Study on the Interactions Between Na+ and N-Methylacetamide and Water by the ABEEM/MM†

doi:10.7503/cjcu20180546

Abstract

Abstract:

The geometries, binding energies of [Na(H₂O)_n]⁺(n=3—8), [Na(NMA)_n]⁺(n=3—8), [Na(NMA)_n(H₂O)_m]⁺(n+m=4,6)(NMA=N-methylacetamide) were studied with the quantum chemical MP2/6-311++G(d,p)//B3LYP/6-31+G(d,p) level of theory and atom-bond electronegativity equalization method fused into molecular mechanics(ABEEM/MM) fluctuating charge force field. Based on the quantum chemical results, the polarizable ABEEM/MM potential energy functions of the above system were constructed, and the relative parameters were optimized and determined. The results show that the structures, binding energies, charge distributions obtained by ABEEM/MM are in good agreement with those from quantum chemical method(QM). The average absolute deviations(AAD) of distances of Na⁺-ligand, angles, and binding energies are less than 0.007 nm, 2.4°, 8.9 kJ/mol, respectively. The relative root mean square deviations(RRMSD) of distances of Na⁺-ligand, angles, and binding energies are less than 3.5%, 2.0%, 12.4%, respectively. The linear correlation coefficients of the charge distributions from ABEEM/MM and QM are above 0.97.

Key words: Atom-bond electronegativity equalization method fused into molecular mechanics(ABEEM/MM), Sodium ion, N-Methylacetamide, Polarizable force field

CLC Number:

O641

TrendMD:

PAN Yiming, ZHANG Jing, TIAN Bo, YAO Jingjing, GONG Lidong, LIU Cui, YANG Zhongzhi. Study on the Interactions Between Na⁺ and N-Methylacetamide and Water by the ABEEM/MM^†[J]. Chem. J. Chinese Universities, 2018, 39(11): 2468.

Figures/Tables 14

Fig.1 ABEEM charge sites of the systems comprising of Na+ with NMA and H2O

Table 1 Parameters of Na+

Ion	χ^*(Pauling)	2η^*(Pauling/electron)	σ/nm	ε/(kJ·mol^-1)
Na⁺	7.076	8.7377	0.333045	0.002772

Table 2 Parameters klp,d of clusters*

Interaction site	A	B	C	D
lp of O in NMA and Na⁺	0.77615	0.13088	1.79200	0.08845
lp of O in H₂O and Na⁺	0.79078	0.14650	1.98999	0.11550
lp of O in NMA and H-(―NH) in NMA	0.72600	0.04960	1.39780	0.10340
lp of O in NMA and H-(―CH₃) in NMA	0.67000
lp of O in NMA and H in H₂O	0.60210	0.12970	1.87070	0.28420
lp of O in H₂O and H-(―NH) in NMA	0.64860	0.05840	0.90990	0.33760
lp of O in H₂O and H-(―CH₃) in NMA	0.57000

Fig.2 Optimized geometries of [Na(H2O)n]+(n=3—8)

Fig.3 Optimized geometries of [Na(NMA)n]+(n=3—8)

Fig.4 Optimized geometries of [Na(NMA)n(H2O)m]+(n+m=4)

Table 3 Comparisions of the structures and average binding energies of [Na(NMA/H2O)n]+(n=3—8) from QM, ABEEM/MM and OPLS-AA

