_N_A_T_U_R_E_v_o_L_._3_3s_1_s_s_E_PT_E_M_BE_R_19_s_s ______ N EWS AND VI EWS-------------------20_1
`
`Crystals from first principles
`
`A new calculation of the polymorphs of silica appears to have broken new ground in deriving crystal
`structure from chemical composition. But X-ray crystallographers need not worry - yet.
`modulus within 10 per cent. The agree(cid:173)
`the authors estimate 0. 7
`oxygen atoms -
`ONE of the continuing scandals in the
`energy
`calculated
`between
`ment
`of an electron charge for every SiO bond ,
`physical sciences is that it remains in
`(enthalpy) of the polymorphs and the few
`or close on two electron charges for those
`general impossible to predict the structure
`measurements available is even better
`0 atoms bound to two Si atoms. So, to
`of even the simplest crystalline solids from
`(1 per cent) , but the authors say they
`ensure that their calculated structures are
`a knowledge of their chemical composi(cid:173)
`could probably do even better if they
`electrically neutral, the authors place elec(cid:173)
`tion. Who, for example, would guess that
`tronic charges at points 1.65 A along
`allowed for the band structure of these
`graphite , not diamond, is the thermo(cid:173)
`polymorphs and the extent to which the
`the four tetrahedral axes of the cluster,
`dynamically stable allotrope of carbon at
`bands are filled at different temperatures.
`neatly simulating in the process the elec(cid:173)
`temperature and pressure?
`ordinary
`Several refinements remain to be ex(cid:173)
`the neighbouring
`trostatic effects of
`Solids such as crystalline water (ice) are
`plored. The chances are that three-body
`oxygen ions found in structures such as
`still thought to lie beyond mortals' ken.
`potentials and even more complicated
`quartz.
`Yet one would have thought that , by
`variations of energy with configuration
`It would be wrong to say that, from this
`now , it should be possible to equip a suffi(cid:173)
`can be demonstrated by calculation and
`point, everything depends on what the
`ciently large computer with a sufficiently
`by comparison, for example, with meas(cid:173)
`programmers have done , but that is how
`large program, type in the formula of the
`ured specific heats. Evidently the treat(cid:173)
`the article reads . Tsuneyuki et al. essen(cid:173)
`chemical and obtain , as output, the atomic
`ment of charge transfer between Si and 0 ,
`tially calculate the electronic structure of
`coordinates of the atoms in a unit cell.
`while effective, is somewhat artificial and
`the cluster for various departures of the
`That time may not yet have arrived , but
`does not allow for cooperative configura(cid:173)
`atoms from their mean positions. They
`S. Tsuneyuki, M. Tsukada and H. Aoki
`tions extending over more than one Sio:(cid:173)
`use pre-calculated atomic orbitals in a
`from the University of Tokyo, with Y.
`tetrahedron.
`Hartree-Fock self-consistent field pro(cid:173)
`Matsui from Okayama University, have
`In themselves, of course, these results
`cedure ( one of the means of allowing for
`brought it a good step nearer. Starting
`are not a fulfilment of the goal of calculat(cid:173)
`electron-electron interactions in many(cid:173)
`with the information that the polymorphic
`ing from first principles the crystal struc(cid:173)
`electron atoms).
`forms of pure silica consist exclusively of
`ture of a compound of which nothing is
`In principle, there is every reason why
`SiO2, they first calculate, from first princi(cid:173)
`known except chemical composition . But
`the energy of the system should be quite a
`ples, the force constants in clusters of the
`that cannot be far away.
`complicated function of the atomic posi(cid:173)
`atoms and then , by molecular dynamics ,
`On the face of things , the most obvious
`tions. The surprise is that the parts of the
`the lattice constants of the four common
`artificially introduced variables are the
`energy surface so far calculated can be
`polymorphs of silica (a-quartz, a-cristo(cid:173)
`known crystal structures of the poly(cid:173)
`accurately represented by potential func(cid:173)
`the two
`balite, coesite and stishovite -
`morphs of silica, used as a starting point
`tions depending only on the distances
`last first recognized in the debris from
`for the molecular dynamics. It should not
`between pairs of atoms in the cluster. Not
`meteoritic impacts).
`be beyond the wit of Tsuneyuki and his
`surprisingly, one of these is a Coulomb
`two computer
`thank
`The authors
`colleagues , with the help of a few com(cid:173)
`term, another corresponds to the van der
`centres in Japan for access to computing
`puter centres, to select from a listing of all
`Waals attractive potential proportional to
`machinery, although they do not say how
`possible structures of an arbitrary material
`6 where r is the separation.
`many Cray-equivalent hours their calcu(cid:173)
`those that can be considered plausible on
`The molecular dynamics is made to
`lations occupied (Phys. Rev. Lett. 61 871 ;
`crystallographic and other grounds.
`seem just routine , no doubt because of the
`1988).
`Perhaps the most striking feature of this
`careful development of the appropriate
`The calculation is not merely a taste of
`laconic paper is the contrast it presents
`programs by Japanese colleagues. Pres(cid:173)
`things to come but a pointer to the
`with the state of the art of calculating the
`sure and temperature are determined by
`obstacles that remain , as well as being, in
`properties of solids as recently as a decade
`the size of a repeating three-dimensional
`its own right, a considerable achievement.
`ago, when it seemed that even the use of
`unit in a periodic lattice and by total
`What the group has done is to invert the
`force constants derived empirically from
`kinetic energy respectively. The known
`usual procedure in which force constants
`the measured properties of crystals did not
`structures of the four polymorphs of silica
`the
`from
`are calculated empirically
`regenerate , on calculation, the authentic
`are each dealt with separately. In each
`properties of crystals. Their strategy is
`properties of those same crystals. But the
`case, the object of the exercise is to tell
`instead to calculate the force constants
`practical importance of the new calculation
`whether the polymorphs are dynamically
`from first principles, for which purpose
`could be considerable, especially with the
`stable, or that they are not spontaneously
`they must calculate the electronic struc(cid:173)
`need to learn something of the crystal
`converted into each other, which all four
`ture of a complex of silicon and oxygen
`structure of materials that are either very
`prove to be. This is taken as an explana(cid:173)
`atoms.
`The snag is that, even with the the price
`zero-dimensional
`('microdot'
`small
`tion of why they are all apparently stable
`of Cray machines and their equivalents
`quantum wells, for example) or which
`under ordinary conditions even though ,
`falling year by year , it remains beyond the
`vary in composition over distances smaller
`thermodynamically, they are metastable.
`capacity of computation to calculate the
`than the limits of X-ray crystallography
`Given previous difficulties in calcula(cid:173)
`properties of a real crystal. So Tsuneyuki
`(such as doped semiconductors). In apply(cid:173)
`ting from first principles the properties of
`et al. start with the simplest of all relevant
`ing calculations to these needs, a demon(cid:173)
`real solids, the results are extremely good.
`the tetrahedral cluster Sia:-.
`structures -
`stration of success can rank, psychologi(cid:173)
`Unit cell dimensions turn out to be within
`But why Sia:-, not SiO4? Because Si
`cally, with the example set by those who
`5 per cent of their measured values, bulk
`readily surrenders electronic charge to
`properties such as density and bulk
`first climbed Everest.
`John Maddox
`
`,·
`
`Merck Exhibit 2170, Page 1
`Mylan Pharmaceuticals Inc. v. Merck Sharp & Dohme Corp.
`IPR2020-00040
`
`