•Using Gaussian and Spartan to calculate the ionization energy of atoms with atomic numbers 1 to 18. The calculations are performed using HF, B3LYP, and MP2 theoretical methods with 6-31G** and 6-311G** basis sets, followed by simple statistical analysis.

Ionization Energies:

A_(g)→ A⁺_(g)+ e ^-                     ΔE = IE1

A⁺_(g)→ A⁺² _(g) + e ^-              ΔE = IE2

"I expected that the error obtained from Hartree-Fock calculations will be larger."

 

Table 1. The values obtained from calculations using HF, B3LYP, and MP2 theoretical methods with 6-31G** and 6-311G** basis sets.

Ionization	6-31G**	H	He	Li	Be	B	C	N	O	F	Ne	Na	Mg	Al	Si	P	S	Cl	Ar
(unit: kcal/mol)	MP2	312.6	556.6	122.9	199.4	182.4	252.2	332.6	298.5	387.6	487.4	114.3	166.1	130.2	179.7	235.0	218.6	283.6	353.9
	HF	312.6	540.6	122.9	182.9	180.4	247.1	322.1	275.0	359.5	453.5	114.3	152.5	128.1	176.0	229.3	210.9	271.7	338.0
	B3LYP	313.9	573.5	129.5	208.7	197.0	262.9	338.0	322.6	400.8	491.0	124.7	178.2	138.7	186.9	239.4	241.6	300.5	364.1
	6-311G**	H	He	Li	Be	B	C	N	O	F	Ne	Na	Mg	Al	Si	P	S	Cl	Ar
	MP2	313.6	556.2	123.1	202.3	188.1	256.3	332.3	298.3	390.0	490.1	114.0	166.1	130.4	179.9	235.4	219.3	285.2	354.0
	HF	313.6	540.8	67.4	185.5	185.1	249.3	321.2	276.4	361.7	455.5	114.0	152.3	128.3	176.1	229.3	210.9	272.6	337.9
	B3LYP	315.1	574.8	129.5	210.1	201.2	266.0	337.5	323.8	406.2	497.5	125.0	178.2	138.7	187.0	240.0	242.5	302.6	365.3
實驗值a	(unit: kcal/mol)	313.6	567.1	124.3	214.9	191.4	259.7	335.1	314.1	401.7	497.2	118.5	176.4	138.1	187.9	241.9	238.9	299.1	363.4

^a: Computational Chemistry Comparison and Benchmark DataBase

 

 

Figure 1. The line charts generated from calculations using HF, B3LYP, and MP2 theoretical methods with 6-31G** and 6-311G** basis sets.

 

Table 2. The absolute error between the calculated values using HF, B3LYP, and MP2 with 6-31G** and 6-311G** basis sets and the experimental values.

絕對誤差	(unit: kcal/mol)
6-31G**	MP2	-1.0	-10.5	-1.4	-15.5	-9.0	-7.5	-2.5	-15.6	-14.1	-9.8	-4.2	-10.3	-7.9	-8.3	-7.0	-20.3	-15.5	-9.6
	HF	-1.0	-26.4	-1.4	-32.1	-11.0	-12.6	-13.0	-39.1	-42.2	-43.7	-4.2	-23.9	-10.0	-11.9	-12.6	-28.0	-27.4	-25.4
	B3LYP	0.3	6.4	5.2	-6.3	5.6	3.2	2.9	8.5	-0.9	-6.2	6.1	1.8	0.6	-1.0	-2.5	2.7	1.4	0.7
絕對誤差	(unit: kcal/mol)
6-311G**	MP2	0.0	-10.8	-1.2	-12.6	-3.3	-3.3	-2.8	-15.8	-11.7	-7.1	-4.5	-10.3	-7.7	-8.0	-6.5	-19.6	-13.9	-9.4
	HF	0.0	-26.3	-56.9	-29.4	-6.3	-10.4	-13.8	-37.7	-40.0	-41.7	-4.5	-24.1	-9.9	-11.9	-12.6	-28.0	-26.5	-25.5
	B3LYP	1.5	7.7	5.2	-4.8	9.8	6.4	2.5	9.7	4.5	0.3	6.4	1.8	0.5	-0.9	-1.9	3.6	3.5	1.8

Table 3. Mean absolute error (MAE)

MAE (unit: kcal/mol)	6-31G**	6-311G**
MP2	9.4	8.3
HF	20.3	22.5
B3LYP	3.5	4.0

Table 4. Standard deviation

Standard deviation (unit: kcal/mol)	6-31G**	6-311G**
MP2	5.3	5.3
HF	13.6	15.1
B3LYP	4.1	3.9

Table 5. Root mean square error (RMSE)

RMSE (unit: kcal/mol)	6-31G**	6-311G**
MP2	10.8	9.7
HF	24.2	26.9
B3LYP	4.3	5.0

According to the results, I found that the largest error is obtained when using the HF method.

Excel 數據

Chatgpt:

    NO.1:

    NO.2: