Variational quantum Monte Carlo calculation of electronic and structural properties of crystals Page: 12 of 14
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unlike the uniform electron gas case, g is indeed highly anisotropic
and is a sensitive funciton of both ^ and i*2 separately. In particu-
lar we find that g+i is very rich in structure. For example, the
correlation hole, h!j!+(i*) - 9++ (>*i,»*) - 1/2, for located at the bond
center has a density distribution which is distinctly related to the
structure and covalent character of these materials. (r*) is nega-
tive near the bond center as expected but h^(i*) is positive only in
the nearby low density antibonding/interstitial regions and not in the
neighboring bond centers.
Finally we have carried out calculations to estimate the quasipar-
ticle excitation energy of a system by- considering the difference in
energy between a system in the ground state with that of a system with
an added hole. By assuming that our variational wavefunction is a suf-
ficiently accurate approximation for the true gound-state wavefunction,
the quasi hole energy may be expressed as
.. . c0
N_1 N <*|clc.t>
- <i|j | H | ij>>
where <p corresponds to a quasihole wavefunction. In our calculation
for diamond, we used the LDA wavefunction for ip 21. Our preliminary
results show quite good agreement with experiment (e.g. a bandwidth of
24.9 ± 1 eV for diamond as compared to the experimental value of 21-24
eV) and with other calculations22.23. However, the present scheme can
only be considered as a way rf obtaining an upperbound for the excita-
tion energy since Eq. (15) in fact rigorously gives the first moment of
the spectral function A^fui) of the state C^ji|/> and not the peak posi-
tion in A^(u>). For the case that a si ngle quasi particle peak is well-
defined and dominant, Eq. (15) would give a good approximation for the
quasiparticle energy as defined as the position of a well-defined peak
We have presented a new method of calculating the total energy
and related properties of crystals using nonlocal pseudopotentials in
conjunction with variational quantum Monte Carlo techniques. The
approach employs a many-electron wavefunction of the Jastrow-Slater
form. Calculations have been carried out successfully for the cohesive
energy and structural properties of carbon- and silicon-based solids.
With both a one-body and a two-body term in the Jastrow factor, it is
found that the approach can yield up to 95% of the electron correlation
energy in the systems studied. Calculations have also been carried out
to compute the single-particle orbital occupancy, electron pair-corre-
lation functions, and quasiparticle excitation energies. These quanti-
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Louie, S.G. Variational quantum Monte Carlo calculation of electronic and structural properties of crystals, article, September 1, 1989; [Berkeley,] California. (https://digital.library.unt.edu/ark:/67531/metadc1093861/m1/12/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.