Slater's rules

To get the size of the valence orbitals correct, Slater proposed a set of rules that tell you what effective nuclear charge $Z_{\text{eff}}$ should be used to take the screening of the core electrons into account.

the s- and p-orbital of the same principal quantum number n [ns,np]
the d-orbital of principal quantum number n [nd]
the f-orbital of principal quantum number n [nf]

an amount of 0.35 (0.30 if it is the 1s orbital) for every other electron in the same group
for the [ns,np] group: an amount 0.85 for every electron in a n-1 group and 1.00 for every electron in a n-2 group and below
for the [nd] and [nf] group: an amount 1.00 for every electron in a group which has either a smaller principal quantum number n or the same n but a smaller azimuthal quantum number l (by the definition of s < p < d < f)

Effective Nuclear Charge $Z_{\text{eff}}$

	1s	2s	2p	3s	3p	3d	4s	4p	4d	5s	5p	4f	5d	6s	6p	5f	6d	7s
H	1	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
He	1.7	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Li	2.7	1.3	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Be	3.7	1.95	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
B	4.7	2.6	2.6	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
C	5.7	3.25	3.25	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
N	6.7	3.9	3.9	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
O	7.7	4.55	4.55	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
F	8.7	5.2	5.2	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Ne	9.7	5.85	5.85	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Na	10.7	6.85	6.85	2.2	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Mg	11.7	7.85	7.85	2.85	-	-	-	-	-	-	-	-	-	-	-	-	-	-
Al	12.7	8.85	8.85	3.5	3.5	-	-	-	-	-	-	-	-	-	-	-	-	-
Si	13.7	9.85	9.85	4.15	4.15	-	-	-	-	-	-	-	-	-	-	-	-	-
P	14.7	10.85	10.85	4.8	4.8	-	-	-	-	-	-	-	-	-	-	-	-	-
S	15.7	11.85	11.85	5.45	5.45	-	-	-	-	-	-	-	-	-	-	-	-	-
Cl	16.7	12.85	12.85	6.1	6.1	-	-	-	-	-	-	-	-	-	-	-	-	-
Ar	17.7	13.85	13.85	6.75	6.75	-	-	-	-	-	-	-	-	-	-	-	-	-
K	18.7	14.85	14.85	7.75	7.75	-	2.2	-	-	-	-	-	-	-	-	-	-	-
Ca	19.7	15.85	15.85	8.75	8.75	-	2.85	-	-	-	-	-	-	-	-	-	-	-
Sc	20.7	16.85	16.85	9.75	9.75	3.0	3.0	-	-	-	-	-	-	-	-	-	-	-
