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Scientific paper
Geometry Predictions, Vibrational Analysis and IR Intensities of XH3Y (X=C, Si, Ge, Y=F, Cl, Br) Calculated by Hybrid Density Functional Theory, MP2 and MP4 Methods
Abraham F. Jalbouta*, Bartosz Trzaskowskib*, Yuanzhi Xiac, Yahong Licd
a Institute de Quimica, Universidad Nacional Autonomaa de Mexico, Mexico City, Mexico b Department of Chemistry, The University of Arizona, Tucson, AZ 85721, USA c Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining 810008, China d Department of Chemistry, Suzhou University, Suzhou 215006, China * Corresponding author: E-mail: trzask@email.arizona.edu
Received: 11-12-2006
Abstract
Hybrid density functional theory B3LYP, B1LYP, B3P86, MPW1PW91 and B3PW91 methods as well as MP2 and MP4 methods at the 6-311++G (3df,3pd) level of theory are used for the calculations of geometrical parameters, infrared vibrational frequencies and absorption intensities of XH3Y (X=C, Si, Ge and Y=F, Cl, Br) set of molecules. All of the calculated results are compared with the most recent experimental data. The advantages of DFT methods are exhibited from the comparison and discussion. The basis set effect is also considered and the optimal theoretical methods for the discussed systems are recommended.
Keywords: Halogenated methane, halogenated silane, halogenated germane, vibrational analysis, density functional theory
1. Introduction
Great efforts have been put in recent years into studying of the basic molecular properties of halogenated carbon family systems. Many different experimental methods have been developed to obtain thermodynamic, magnetic, spectroscopic and other properties of these com-pounds.1-7 In recent few decades, with the development of quantum mechanics theory and computational technology, theoretical and computational studies on the haloge-nated carbon family species became more and more popu-lar.8-11 Computational methods are used not only due to the convenience and high efficiency, but also since satisfactory accuracy can be obtained from these methods. Due to this fact many properties of halogenated methane, silanes and germanes, such as geometry structure, vibration spectra and thermochemical properties, are available nowadays as a result of theoretical calculations.12-20 The calculations has provides us with information about molecular physical properties as well as reactive behaviors
which do not only widen our knowledge, but also may boost more creative insights and predictions.
Although the study of this topic is very popular, there are still many unsolved problems in the area of theoretical study on the properties of halogenated carbon family systems. First of all, previous computational studies have been focused mostly on one molecular system or one property of the halogenated carbon family species. Therefore comparisons of properties between different halogen-containing methanes, silanes, and germanes are scarce. On the other hand a comprehensive and systematic investigation of the similarities and differences of halogenated carbon family is indispensable for a better understanding of the chemistry of this class of compounds. Secondly, it is usually supposed that the higher level of theory used in computational studied corresponds to the higher accuracy of results. It is known, however, that for small organic systems DFT methods, and B3LYP method in particular, can give more reliable results than higher level ab-initio met-hods.21-24 Moreover, there are many density functional methods available nowadays, and the most commonly
1	used B3LYP functional is not always the best choice to	The calculated angle values are different from experimen-	1
2	study a certain class of molecules. Furthermore, to the	tal values by approximately 2 degrees. Surprisingly, previ-	2
3	best of our knowledge, previous studies in this area main-	ous investigations on this problem suggest tat the best	3
4	ly focus on the effect of using different methods and no	method to predict H-C-Cl and H-C-H angle values is to	4
5	data from the calculation with a basis set as large as 6-	use the semi empirical method (PM3) which gives values	5
6	311++G (3df, 3pd) are available. A comparison between	only 0.6 degree higher than experimental results.26	6
7	the results obtained for the 6-311++G (3df, 3pd) basis set	For the SiH3F system the calculated X-Y distances	7
8	and smaller basis sets should provide more insight into the	are between 1.600 and 1.611 A, H-X-Y angles are bet-	8
9	importance of the basis set effect.	ween 108.5 and 118.6 degree, and the H-X-H angle ranges	9
