series of first principle molecular dynamics simulations @xcite of water with and without intramolecular bond and angle constraints under ambient and high pressure and temperature conditions .
the simulations consist of 54 water molecules in a periodically repeated cubic cell with a lateral dimension of either 11.74   or 10.10  , which correspond to densities of 1.00 g / cc and 1.57 g / cc , respectively . at each density , we have compared simulations where the intra - molecular geometry of the water molecules are rigid to those where the geometries of the water molecules are fully flexible .
.details of the simulations . [ cols="^,<,^,^,^,^,^ " , ]     [ diffusion ]    in addition to possible changes in structure and dynamics , we have examined how the rigid molecule approximation changes the electronic properties of water . in order to do this
we have performed a localized orbital analysis by computing the mlwfs for a series of well - separated snapshots from the rigid water simulation b and the flexible water simulation c. within the pseudopotential approximation , there are four doubly occupied mlwfs around each of the water molecules in the simulations .
two of the mlwfs are localized on the oxygen - hydrogen covalent bonds , and the other two are localized on the lone - pair locations of the oxygen atoms . given the large amount of data that the mlwfs represent , in the following , we only consider the centers of the mlwfs rather than the orbitals themselves . in fig .
[ gow ] , the oxygen - mlwf center rdfs for simulations b and c are shown .
the rdfs consist of two distinct distributions centered at r@xmath10.33   and r@xmath10.49  , which correspond to lone - pair and covalent bond locations , respectively . for comparison , the dashed vertical lines in fig
.  [ gow ] represent the locations of the mlwf centers around the oxygen atom of an isolated gas phase water molecule .
surprisingly , the rigid water approximation does not significantly alter the large changes in the mlwf centers that are expected when going from an isolated water molecule to the liquid state . as can be seen in fig .
[ gow ] , the lone pair distributions are shifted away from the oxygen atoms by @xmath10.03  , and the covalent bond distributions are shifted toward the oxygen atoms by @xmath10.04  .    as proposed by silvestrelli
_ et al . _
@xcite , an approximate dipole moment for each water molecule in the liquid can be defined by assigning the total charge of each mlwf to a point charge located at its corresponding center . because the mlwf on neighboring water molecules in the liquid do not significantly overlap , this provides a less ambiguous definition of the molecular dipole moments than arbitrarily assigning electron density to individual water molecules . as pointed out in ref .
, dipole moments computed in this manner from static configurations may not be representative of the experimentally measured dipole moments in the fluid .
however , the mlwf dipole moments are useful for examining qualitative differences in the polarization of water as a function of different approximations or of solutes present in the liquid .    in fig .
[ dipole ] , the probability distributions of molecular dipole moments for rigid and flexible water systems calculated from the mlwf centers are shown .
[ dipole ] indicates that the rigid water approximation has a rather small effect on distribution of dipole moments in the liquid .
in particular , the average moment in simulation b is shifted to 3.08 debye as compared to 3.20 debye in simulation c. apparently , an explicit description of high frequency o - h stretch and h - o - h bending modes is not necessary to reproduce the broad range of moments that are characteristic of the liquid .
it is also interesting to note that the latest experimental estimate based on an analysis of the x - ray structure factor of water indicates that the dipole moment of water in the liquid is 2.9 debye @xcite , which is in closer agreement with the rigid water model than the flexible simulation .
the decrease in the average dipole moment obtained from the rigid water approximation offers another explanation for the observed softening of the liquid structure .
in addition to mimicking quantum effects , it is possible that the rigid water approximation to some extent corrects for the general tendency of simple gga - based functionals to overestimate the polarizability of molecules @xcite .
for example , the static isotropic polarizability of an isolated water molecule is 10.74 au with the pbe functional as compared to the experimental value of 9.64 au @xcite .
it is interesting to note that hybrid dft functionals , which include some amount of hartree - fock exchange , appear to significantly improve on the polarizability of water .
in particular , the average polarizability of the water molecule is 9.78 au with hybrid pbe0 functional @xcite .    in addition to water under ambient conditions
, we have also examined how the rigid water approximation affects the properties of water under extreme temperatures and pressures . in particular , we have performed a simulation of rigid water ( simulation d ) and of flexible water ( simulation e ) at a density of 1.57 g / cc and an average temperature of @xmath1600 k. these high density and temperature conditions correspond to a regime where molecular dissociation is still considered a rare event @xcite .
however , the pressure ( @xmath110 gpa ) is high enough to cause a large increase in the nearest neighbor coordination of each water from 4.5 at ambient conditions to nearly 13 at high pressure @xcite .
the oxygen - oxygen , oxygen - hydrogen and hydrogen - hydrogen rdfs for simulations d and e are compared in figs .
[ goo - hp ] to [ ghh - hp ] .
except for the expected intramolecular differences due to the constraints , the rdfs obtained from simulations d and e are remarkably similar .
in particular , both the large increase in the number of nearest neighbors as well as the stiffness of the first peak in g@xmath4(r ) as a function of compression are reproduced by the rigid water model @xcite .
as higher densities and temperatures are considered , intramolecular dissociation will become an common event in flexible water simulations @xcite and the rigid water approximation is expected to be inappropriate for the description of the liquid .
in summary , we have used a series of car - parrinello molecular dynamics simulations to examine how the rigid water approximation affects the computed properties of water in the liquid state at ambient conditions . in agreement with previous observations based on empirical interaction potentials @xcite
, the rigid water approximation is found to cause an overall decrease in structure and an increase in diffusion of the liquid .
these changes result in properties that are in better agreement with experimental measurements than the corresponding first principles simulations with flexible water molecules . at higher temperatures and densities in a regime where intramolecular dissociation is still a rare event , the differences between simulations where water molecules are either rigid or flexible become negligible .
in addition to an improved structural and dynamical description of water , the rigid water model enables the use of time steps as large as 0.24 fs within the car - parrinello scheme ( i.e. @xmath13 times larger than in a flexible water simulation ) .
a similar conclusion was reached in ref .   for first - principle simulations of a cytosine molecule in the gas phase .
this represents an important advantage for first - principle simulations of aqueous solutions where chemical reactions do not occur , and opens up the possibility of investigating phenomena that take place on a long timescale .
for example , understanding how water orients around a hydrophobic solute may require simulations of the order of 100 to 200 ps .
the rigid water approximation presented here may prove to be an accurate and efficient approach for describing the interaction between a hydrophobic solute and water within a first - principles context .
+ the authors would like to thank j.  c.  grossman for many useful discussions .
this work was performed under the auspices of the u.s .
dept .  of energy at the university of california / lawrence livermore national laboratory under contract no .  w-7405-eng-48 .
we present the results of car - parrinello ( cp ) simulations of water at ambient conditions and under pressure , using a rigid molecule approximation . throughout our calculations , 
 water molecules were maintained at a fixed intramolecular geometry corresponding to the average structure obtained in fully unconstrained simulations . 
 this allows us to use larger time steps than those adopted in ordinary cp simulations of water , and thus to access longer time scales . in the absence of chemical reactions or dissociation effects , these calculations open the way to _ 
 ab initio _ simulations of aqueous solutions that require timescales substantially longer than presently feasible ( e.g.  simulations of hydrophobic solvation ) . 
 our results show that structural properties and diffusion coefficients obtained with a rigid model are in better agreement with experiment than those determined with fully flexible simulations . 
 possible reasons responsible for this improved agreement are discussed .