Ti	21.7	17.85	17.85	10.75	10.75	3.65	3.15	-	-	-	-	-	-	-	-	-	-	-
V	22.7	18.85	18.85	11.75	11.75	4.3	3.3	-	-	-	-	-	-	-	-	-	-	-
Cr	23.7	19.85	19.85	12.75	12.75	4.6	2.95	-	-	-	-	-	-	-	-	-	-	-
Mn	24.7	20.85	20.85	13.75	13.75	5.6	3.6	-	-	-	-	-	-	-	-	-	-	-
Fe	25.7	21.85	21.85	14.75	14.75	6.25	3.75	-	-	-	-	-	-	-	-	-	-	-
Co	26.7	22.85	22.85	15.75	15.75	6.9	3.9	-	-	-	-	-	-	-	-	-	-	-
Ni	27.7	23.85	23.85	16.75	16.75	7.55	4.05	-	-	-	-	-	-	-	-	-	-	-
Cu	28.7	24.85	24.85	17.75	17.75	11.0	11.35	-	-	-	-	-	-	-	-	-	-	-
Zn	29.7	25.85	25.85	18.75	18.75	12.0	12.0	-	-	-	-	-	-	-	-	-	-	-
Ga	30.7	26.85	26.85	19.75	19.75	13.0	12.65	12.65	-	-	-	-	-	-	-	-	-	-
Ge	31.7	27.85	27.85	20.75	20.75	14.0	13.3	13.3	-	-	-	-	-	-	-	-	-	-
As	32.7	28.85	28.85	21.75	21.75	15.0	13.95	13.95	-	-	-	-	-	-	-	-	-	-
Se	33.7	29.85	29.85	22.75	22.75	16.0	14.6	14.6	-	-	-	-	-	-	-	-	-	-
Br	34.7	30.85	30.85	23.75	23.75	17.0	15.25	15.25	-	-	-	-	-	-	-	-	-	-
Kr	35.7	31.85	31.85	24.75	24.75	18.0	15.9	15.9	-	-	-	-	-	-	-	-	-	-
Rb	36.7	32.85	32.85	25.75	25.75	19.0	16.9	16.9	-	11.2	-	-	-	-	-	-	-	-
Sr	37.7	33.85	33.85	26.75	26.75	20.0	17.9	17.9	-	11.85	-	-	-	-	-	-	-	-
Y	38.7	34.85	34.85	27.75	27.75	21.0	18.9	18.9	12.0	12.0	-	-	-	-	-	-	-	-
Zr	39.7	35.85	35.85	28.75	28.75	22.0	19.9	19.9	12.65	12.15	-	-	-	-	-	-	-	-
Nb	40.7	36.85	36.85	29.75	29.75	23.0	20.9	20.9	12.95	11.8	-	-	-	-	-	-	-	-
Mo	41.7	37.85	37.85	30.75	30.75	24.0	21.9	21.9	13.6	11.95	-	-	-	-	-	-	-	-
Tc	42.7	38.85	38.85	31.75	31.75	25.0	22.9	22.9	14.6	12.6	-	-	-	-	-	-	-	-
Ru	43.7	39.85	39.85	32.75	32.75	26.0	23.9	23.9	14.9	12.25	-	-	-	-	-	-	-	-
Rh	44.7	40.85	40.85	33.75	33.75	27.0	24.9	24.9	15.55	12.4	-	-	-	-	-	-	-	-
Pd	45.7	41.85	41.85	34.75	34.75	28.0	25.9	25.9	19.0	-	-	-	-	-	-	-	-	-
Ag	46.7	42.85	42.85	35.75	35.75	29.0	26.9	26.9	20.0	20.35	-	-	-	-	-	-	-	-
Cd	47.7	43.85	43.85	36.75	36.75	30.0	27.9	27.9	21.0	21.0	-	-	-	-	-	-	-	-
In	48.7	44.85	44.85	37.75	37.75	31.0	28.9	28.9	22.0	21.65	21.65	-	-	-	-	-	-	-
Sn	49.7	45.85	45.85	38.75	38.75	32.0	29.9	29.9	23.0	22.3	22.3	-	-	-	-	-	-	-
Sb	50.7	46.85	46.85	39.75	39.75	33.0	30.9	30.9	24.0	22.95	22.95	-	-	-	-	-	-	-
Te	51.7	47.85	47.85	40.75	40.75	34.0	31.9	31.9	25.0	23.6	23.6	-	-	-	-	-	-	-
I	52.7	48.85	48.85	41.75	41.75	35.0	32.9	32.9	26.0	24.25	24.25	-	-	-	-	-	-	-