n-H₂O	R_Na…O/nm			R_O—H/nm			R_O…H/nm
n-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	0.2265	0.2283	0.2424	0.0968	0.0961	0.0965	—	—	—
4	0.2294	0.2303	0.2442	0.0967	0.0952	0.0964	—	—	—
5	0.2289	0.2292	0.2439	0.0968	0.0955	0.0966	0.1942	0.1983	0.1826
6	0.2286	0.2289	0.2437	0.0969	0.0954	0.0967	0.1945	0.1982	0.1828
7	0.2284	0.2286	0.2434	0.0969	0.0953	0.0967	0.1936	0.1975	0.1811
8	0.2282	0.2285	0.2430	0.0969	0.0952	0.0967	0.1931	0.1967	0.1800
AAD	—	0.0006	0.0151	—	0.0014	0.0002	—	0.0039	0.0122
RRMSD(%)	—	0.37	6.61	—	1.46	0.22	—	1.99	6.31
n-H₂O	∠Na…O—H/(°)			∠O…H—O/(°)			ΔE/(kJ·mol^-1)
n-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	127.27	127.56	129.06	—	—	—	83.86	71.48	84.96
4	127.17	127.17	129.31	—	—	—	77.11	68.10	80.22
5	131.72	131.80	137.48	158.08	157.55	170.46	74.04	67.55	75.65
6	126.35	126.80	145.07	158.28	157.85	170.44	71.82	65.45	72.45
7	127.12	127.50	145.11	162.32	162.07	171.01	67.74	59.02	68.48
8	128.04	128.30	145.31	164.93	164.86	171.45	64.36	54.21	65.25
AAD	—	0.24	10.62	—	0.32	9.94	—	8.85	1.35
RRMSD(%)	—	0.23	10.16	—	0.23	6.36	—	12.38	2.17
n-NMA	R_Na…O/nm			$R CO$ /nm			R_O…H/nm
n-NMA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	0.2196	0.2323	0.2417	0.1245	0.1224	0.1236	—	—	—
4	0.2273	0.2329	0.2429	0.1243	0.1224	0.1235	—	—	—
5	0.2276	0.2327	0.2427	0.1243	0.1223	0.1234	0.1887	0.1944	0.1799
6	0.2266	0.2374	0.2425	0.1240	0.1226	0.1234	0.2417	0.2507	0.1789
7	0.2278	0.2341	0.2426	0.1242	0.1224	0.1405	0.2133	0.2202	0.1792
8	0.2477	0.2481	0.2469	0.1240	0.1227	0.1232	0.1928	0.1991	0.1803
AAD	—	0.0068	0.0140	—	0.0018	0.0034	—	0.0070	0.0296
RRMSD(%)	—	3.42	6.72	—	1.44	5.37	—	3.38	17.40
n-NMA	∠Na…O=C/(°)			∠O…H—C/N/(°)			ΔE/(kJ·mol^-1)
n-NMA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	167.69	167.57	171.99	—	—	—	122.25	113.06	46.05
4	145.37	144.91	168.01	—	—	—	106.76	103.87	42.15
5	142.92	142.47	167.92	175.48	176.43	169.53	97.80	100.03	36.37
6	150.48	149.92	164.46	168.43	166.34	169.99	83.14	78.86	32.46
7	139.30	139.42	166.45	173.98	173.63	170.14	82.06	79.78	29.59
8	129.32	130.78	160.41	176.46	177.48	169.01	84.52	85.59	26.40
AAD	—	0.53	20.70	—	1.10	4.70	—	3.66	60.59
RRMSD(%)	—	0.48	15.43	—	0.73	2.99	—	4.65	62.93

Table 3 Comparisions of the structures and average binding energies of [Na(NMA/H2O)n]+(n=3—8) from QM, ABEEM/MM and OPLS-AA

