Calculate the structure and frequencies of XH_n (X = H~Ne) by using B3LYP theoretical method with 6-31+G(d,p) then compare with the experimental values.

Table 1

frequency	H2	exp	absolute error	LiH	exp	absolute error	BeH2	exp	absolute error	BH3	exp	absolute error	CH4	exp	absolute error	NH3	exp	absolute error	H2O	exp	absolute error	HF	exp	absolute error
Unit: cm-1	4465.7	4161.2	304.48	1402.0	1359.7	42.3	735.9	697.9	38.0	1157.6	1147.5	10.1	1347.3	1306.0	41.3	1000.3	950.0	50.3	1603.4	1595.0	8.4	4069.8	3961.4	108.37
							735.9			1205.2	1196.7	8.5	1347.3			1673.6	1627.0	46.6	3809.6	3657.0	152.6
							2038.4			1205.2			1347.3			1673.6			3931.5	3756.0	175.5
							2260.6	2159.1	101.5	2576.8	2601.6	-24.8	1563.8	1534.0	29.8	3484.7	3337.0	147.7
										2704.4			1563.8			3627.6	3444.0	183.6
										2704.4			3037.1	2917	120.1	3627.6
													3150.1	3019.0	131.1
													3150.1
													3150.1

 

Calculate the single point energy of XH_n (X = H~Ne) by using CCSD(T) theoretical method with aug-cc-pVTZ ( the structure obtained from the previous homework ), and then use those energy to calculate the standard enthalpy of formation (ΔH°_f)  then compare with the experimental values.

Table 2

theory	B3LYP
basis set	6-31+G(d,p)
	bond length (Å)	Experimental bond length (Å)
H2	0.743	0.741
LiH	1.614	1.595
BeH2	1.331	1.326
BH3	1.193	1.19
CH4	1.093	1.087
NH3	1.016	1.012
H2O	0.965	0.958
HF	0.928	0.917

 

Table 3

theory	B3LYP
basis set	aug-cc-pVTZ
	bond length (Å)	Experimental bond length (Å)
H2	0.743	0.741
LiH	1.590	1.595
BeH2	1.325	1.326
BH3	1.188	1.19
CH4	1.088	1.087
NH3	1.013	1.012
H2O	0.962	0.958
HF	0.924	0.917

 

Table 4

theory	MP2
basis set	6-31+G(d,p)
	bond length (Å)	Experimental bond length (Å)
H2	0.734	0.741
LiH	1.623	1.595
BeH2	1.328	1.326
BH3	1.186	1.19
CH4	1.087	1.087
NH3	1.012	1.012
H2O	0.963	0.958
HF	0.927	0.917

 

Table 5

theory	MP2
basis set	aug-cc-pVTZ
	bond length (Å)	Experimental bond length (Å)
H2	0.737	0.741
LiH	1.605	1.595
BeH2	1.330	1.326
BH3	1.187	1.19
CH4	1.086	1.087
NH3	1.012	1.012
H2O	0.961	0.958
HF	0.923	0.917

 

Table 6

bond length (Å)	B3LYP/6-31+G**	B3LYP/aug-cc-pVTZ	MP2/6-31+G**	MP2/aug-cc-pVTZ
H2	0.002	0.002	-0.007	-0.004
LiH	0.019	-0.005	0.028	0.01
BeH2	0.005	-0.001	0.002	0.004
BH3	0.003	-0.002	-0.004	-0.003
CH4	0.006	0.001	0	-0.001
NH3	0.004	0.001	0	0
H2O	0.007	0.004	0.005	0.003
HF	0.011	0.007	0.01	0.006
MUE	0.007	0.003	0.007	0.004

Figure 1

 

Table 7  Absolute error of bond angles

bond angles (°)	B3LYP/6-31+G**	B3LYP/aug-cc-pVTZ	MP2/6-31+G**	MP2/aug-cc-pVTZ
BeH2	0	0	0	0
BH3	0	0	0	0
CH4	0	0	0	0
NH3	1.4	0.5	1.4	0.1
H2O	0.9	0.6	0.9	-0.4
MUE	0.5	0.2	0.5	0.1

Figure 2

 

Table 8

theory	B3LYP
basis set	6-31+G(d,p)
	Experimental value	The heat of formation(kcal/mol)
H2	0.0	-2.1
LiH	33.6	34.2
BeH2	30.0	33.8
BH3	21.0	17.5
CH4	-17.8	-20.2
NH3	-11.0	-12.9
H2O	-57.8	-54.6
HF	-65.3	-62.2

Figure 3

 

Table 9

theory	CCSDT
basis set	aug-cc-pVTZ
SP (B3LYP/6-31+G**)	Experimental value	The heat of formation(kcal/mol)
H2	0.0	1.0
LiH	33.6	34.3
BeH2	30.0	42.3
BH3	21.0	27.3
CH4	-17.8	-11.6
NH3	-11.0	-4.2
H2O	-57.8	-53.3
HF	-65.3	-63.3