Xe	53.7	49.85	49.85	42.75	42.75	36.0	33.9	33.9	27.0	24.9	24.9	-	-	-	-	-	-	-
Cs	54.7	50.85	50.85	43.75	43.75	37.0	34.9	34.9	28.0	25.9	25.9	-	-	20.2	-	-	-	-
Ba	55.7	51.85	51.85	44.75	44.75	38.0	35.9	35.9	29.0	26.9	26.9	-	-	20.85	-	-	-	-
La	56.7	52.85	52.85	45.75	45.75	39.0	36.9	36.9	30.0	27.9	27.9	-	21.0	21.0	-	-	-	-
Ce	57.7	53.85	53.85	46.75	46.75	40.0	37.9	37.9	31.0	28.05	28.05	30.0	21.0	21.0	-	-	-	-
Pr	58.7	54.85	54.85	47.75	47.75	41.0	38.9	38.9	32.0	27.35	27.35	30.3	-	20.85	-	-	-	-
Nd	59.7	55.85	55.85	48.75	48.75	42.0	39.9	39.9	33.0	27.5	27.5	30.95	-	20.85	-	-	-	-
Pm	60.7	56.85	56.85	49.75	49.75	43.0	40.9	40.9	34.0	27.65	27.65	31.6	-	20.85	-	-	-	-
Sm	61.7	57.85	57.85	50.75	50.75	44.0	41.9	41.9	35.0	27.8	27.8	32.25	-	20.85	-	-	-	-
Eu	62.7	58.85	58.85	51.75	51.75	45.0	42.9	42.9	36.0	27.95	27.95	32.9	-	20.85	-	-	-	-
Gd	63.7	59.85	59.85	52.75	52.75	46.0	43.9	43.9	37.0	28.95	28.95	33.9	21.0	21.0	-	-	-	-
Tb	64.7	60.85	60.85	53.75	53.75	47.0	44.9	44.9	38.0	28.25	28.25	34.2	-	20.85	-	-	-	-
Dy	65.7	61.85	61.85	54.75	54.75	48.0	45.9	45.9	39.0	36.05	36.05	38.0	-	29.85	-	-	-	-
Ho	66.7	62.85	62.85	55.75	55.75	49.0	46.9	46.9	40.0	37.05	37.05	39.0	-	30.85	-	-	-	-
Er	67.7	63.85	63.85	56.75	56.75	50.0	47.9	47.9	41.0	38.05	38.05	40.0	-	31.85	-	-	-	-
Tm	68.7	64.85	64.85	57.75	57.75	51.0	48.9	48.9	42.0	39.05	39.05	41.0	-	32.85	-	-	-	-
Yb	69.7	65.85	65.85	58.75	58.75	52.0	49.9	49.9	43.0	40.05	40.05	42.0	-	33.85	-	-	-	-
Lu	70.7	66.85	66.85	59.75	59.75	53.0	50.9	50.9	44.0	41.05	41.05	43.0	34.0	34.0	-	-	-	-
Hf	71.7	67.85	67.85	60.75	60.75	54.0	51.9	51.9	45.0	42.05	42.05	44.0	34.65	34.15	-	-	-	-
Ta	72.7	68.85	68.85	61.75	61.75	55.0	52.9	52.9	46.0	43.05	43.05	45.0	35.3	34.3	-	-	-	-
W	73.7	69.85	69.85	62.75	62.75	56.0	53.9	53.9	47.0	44.05	44.05	46.0	35.95	34.45	-	-	-	-
Re	74.7	70.85	70.85	63.75	63.75	57.0	54.9	54.9	48.0	45.05	45.05	47.0	36.6	34.6	-	-	-	-
Os	75.7	71.85	71.85	64.75	64.75	58.0	55.9	55.9	49.0	46.05	46.05	48.0	37.25	34.75	-	-	-	-
Ir	76.7	72.85	72.85	65.75	65.75	59.0	56.9	56.9	50.0	47.05	47.05	49.0	37.9	34.9	-	-	-	-
Pt	77.7	73.85	73.85	66.75	66.75	60.0	57.9	57.9	51.0	48.05	48.05	50.0	38.2	34.55	-	-	-	-
Au	78.7	74.85	74.85	67.75	67.75	61.0	58.9	58.9	52.0	49.05	49.05	51.0	42.0	42.35	-	-	-	-
Hg	79.7	75.85	75.85	68.75	68.75	62.0	59.9	59.9	53.0	50.05	50.05	52.0	43.0	43.0	-	-	-	-