n-H₂O	R_Na…O/nm			R_O—H/nm			R_O…H/nm
n-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	0.2265	0.2283	0.2424	0.0968	0.0961	0.0965	—	—	—
4	0.2294	0.2303	0.2442	0.0967	0.0952	0.0964	—	—	—
5	0.2289	0.2292	0.2439	0.0968	0.0955	0.0966	0.1942	0.1983	0.1826
6	0.2286	0.2289	0.2437	0.0969	0.0954	0.0967	0.1945	0.1982	0.1828
7	0.2284	0.2286	0.2434	0.0969	0.0953	0.0967	0.1936	0.1975	0.1811
8	0.2282	0.2285	0.2430	0.0969	0.0952	0.0967	0.1931	0.1967	0.1800
AAD	—	0.0006	0.0151	—	0.0014	0.0002	—	0.0039	0.0122
RRMSD(%)	—	0.37	6.61	—	1.46	0.22	—	1.99	6.31
n-H₂O	∠Na…O—H/(°)			∠O…H—O/(°)			ΔE/(kJ·mol^-1)
n-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	127.27	127.56	129.06	—	—	—	83.86	71.48	84.96
4	127.17	127.17	129.31	—	—	—	77.11	68.10	80.22
5	131.72	131.80	137.48	158.08	157.55	170.46	74.04	67.55	75.65
6	126.35	126.80	145.07	158.28	157.85	170.44	71.82	65.45	72.45
7	127.12	127.50	145.11	162.32	162.07	171.01	67.74	59.02	68.48
8	128.04	128.30	145.31	164.93	164.86	171.45	64.36	54.21	65.25
AAD	—	0.24	10.62	—	0.32	9.94	—	8.85	1.35
RRMSD(%)	—	0.23	10.16	—	0.23	6.36	—	12.38	2.17
n-NMA	R_Na…O/nm			$R CO$ /nm			R_O…H/nm
n-NMA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	0.2196	0.2323	0.2417	0.1245	0.1224	0.1236	—	—	—
4	0.2273	0.2329	0.2429	0.1243	0.1224	0.1235	—	—	—
5	0.2276	0.2327	0.2427	0.1243	0.1223	0.1234	0.1887	0.1944	0.1799
6	0.2266	0.2374	0.2425	0.1240	0.1226	0.1234	0.2417	0.2507	0.1789
7	0.2278	0.2341	0.2426	0.1242	0.1224	0.1405	0.2133	0.2202	0.1792
8	0.2477	0.2481	0.2469	0.1240	0.1227	0.1232	0.1928	0.1991	0.1803
AAD	—	0.0068	0.0140	—	0.0018	0.0034	—	0.0070	0.0296
RRMSD(%)	—	3.42	6.72	—	1.44	5.37	—	3.38	17.40
n-NMA	∠Na…O=C/(°)			∠O…H—C/N/(°)			ΔE/(kJ·mol^-1)
n-NMA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
3	167.69	167.57	171.99	—	—	—	122.25	113.06	46.05
4	145.37	144.91	168.01	—	—	—	106.76	103.87	42.15
5	142.92	142.47	167.92	175.48	176.43	169.53	97.80	100.03	36.37
6	150.48	149.92	164.46	168.43	166.34	169.99	83.14	78.86	32.46
7	139.30	139.42	166.45	173.98	173.63	170.14	82.06	79.78	29.59
8	129.32	130.78	160.41	176.46	177.48	169.01	84.52	85.59	26.40
AAD	—	0.53	20.70	—	1.10	4.70	—	3.66	60.59
RRMSD(%)	—	0.48	15.43	—	0.73	2.99	—	4.65	62.93

Table 4 Linear correlations of charge distributions of [Na(NMA/H2O)n]+(n=3—8) from QM and ABEEM/MM

n-H₂O	Y = AX + B	R	S	U_max	q_Na/a.u.
n-H₂O	Y = AX + B	R	S	U_max	QM	ABEEM/MM
3	Y=1.2304X-0.0230	0.9771	0.0970	0.2249	0.7899	0.7598
4	Y=1.3037X-0.0234	0.9878	0.0699	0.1983	0.7523	0.7597
5	Y=1.3403X-0.0213	0.9870	0.0728	0.2208	0.7474	0.7596
6	Y=1.3619X-0.0190	0.9874	0.0715	0.2360	0.7444	0.7587
7	Y=1.3604X-0.0164	0.9891	0.0652	0.2316	0.7398	0.7585
8	Y=1.3588X-0.0144	0.9905	0.0601	0.2268	0.7356	0.7584
n-NMA	Y = AX + B	R	S	U_max	q_Na/a.u.
n-NMA	Y = AX + B	R	S	U_max	QM	ABEEM/MM
3	Y=1.1628X-0.0044	0.9864	0.0463	0.1112	0.7747	0.8068
4	Y=1.1930X-0.0039	0.9875	0.0430	0.1012	0.7326	0.8351
5	Y=1.2050X-0.0034	0.9864	0.0446	0.1048	0.7290	0.8327
6	Y=1.1818X-0.0025	0.9878	0.0404	0.1113	0.7369	0.8387
7	Y=1.1974X-0.0023	0.9861	0.0436	0.1179	0.7251	0.8183
8	Y=1.1891X-0.0019	0.9878	0.0403	0.0983	0.7606	0.8570