Figure 4

 

Table 10

theory	B3LYP
basis set	aug-cc-pVTZ
	Experimental value	The heat of formation(kcal/mol)
H2	0.0	-0.6
LiH	33.6	32.9
BeH2	30.0	36.8
BH3	21.0	19.4
CH4	-17.8	-18.2
NH3	-11.0	-13.6
H2O	-57.8	-55.6
HF	-65.3	-62.8

Figure 5

 

Table 11

theory	CCSDT
basis set	aug-cc-pVTZ
SP (B3LYP/aptz)	Experimental value	The heat of formation(kcal/mol)
H2	0.0	1.0
LiH	33.6	34.4
BeH2	30.0	42.4
BH3	21.0	27.3
CH4	-17.8	-11.3
NH3	-11.0	-4.2
H2O	-57.8	-53.3
HF	-65.3	-63.3

Figure 6

 

Table 12

absolute error
The heat of formation (unit kcal/mole)	B3LYP/6-31+G**	CCSDT/aug-cc-pVTZ SP B3LYP/6-31+G**
H2	2.1	-1.0
LiH	-0.7	-0.7
BeH2	-3.8	-12.4
BH3	3.5	-6.2
CH4	2.4	-6.2
NH3	1.9	-6.8
H2O	-3.2	-4.4
HF	-3.1	-1.9

 

 

Figure 7

 

Table 13

absolute error
The heat of formation (unit kcal/mole)	B3LYP/aug-cc-pVTZ	CCSDT/aug-cc-pVTZ SP B3LYP/aug-cc-pVTZ
H2	0.6	-1.0
LiH	0.7	-0.8
BeH2	-6.8	-12.4
BH3	1.6	-6.3
CH4	0.4	-6.5
NH3	2.6	-6.8
H2O	-2.1	-4.5
HF	-2.4	-2.0

 

Figure 8

 

Figure 9

 

Table 14

theory	MP2
basis set	6-31+G(d,p)
	Experimental value	The heat of formation
H2	0.0	8.7
LiH	33.6	46.1
BeH2	30.0	46.7
BH3	21.0	35.3
CH4	-17.8	4.1
NH3	-11.0	12.8
H2O	-57.8	-45.3
HF	-65.3	-61.2

Figure 10

 

Table 15

theory	CCSDT
basis set	aug-cc-pVTZ
SP (MP2/6-31+G**)	Experimental value	The heat of formation
H2	0.0	1.2
LiH	33.6	34.3
BeH2	30.0	42.4
BH3	21.0	27.5
CH4	-17.8	-11.4
NH3	-11.0	-4.1
H2O	-57.8	-53.3
HF	-65.3	-63.3

Figure 11

 

 

Table 16

theory	MP2
basis set	aug-cc-pVTZ
	Experimental value	The heat of formation
H2	0.0	5.9
LiH	33.6	39.5
BeH2	30.0	41.5
BH3	21.0	29.0
CH4	-17.8	-8.5
NH3	-11.0	-2.9
H2O	-57.8	-57.2
HF	-65.3	-67.6

Figure 12

 

 

Table 17

theory	CCSDT
basis set	aug-cc-pVTZ
SP (MP2/aptz)	Experimental value	The heat of formation
H2	0.0	1.1
LiH	33.6	34.3
BeH2	30.0	42.4
BH3	21.0	27.4
CH4	-17.8	-11.3
NH3	-11.0	-4.1
H2O	-57.8	-53.2
HF	-65.3	-63.2

Figure 13

 

 

Table 18

absolute error
The heat of formation (unit kcal/mole)	MP2/6-31+G**	CCSDT/aug-cc-pVTZ SP MP2/6-31+G**
H2	-8.7	-1.2
LiH	-12.5	-0.7
BeH2	-16.7	-12.4
BH3	-14.3	-6.4
CH4	-21.9	-6.5
NH3	-23.7	-6.9
H2O	-12.5	-4.5
HF	-4.0	-2.0

Figure 14

 

Table 19

absolute error
The heat of formation (unit kcal/mole)	MP2/aug-cc-pVTZ	CCSDT/aug-cc-pVTZ SP MP2/aug-cc-pVTZ
H2	-5.9	-1.1
LiH	-5.9	-0.7
BeH2	-11.6	-12.4
BH3	-7.9	-6.4
CH4	-9.3	-6.5
NH3	-8.1	-6.9
H2O	-0.6	-4.5
HF	2.4	-2.0

 

Figure 15

 

Figure 16

 

chatgpt

Reference

Potential Energy Surfaces for Structure and Dynamics

Experimental Geometry Data

Enthalpy of Atomization. Experimental values

 

 

 

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