Table I
Total energies E , the comparison with experiment, and the virial theorem (values of E p /E k ) for states of Al.
State Calculated E (a.u.) Estimate of correlation energy differencea (a.u.) E p /E k 3s 3p 3d , 4 P −241.59985 −0.05239 −2.0000696 3s 3p 3d , 4 D −241.60370 −0.05184 −2.0000714 3s 3p 3d , 4 F −241.61495 ⋯ −2.0000308 3s 2 3p , 2 P −241.87623b 0 −2.0001188b 3p 3 , 2 P −241.43765 ⋯ −2.0000653 3p 3 , 2 D −241.47071 ⋯ −2.0000606 3p 3 , 4 S −241.52175b ⋯ −2.0000611b
a The experimental data (Ref.
7 ) for these estimates were available only for the first two excited states listed in the table.
b See Ref.
3 .
Table II
Orbital exponents ζ of the basis functions for the states of Al.
State 3s 3p 3d 3s 3p 3d 3s 3p 3d 3p 3 3p 3
Basis function 4 P 4 D 4 F 2 P 2 D 1s 13.00000 13.00000 13.00000 13.00000 13.00000 3s 14.80492 14.81882 14.47895 14.77241 14.76338 3s 10.87137 10.87137 10.82689 10.68695 10.77432 3s 6.86120 6.86120 6.86072 6.87467 6.88792 3s 4.36446 4.36446 4.36122 4.38249 4.38364 3s 1.69359 1.69359 1.70703 1.56276 1.95436 3s 1.24555 1.24555 1.19260 3s 0.48000 0.48118 0.47000 2p 6.50000 6.50000 6.50000 6.50000 6.50000 4p 13.95267 15.71772 14.62560 13.49175 14.92449 4p 7.29990 7.35528 7.29924 7.34672 7.36577 4p 4.73880 4.71777 4.70819 4.81223 4.75528 4p 2.27631 2.21533 2.19287 2.56436 2.33760 4p 1.48531 1.46381 1.52026 1.70371 1.52048 4p 1.31789 1.37205 1.19212 1.05520 1.03459 4p 0.72599 0.89615 0.59615 0.72743 0.68690 3d 4.33333 4.33333 4.33333 5d 2.71844 2.71844 2.69958 5d 1.29892 1.26724 1.29194 5d 0.61261 0.63032 0.62085 5d 0.37895 0.39095 0.37284
Table III
Eigenvectors of coefficients C i λ p for the states 4 P , 4 D , and 4 F of the configuration 3s 3p 3d of Al.
Orbital
State 1s 2s 3s 2p 3p 3d 1s 0.96742 1s −0.25110 1s 0.06384 2p 0.54049 2p −0.12249 3d 0.00670 3s 0.03225 3s −0.01195 3s 0.00432 4p 0.00616 4p −0.00119 5d 0.04811 3s 3p 3d 3s 0.01652 3s 0.09899 3s −0.03031 4p 0.20813 4p −0.04562 5d 0.21115 3s 0.00124 3s 0.51494 3s −0.13660 4p 0.36585 4p −0.05306 5d 0.62343 4 P 3s 0.00024 3s 0.48532 3s −0.17165 4p 0.04528 4p 0.34217 5d 0.32886 3s 0.00003 3s 0.00442 3s 0.69028 4p −0.06245 4p 0.33860 3s −0.00002 3s −0.00115 3s 0.37890 4p 0.04559 4p 0.36716 3s 0.00000 3s 0.00004 3s 0.00263 4p −0.00234 4p 0.03651 1s 0.96742 1s −0.25110 1s 0.06387 2p 0.53997 2p −0.12247 3d 0.00565 3s 0.03212 3s −0.01189 3s 0.00432 4p 0.00451 4p −0.00088 5d 0.03860 3s 3p 3d 3s 0.01671 3s 0.09890 3s −0.03036 4p 0.21002 4p −0.04673 5d 0.18523 3s 0.00117 3s 0.51499 3s −0.13655 4p 0.36888 4p −0.05118 5d 0.64729 4 D 3s 0.00027 3s 0.48529 3s −0.17191 4p 0.04390 4p 0.38597 5d 0.31081 3s 0.00002 3s 0.00444 3s 0.69157 4p −0.11437 4p −0.03796 3s −0.00002 3s −0.00116 3s 0.37785 4p 0.09793 4p 0.70319 3s 0.00000 3s 0.00004 3s 0.00217 4p −0.00399 4p 0.02194 1s 0.96751 1s −0.25116 1s 0.06311 2p 0.54033 2p −0.11593 3d 0.01447 3s 0.03580 3s −0.01254 3s 0.00502 4p 0.00554 4p −0.00085 5d 0.11265 3s 3p 3d 3s 0.01177 3s 0.10067 3s −0.03189 4p 0.21259 4p −0.04532 5d 0.46021 3s 0.00283 3s 0.51422 3s −0.13239 4p 0.36545 4p −0.04571 5d 0.63796 4 F 3s −0.00035 3s 0.48536 3s −0.17309 4p 0.04127 4p 0.36213 5d 0.02105 3s 0.00025 3s 0.00332 3s 0.69042 4p −0.03342 4p 0.27126 3s −0.00017 3s −0.00039 3s 0.38611 4p 0.01627 4p 0.42763 3s 0.00003 3s −0.00002 3s 0.00184 4p −0.00140 4p 0.04225
Table IV
Eigenvectors of coefficients C i λ p for the states 3p 3 , 2 P and 3p 3 , 2 D of Al.
Orbital
State 1s 2s 2p 3p 1s 0.96738 1s −0.25080 2p 0.54122 2p −0.10398 3s 0.03297 3s −0.01035 4p 0.00650 4p −0.00106 3p 3 3s 0.01622 3s 0.10163 4p 0.19720 4p −0.03634 3s 0.00079 3s 0.50054 4p 0.36847 4p −0.04902 2 P 3s 0.00036 3s 0.49556 4p 0.04401 4p 0.15274 3s −0.00002 3s 0.00371 4p −0.01625 4p 0.42995 4p 0.00774 4p 0.46299 4p −0.00238 4p 0.08713 1s 0.96739 1s −0.25079 2p 0.54074 2p −0.10432 3s 0.03284 3s −0.01067 4p 0.00500 4p −0.00079 3p 3 3s 0.01610 3s 0.09840 4p 0.20407 4p −0.03834 3s 0.00110 3s 0.50423 4p 0.37139 4p −0.04580 2 D 3s 0.00029 3s 0.49439 4p 0.03703 4p 0.25106 3s −0.00001 3s 0.00459 4p −0.02015 4p 0.41504 4p 0.01094 4p 0.40152 4p −0.00291 4p 0.05545
Table V
Orbital energies ∊ (a.u.) for the states of Al.
State 3s 3p 3d 3s 3p 3d 3s 3p 3d 3p 3 3p 3
Orbital 4 P 4 D 4 F 2 P 2 D 1s −58.73293 −58.73142 −58.69173 −58.65862 −58.64573 2s −5.13318 −5.13173 −5.08970 −5.05381 −5.04169 3s −0.63187 −0.63042 −0.58607 2p −3.44671 −3.44524 −3.40343 −3.37640 −3.36438 3p −0.38835 −0.39142 −0.36235 −0.20615 −0.22403 3d −0.05734 −0.06118 −0.07484