Fig.6 Linear correlation of charge distributions from ABEEM/MM and QM of [Na(NMA/H2O)n]+(n=3—8)

Table 5 Comparisions of the structures and average binding energies of [Na(NMA)n(H2O)m]+(n+m=4, 6) from QM, ABEEM/MM and OPLS-AA

n-NMA	m-H₂O	R_Na…O/nm			$R CO / O — H$ /nm			R_O…H/nm
n-NMA	m-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
1	3	0.2283	0.2478	0.2439	0.1007	0.0999	0.1003	—	—	—
2	2	0.2267	0.2279	0.2135	0.1059	0.1046	0.1055	—	—	—
3	1	0.2284	0.2354	0.2432	0.1134	0.1118	0.1127	0.2034	0.2246	—
1	5	0.2399	0.2397	0.2488	0.0997	0.0981	0.0990	0.1826	0.1990	0.1807
2	4	0.2400	0.2396	0.2504	0.1028	0.1014	0.1020	0.1796	0.1938	0.1922
3	3	0.2386	0.2389	0.2500	0.1064	0.1044	0.1053	0.1795	0.1972	0.2087
4	2	0.2269	0.2315	0.2420	0.1107	0.1092	0.1102	0.1843	0.2075	0.1739
5	1	0.2379	0.2397	0.2477	0.1165	0.1149	0.1156	0.2180	0.2307	—
AAD		—	0.0044	0.0124	—	0.0015	0.0007	—	0.0176	0.0135
RRMSD(%)		—	0.91	1.52	—	1.43	0.70	—	9.35	9.23
n-NMA	m-H₂O	∠Na…O—C/H/(°)			∠O…H—C/N/O/(°)			ΔE/(kJ·mol^-1)
n-NMA	m-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
1	3	138.89	137.69	140.42	—	—	—	86.24	92.33	71.61
2	2	149.76	149.32	149.36	—	—	—	93.27	101.47	62.91
3	1	149.82	150.49	159.65	127.54	121.83	—	100.84	105.65	52.60
1	5	128.16	132.44	134.95	152.43	145.91	160.24	75.45	72.09	63.75
2	4	126.06	129.91	135.77	158.06	154.91	144.71	79.74	82.94	58.00
3	3	124.28	127.22	138.50	158.76	156.61	132.70	80.63	81.82	52.07
4	2	147.64	144.38	155.85	177.43	173.11	177.37	81.38	89.30	46.06
5	1	136.82	139.30	145.65	163.63	165.48	—	86.15	92.22	39.68
AAD		—	2.39	7.44	—	3.95	11.82	—	5.10	29.63
RRMSD(%)		—	1.99	6.21	—	2.75	9.36	—	6.51	37.53

Table 5 Comparisions of the structures and average binding energies of [Na(NMA)n(H2O)m]+(n+m=4, 6) from QM, ABEEM/MM and OPLS-AA

