●物理化学 3-1 Covalence bond Theory E ∫wmvz∫(cw+cw2)(cw+Cw2r 十 dT E(C2+C2+2C,,)=CHn+C2H2+2C,C2 H2 H V HU at H12=h121 ∫v 11 22 12 21 E(C1+C2S2)=C1H1+C2H12 2021/8/21 复旦大学化学系
物理化学I 2021/8/21 复旦大学化学系 11 = d H d E * * ˆ ( ) ( ) ( ) C C d C C H C C d 2 1 1 2 2 1 1 2 2 1 1 2 2 + + + = ˆ 22 1 2 12 2 11 2 2 1 2 12 1 2 2 2 E(C1 +C + 2C C S ) = C H +C H + 2C C H H = H d ij i j ˆ S = d ij i j E C1 +C2 S12 = C1 H11 +C2 H12 ( ) H11 = H22 H12 = H21 S11 = S22 = 1 S12 = S21 3-1 Covalence bond Theory
●物理化学 3-1 Covalence bond Theory FE 0 (H1-EC1+(H12-ES12)C2=0 inax aCI f aggeneys OE 0 (Hn2-Esn2C+(H22-ecr=0 equations aC Secular determinant H-E H-ES 12 0 12 Es H-E 12 22 、H1+H12 E n1-112 1+S12 12 y1+y -l2 2+2S12 2-2S 12 2021/8/21 复旦大学化学系
物理化学I 2021/8/21 复旦大学化学系 12 (H11 − E)C1 + (H12 − ES12)C2 = 0 (H12 − ES12)C1 + (H22 − E)C2 = 0 0 1 = C E 0 2 = C E 0 1 2 1 2 2 2 1 1 1 2 1 2 = − − − − H ES H E H E H ES 12 11 12 1 S H H EI + + = 12 11 12 1 S H H EII − − = 12 1 2 2 2S I + + = 12 1 2 2 2S II − − = Secular determinant Linear homogeneous equations 3-1 Covalence bond Theory
●物理化学 3-1 Covalence bond Theory Problem Carry out a linear variation calculation for a particle of mass m in one-dimensional infinite potential well of width L Use w=1x+y and l2x'-x as trial eigenfunction Compare the result with the exact ground state energy. 2021/8/21 复旦大学化学系
物理化学I 2021/8/21 复旦大学化学系 13 Problem: Carry out a linear variation calculation for a particle of mass m in one-dimensional infinite potential well of width l. Use and as trial eigenfunction. Compare the result with the exact groundstate energy. 2 3 1 = l x − x 2 5 7 2 = l x − x 3-1 Covalence bond Theory
●物理化学 3-1 Covalence bond Theory =w%2z=的(1)(2(2)1)d142=5不×全?)2 Hn=9)m(2)(1(2 overlap ∫.()(2,0)+(2)+月(12】1(1m( O=1+ 2R EH+EH +o H12=v1形v2z=(1)(2)(2)(1)d;dr2 ∫(n(2,2)+B(+12】(2m(r SbeH+ sbeh+ a 12R A R R 3 E,=1n=2E,+ o+A H,,-H, E 12=2EH 1+s 12 1+s 1-S 2021/8/21 复旦大学化学系
物理化学I 2021/8/21 复旦大学化学系 14 2 2 2 2 3 1 = = + + − R S e R R S12 = 1 2 d = a (1)b (2)a (2)b (1)d 1 d 2 ab 2 12 11 12 1 2 1 ab I H S Q A E S H H E + + = + + + = 2 12 11 12 1 2 1 ab II H S Q A E S H H E − − = + − − = 11 1 2 1 2 1 2 H H d d a b a b ( ) ( ) ˆ ( ) ( ) = overlap 1 2 (1,2) (1) (2) ˆ (2) ˆ (1) ˆ (1) (2) H H H d d = a b a + b + ab a b = EH + EH +Q R e R Q 1 2 1 − = + 3-1 Covalence bond Theory 12 1 2 1 2 2 1 1 2 H H d H d d a b a b ( ) ( ) ˆ ( ) ( ) ˆ = = 1 2 (1,2) (2) (1) ˆ (1) ˆ (2) ˆ a (1)b (2) Ha Hb Hab a b d d = + + = SabEH + SabEH + A 2 2 R e R R A − = − 3 1 2
●物理化学 3-1 Covalence bond Theory E +=2E再+ Q+4 l+S12 1+S2 实验值 b 理论值 H 11 H E 12=2E 1-S, Heitler -London 087AD=3.22eI FORCE CURVE FOR H-H INTERACTIONS Shoujing wang王守竟 70=0.74AD=376e D=474e 70=0.742A INTERNUCLEAR SEPARATIONKIN au 2021/8/21 复旦大学化学系
物理化学I 2021/8/21 复旦大学化学系 15 r0 = 0.74A De = 3.76eV r0 = 0.742A De = 4.74eV Heitler-London Shoujing Wang 王守竟 r0 = 0.87A De = 3.22eV 3-1 Covalence bond Theory 2 12 11 12 1 2 1 ab I H S Q A E S H H E + + = + + + = 2 12 11 12 1 2 1 ab II H S Q A E S H H E − − = + − − =