The started point of TBA:When the electrons are close enough to an atomic kernel,electron motion will be mainly governed by the atomic potential,while the influence of other atomic potential is very weak.The wave function ofelectrons in the crystal should be the linear combination of all the atomic orbit wave function: y(r）=∑ang,(r-Rn）Rm=ma1+m,a2+m,a3 Substitute it into the eq 【+uoo)=w We get >am [s,+U(r)-V(r-R)p (r-R)=E>am (r-R) In the TBA model,atomic interdistance is supposed to be larger than the radius ofatomic orbit.So,the overlapping ofat the lattice point is believed to be zero i(r-R)o;(r-R)dr=om
The started point of TBA: When the electrons are close enough to an atomic kernel, electron motion will be mainly governed by the atomic potential, while the influence of other atomic potential is very weak. The wave function of electrons in the crystal should be the linear combination of all the atomic orbit wave function: ( ) m i m ( ) m r r R = − a 1 2 3 R m a m a m a m = + + 1 2 3 We get m i m i m m i m ( ) ( ) ( ) ( ) m m a U V E a + − − − = − r r R r R r R Substitute it into the eq ( ) ( ) ( ) 2 2 2 U r r E r m − + = In the TBA model, atomic interdistance is supposed to be larger than the radius of atomic orbit. So, the overlapping of j at the lattice point is believed to be zero. ( ) ( )d i n i m nm r − − = r R r R
Left-handed multiply (r-R)at the two sides and integral ∑an{edn+∫r-R)[U(r)-r(r-R】g(r-R)dr}=Ea m Let =r-Rm,considering U(r)=U(r+R),simplifying the integral ∫p[5-(R.-R)][U(5)-V(5)]o,(5)d5=-J(R-R) U(x)-V(x) XCH004023 Which indicates that the integral is only correlated with the relative position of two lattice points(R- (n-2)a (n-1)a na (n+1)a (n+2)a (n+3)a R),so,-J(R-R)is introduced. ""indicates the symbol of U(5)-V(5) Atom
Left-handed multiply i * (r-Rn ) at the two sides and integral m i nm i n m i m n ( ) ( ) ( ) ( )d m a U V r Ea + − − − − = r R r r R r R Let ＝r－Rm，considering U(r) ＝U(r＋Rm) ，simplifying the integral ( ) ( ) ( ) ( )d ( ) i n m i n m U V J − − − = − − R R R R Which indicates that the integral is only correlated with the relative position of two lattice points (Rn－ Rm), so, - is introduced. “-” indicates the symbol of ( ) n m J R R− U V ( ) − ( )