Tl	80.7	76.85	76.85	69.75	69.75	63.0	60.9	60.9	54.0	51.05	51.05	53.0	44.0	43.65	43.65	-	-	-
Pb	81.7	77.85	77.85	70.75	70.75	64.0	61.9	61.9	55.0	52.05	52.05	54.0	45.0	44.3	44.3	-	-	-
Bi	82.7	78.85	78.85	71.75	71.75	65.0	62.9	62.9	56.0	53.05	53.05	55.0	46.0	44.95	44.95	-	-	-
Po	83.7	79.85	79.85	72.75	72.75	66.0	63.9	63.9	57.0	54.05	54.05	56.0	47.0	45.6	45.6	-	-	-
At	84.7	80.85	80.85	73.75	73.75	67.0	64.9	64.9	58.0	55.05	55.05	57.0	48.0	46.25	46.25	-	-	-
Rn	85.7	81.85	81.85	74.75	74.75	68.0	65.9	65.9	59.0	56.05	56.05	58.0	49.0	46.9	46.9	-	-	-
Fr	86.7	82.85	82.85	75.75	75.75	69.0	66.9	66.9	60.0	57.05	57.05	59.0	50.0	47.9	47.9	-	-	42.2
Ra	87.7	83.85	83.85	76.75	76.75	70.0	67.9	67.9	61.0	58.05	58.05	60.0	51.0	48.9	48.9	-	-	42.85
Ac	88.7	84.85	84.85	77.75	77.75	71.0	68.9	68.9	62.0	59.05	59.05	61.0	52.0	49.9	49.9	-	43.0	43.0
Th	89.7	85.85	85.85	78.75	78.75	72.0	69.9	69.9	63.0	60.05	60.05	62.0	53.0	50.9	50.9	-	43.65	43.15
Pa	90.7	86.85	86.85	79.75	79.75	73.0	70.9	70.9	64.0	61.05	61.05	63.0	54.0	50.2	50.2	52.65	43.0	43.0
U	91.7	87.85	87.85	80.75	80.75	74.0	71.9	71.9	65.0	62.05	62.05	64.0	55.0	50.35	50.35	53.3	43.0	43.0
Np	92.7	88.85	88.85	81.75	81.75	75.0	72.9	72.9	66.0	63.05	63.05	65.0	56.0	50.5	50.5	53.95	43.0	43.0
Pu	93.7	89.85	89.85	82.75	82.75	76.0	73.9	73.9	67.0	64.05	64.05	66.0	57.0	49.8	49.8	54.25	-	42.85
Am	94.7	90.85	90.85	83.75	83.75	77.0	74.9	74.9	68.0	65.05	65.05	67.0	58.0	49.95	49.95	54.9	-	42.85
Cm	95.7	91.85	91.85	84.75	84.75	78.0	75.9	75.9	69.0	66.05	66.05	68.0	59.0	50.95	50.95	55.9	43.0	43.0
Bk	96.7	92.85	92.85	85.75	85.75	79.0	76.9	76.9	70.0	67.05	67.05	69.0	60.0	50.25	50.25	56.2	-	42.85
Cf	97.7	93.85	93.85	86.75	86.75	80.0	77.9	77.9	71.0	68.05	68.05	70.0	61.0	58.05	58.05	60.0	-	51.85
Es	98.7	94.85	94.85	87.75	87.75	81.0	78.9	78.9	72.0	69.05	69.05	71.0	62.0	59.05	59.05	61.0	-	52.85
Fm	99.7	95.85	95.85	88.75	88.75	82.0	79.9	79.9	73.0	70.05	70.05	72.0	63.0	60.05	60.05	62.0	-	53.85
Md	100.7	96.85	96.85	89.75	89.75	83.0	80.9	80.9	74.0	71.05	71.05	73.0	64.0	61.05	61.05	63.0	-	54.85
No	101.7	97.85	97.85	90.75	90.75	84.0	81.9	81.9	75.0	72.05	72.05	74.0	65.0	62.05	62.05	64.0	-	55.85

Slater, J. C., Atomic Shielding Constants, Phys. Rev. 36, pp. 57�64, 1930. doi:10.1103/PhysRev.36.57