n-NMA	m-H₂O	R_Na…O/nm			$R CO / O — H$ /nm			R_O…H/nm
n-NMA	m-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
1	3	0.2283	0.2478	0.2439	0.1007	0.0999	0.1003	—	—	—
2	2	0.2267	0.2279	0.2135	0.1059	0.1046	0.1055	—	—	—
3	1	0.2284	0.2354	0.2432	0.1134	0.1118	0.1127	0.2034	0.2246	—
1	5	0.2399	0.2397	0.2488	0.0997	0.0981	0.0990	0.1826	0.1990	0.1807
2	4	0.2400	0.2396	0.2504	0.1028	0.1014	0.1020	0.1796	0.1938	0.1922
3	3	0.2386	0.2389	0.2500	0.1064	0.1044	0.1053	0.1795	0.1972	0.2087
4	2	0.2269	0.2315	0.2420	0.1107	0.1092	0.1102	0.1843	0.2075	0.1739
5	1	0.2379	0.2397	0.2477	0.1165	0.1149	0.1156	0.2180	0.2307	—
AAD		—	0.0044	0.0124	—	0.0015	0.0007	—	0.0176	0.0135
RRMSD(%)		—	0.91	1.52	—	1.43	0.70	—	9.35	9.23
n-NMA	m-H₂O	∠Na…O—C/H/(°)			∠O…H—C/N/O/(°)			ΔE/(kJ·mol^-1)
n-NMA	m-H₂O	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA	QM	ABEEM/MM	OPLS-AA
1	3	138.89	137.69	140.42	—	—	—	86.24	92.33	71.61
2	2	149.76	149.32	149.36	—	—	—	93.27	101.47	62.91
3	1	149.82	150.49	159.65	127.54	121.83	—	100.84	105.65	52.60
1	5	128.16	132.44	134.95	152.43	145.91	160.24	75.45	72.09	63.75
2	4	126.06	129.91	135.77	158.06	154.91	144.71	79.74	82.94	58.00
3	3	124.28	127.22	138.50	158.76	156.61	132.70	80.63	81.82	52.07
4	2	147.64	144.38	155.85	177.43	173.11	177.37	81.38	89.30	46.06
5	1	136.82	139.30	145.65	163.63	165.48	—	86.15	92.22	39.68
AAD		—	2.39	7.44	—	3.95	11.82	—	5.10	29.63
RRMSD(%)		—	1.99	6.21	—	2.75	9.36	—	6.51	37.53

Table 6 Linear correlations of charge distributions of [Na(NMA)n(H2O)m]+(n+m=4, 6) from QM and ABEEM/MM

n-NMA	m-H₂O	Y = AX + B	R	S	U_max	q_Na/a.u.
n-NMA	m-H₂O	Y = AX + B	R	S	U_max	QM	ABEEM/MM
1	3	Y=1.2818X-0.0128	0.9845	0.0649	0.1586	0.7496	0.7895
2	2	Y=1.2601X-0.0084	0.9827	0.0611	0.1251	0.7505	0.8224
3	1	Y=1.2170X-0.0054	0.9822	0.0560	0.1476	0.7491	0.8176
1	5	Y=1.2936X-0.0104	0.9822	0.0724	0.2036	0.7646	0.7749
2	4	Y=1.2916X-0.0079	0.9816	0.0668	0.1562	0.7533	0.8088
3	3	Y=1.2370X-0.0052	0.9773	0.0665	0.1905	0.7453	0.8012
4	2	Y=1.2408X-0.0044	0.9803	0.0585	0.2274	0.7373	0.8315
5	1	Y=1.1906X-0.0030	0.9889	0.0403	0.1114	0.7419	0.8553

Fig.7 Linear correlation of charge distributions from ABEEM/MM and QM of [Na(NMA)n(H2O)m]+(n+m=4, 6)

Table 7 Comparisions of the time of optimization from QM and ABEEM/MM

m-H₂O	t/s		n-NMA	t/s		n-NMA	m-H₂O	t/s
m-H₂O	QM^a	ABEEM/MM^b	n-NMA	QM^a	ABEEM/MM^b	n-NMA	m-H₂O	QM^a	ABEEM/MM^b
3	94.50	0.02	3	11266.00	3.79	1	3	1735.80	2.86
4	124.54	0.55	4	33110.20	6.65	2	2	5575.00	1.91
5	311.00	1.20	5	75958.80	9.09	3	1	12766.60	4.28
6	257.40	2.69	6	150446.40	14.54	1	5	3428.90	2.37
7	1260.05	2.30	7	193496.96	21.17	2	4	11621.40	3.1
8	1765.00	3.59	8	633740.90	18.18	3	3	20328.00	4.88
						4	2	53743.90	8.67
						5	1	101921.90	10.59

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