Question

Help me http://physicshelpforum.com/showthread.php?p=28062#post28062

Answer 1

@iambatman

Answer 2

i think this is too high for us. try: reddit.com/r/askphysics or physics.stackexchange.com

Answer 3

please, do you need to calculate the electrostatic energy of your unit cell?

Answer 4

have you ever read tight-binding model before?

Answer 5

Yes I learned it at my course on structure of matter

Answer 6

actually, i need to calculate density of state (DOS) and energy band structure of VO2

Answer 7

I have to revise that model, because many years are passed from when I was at university

Answer 8

would you mind helping me? i am a little bit confused about determining its simplflified unit cell and probabilty of electron hopping

Answer 9

yes, I try, nevertheless I need some times in order to revise my notions of solid state physics

Answer 10

ok

Answer 11

please wait, I'm taking my textbook...

Answer 12

Ok :)

Answer 13

my reference is this below:
Ashcroft-Mermin "Solid State Physics" Saunders College
we have to diagonalize the subsequent Hamiltonian:
\[H _{at}+\Delta U(r)\]
where
\[\Delta U(r)\]
is a little correction to the atomic potential

Answer 14

are you familiar with Quantum Mechanics, please?

Answer 15

pratically is an application of the perturbative theory of the quantum mechanics.
We can give an approximation of the s-level energy of an atom

Answer 16

your problem can be stated as follows:
\[(H _{at}+\Delta U(r))\psi (r)=\epsilon (k) \psi (r)\]

Answer 17

where \[k \]
is ranging in the first Brillouin zone with the Born-Von karman boundary conditions

Answer 18

and
\[\psi (r)=\sum_{R} e ^{ik \cdot R}\phi (r-R)\]
R is the position vector within the unit cell
please note that:k, r and R are all vector quantity

Answer 19

oops ...are all vector quantities

Answer 20

after some algebraic manipulation, and under other hypothesis, we can find the correction of the s-band energy E_s as below:
\[\epsilon (k)=E _{s}-\beta -\sum_{nearest-neighbors} \gamma (R) \cos(k \cdot R)\]

Answer 21

where:
\[\beta =-\int\limits dr \Delta U(r)|\phi(r)|^{2}\]
\[\gamma= -\int\limits dr \phi ^{*}(r)\Delta U(r) \phi (r-R)\]
and
\[\phi (r)\]
is a superposition of atomic wave function, namely:
\[\phi (r)=\sum_{n}b _{n}\psi _{n}(r)\]

Answer 22

now, we can calculate our \[\epsilon (k)\]
using the preceding formula, taking in account only the nearest neighbors atoms to the central atom