RETURN

(3d 3 4s 2 ) 4 F       Z=22       Ti -

F( r ) = Σ j   C j   S nl ( α j ,r) Y l,m ( r )

Table 1.

ROOTHAAN-HARTREE-FOCK WAVE FUNCTIONS:

Clementi E., Roetti C. // Atomic data and Nuclear data Tables v.14, 177-478 (1974)

j S nl j (α j ,r) C j
nl j α j 1s - electron 2s - electron 3s - electron 4s - electron
1 1s 21.892100 -0.946980 -0.288760 -0.105510 -0.015330
2 1s 34.982100 -0.019250 -0.001240 0.001230 0.000060
3 2s 19.058200 -0.041990 -0.151600 -0.052410 -0.008230
4 2s 9.137380 -0.004650 0.953700 0.352510 0.053450
5 3s 8.389220 0.002910 0.188380 0.239090 0.036030
6 3s 4.920620 -0.002420 0.024780 -0.489650 -0.060850
7 3s 3.442340 0.002900 -0.013540 -0.513000 -0.141910
8 4s 3.422810 -0.001420 0.006360 -0.202920 0.019520
9 4s 1.547460 0.000080 -0.000160 -0.015820 0.304420
10 4s 0.853870 -0.000030 0.000070 0.005640 0.541050
11 4s 0.432900 0.000010 -0.000020 -0.001690 0.362320
ORB.ENERGY,a.u. -182.956050 -21.083060 -2.545920 -0.015610
NORM 0.999997 0.999976 1.000011 0.999994
< R > 0.070114 0.325028 1.022212 5.801439
< R2 > 0.006597 0.124733 1.204664 42.772730
< 1/R > 21.533940 4.527622 1.358328 0.232354
< 1/R**2 > 933.772341 84.052502 11.056583 0.287998
j S nl j (α j ,r) C j
nl j α j 2p - electron 3p - electron
1 2p 10.066100 0.694280 -0.232880
2 2p 16.977700 0.048850 -0.017850
3 3p 8.284940 0.306350 -0.162790
4 3p 4.618610 0.008470 0.445100
5 3p 2.818430 0.000480 0.669030
6 3p 1.462280 -0.000140 0.036730
ORB.ENERGY,a.u. -17.455400 -1.483300
NORM 0.999992 1.000002
< R > 0.289578 1.109058
< R2 > 0.103143 1.450510
< 1/R > 4.438809 1.225031
< 1/R**2 > 27.119799 3.298051
j S nl j (α j ,r) C j
nl j α j 3d- electron
1 3d 1.800100 0.479190
2 3d 9.135230 0.026660
3 3d 4.741340 0.167630
4 3d 3.229330 0.294830
5 3d 0.944200 0.239420
ORB.ENERGY,a.u. -0.117950
NORM 1.000000
< R > 1.719947
< R2 > 4.010736
< 1/R > 0.812112
< 1/R**2 > 0.944839

Total Energy= -848.65324171 a.u.

Kinetic Energy= 848.37457762 a.u.

Potential Energy= -1697.02781933 a.u.

Virial Ratio = -2.00032847

***** TESTING *****

1.0 - <1s 1s> = 0.2806E-05

1.0 - <2s 2s> = 0.2389E-04

1.0 - <3s 3s> = -0.1144E-04

1.0 - <4s 4s> = 0.6193E-05

1.0 - <2p 2p> = 0.8443E-05

1.0 - <3p 3p> = -0.1720E-05

1.0 - <3d 3d> = -0.4258E-06

<1s 2s> = 0.4931E-05

<1s 3s> = 0.8863E-05

<2s 3s> = -0.5687E-05

<1s 4s> = 0.1014E-04

<2s 4s> = -0.2760E-05

<3s 4s> = 0.3053E-05

<2p 3p> = -0.1016E-05

RETURN