I am trying to understand the working principle of basis sets in quantum chemistry. As far as I understand in the Hartree-Fock method, the basis set is used to calculate the matrix representation of Fock operator in each iteration in the SCF procedure. Usually each basis function in a chosen basis set is represented as a linear combination of several primitive Gaussian type orbital (GTO). I want to use cc-PVDZ basis for C atom which I can take from the EMSL Basis Set Exchange Library. For example in the Gaussian format:
! cc-pVDZ EMSL Basis Set Exchange Library 10/19/17 2:40 AM ! Elements References ! -------- ---------- ! H : T.H. Dunning, Jr. J. Chem. Phys. 90, 1007 (1989). ! He : D.E. Woon and T.H. Dunning, Jr. J. Chem. Phys. 100, 2975 (1994). ! Li - Ne: T.H. Dunning, Jr. J. Chem. Phys. 90, 1007 (1989). ! Na - Mg: D.E. Woon and T.H. Dunning, Jr. (to be published) ! Al - Ar: D.E. Woon and T.H. Dunning, Jr. J. Chem. Phys. 98, 1358 (1993). ! Sc - Zn: N.B. Balabanov and K.A. Peterson, J. Chem. Phys. 123, 064107 (2005), ! N.B. Balabanov and K.A. Peterson, J. Chem. Phys. 125, 074110 (2006) ! Ca : J. Koput and K.A. Peterson, J. Phys. Chem. A, 106, 9595 (2002). ! **** C 0 S 8 1.00 6665.0000000 0.0006920 1000.0000000 0.0053290 228.0000000 0.0270770 64.7100000 0.1017180 21.0600000 0.2747400 7.4950000 0.4485640 2.7970000 0.2850740 0.5215000 0.0152040 S 8 1.00 6665.0000000 -0.0001460 1000.0000000 -0.0011540 228.0000000 -0.0057250 64.7100000 -0.0233120 21.0600000 -0.0639550 7.4950000 -0.1499810 2.7970000 -0.1272620 0.5215000 0.5445290 S 1 1.00 0.1596000 1.0000000 P 3 1.00 9.4390000 0.0381090 2.0020000 0.2094800 0.5456000 0.5085570 P 1 1.00 0.1517000 1.0000000 D 1 1.00 0.5500000 1.0000000 ****
In the lines such as
S 8 1.00
I know that the letter S is the orbital type, 8 is the number of GTO in this orbital's expansion, but what is 1.00 for?The GTO for a p-type orbital has the form $x^l y^m z^n \exp(-ar^2)$ where the powers satisfy $l+m+n=1$ and thus there are three possible sets of $\{l,m,n\}$. But for instance in that link for lines with p-type orbitals, which possibilities shall I pick? The same question for d-type orbitals.