10	To solve all above-mentioned problems, we have	from 110.3 to 110.5 degree, depending on the computatio-	10
11	carried out computational studies on the geometry optimi-	nal method used. In case of the SiH3Cl system, the X-Y di-	11
12	zation and frequency analysis of XH3Y, where X=C, Si,	stances are longer, and the calculated values are between	12
13	Ge and Y=F, Cl, Br. Five different DFT methods (B3LYP,	2.220 and 2.238A. On the other hand the calculated	13
14	B1LYP, B3P86, MPW1PW91, B3PW91) and two high le-	H-X-Y angle of SiH3Cl is smaller than in the previous ca-	14
15	vel ab-initio methods (MP2, MP4) have been used at the	se (ranging from 108.5 to 108.6 degrees), while the H-X-H	15
16	6-311++G (3df, 3pd) level of theory. From our theoretical	angles are larger (110.5 to 110.6 degrees). A similar trend	16
17	study and the available experimental data, as well as from	in variations of geometrical parameters may be observed in	17
18	results of previous theoretical investigations, we collect	the case of the SiH3Br system. The Si-H distances of the	18
19	more examples to discuss the applicability of different	SiH3Y systems are only slight different, with the shortest	19
20	calculation methods (DFT and high level ab-initio met-	bond being present in the SiH3Br system. The trend in Ge-	20
21	hods). We also provide data obtained using the large 6-	H3Y (Y=F, Cl, Br) class of molecules is the same as in Si-	21
22	311++G (3df,3pd) basis set and discuss the basis set ef-	H3Y. These results can be easily explained, since when the	22
23	fect. Using all these approaches we have performed a	radius of the halogen atoms increases, the X-Y distance in-	23
24	systematic calculation on the geometry structure and fre-	creases as well. This in turn leads to a smaller repulsion bet-	24
25	quency values of nine halogenated carbon family substan-	ween the X-Y bond and the lone pair of the halogen atom,	25
26	ces. It allows us to obtain important data to discuss the	resulting in the smaller value of the H-X-Y angle. Once the	26
27	difference in the properties of these analogies as well as	H-X-Y angle gets smaller, it's reasonable to assume that	27
28	provide the reliable reference for possible future studies.	the H-X-H angle would get larger. The slight change of the	28
29	X-H distance may be caused by the different electronegati-	29
30	vity value of the halogen atom. If the electronegativity va-	30
31	2. Computational Details	lue of Y is decreased, the X-Y bond is weakened, while the	31
32	X-H bond becomes stronger. On the other hand, for a given	32
33	All calculations in this study have been performed	Y, the values of the X-Y and X-H distances as well as	33
34	with the Gaussian 03 program package.25 Each stationary	H-X-H angles are all increased in the C, Si and Ge order,	34
35	point of the nine halogenated species, CH3F, CH3Cl,	while the H-X-Y gets shorter.	35
36	CH3Br, SiH3F, SiH3Cl, SiH3Br, GeH3F, GeH3Cl and Ge-	The calculated frequencies and IR intensities of all	36
37	H3Br, has been fully optimized with five different DFT	monohalogenated species as well as available experimen-	37
38	methods (B3LYP, B1LYP, B3P86, MPW1PW91,	tal data are given in Table 2. Table 2a shows the absolute	38
39	B3PW91) and two high level ab-initio methods (MP2,	vibrational frequencies, whereas Table 2b shows scaled	39
40	MP4) with 6-311++G (3df,3pd) basis set. Frequencies ha-	vibrational frequencies based on an important study by	40
41	ve been calculated at the same level of theory as geometry	Scott and Radom30 by which a comprehensive evaluation	41
42	optimizations, and each stationary point has been confir-	of scale factors for harmonic vibrational frequencies was	42
43	med to be at a local minimum by frequency analysis. Thus	performed. In that work a series of 122 molecules were	43
44	for each system, a total of seven geometries and seven vi-	computed with the Hartree-Fock, Moller-Plesset, quadra-	44
45	brational frequencies has been reported. All the reported	tic configuration interaction (QCI), and density functional	45
46	data are unscaled.	theory (DFT) methods. A scale factor of 0.9496 was re-	46
47	ported, that can be helpful in the present computations.	47
48	The present basis set used is larger but the scale factors	48
49	3. Results and Discussion	will suffice. Therefore, we have used a scale factor of	49
50	0.9496 as recommended by Scott and Radom. However,	50
51	Geometrical parameters of all molecules are given	as Table 2b shows the experimental correlations without	51
52	in Table 1, and two bond lengths (X-Y and X-H) and two	scaling is better, this might be due to the unusual behavior	52
53	angles (H-X-Y and H-X-H) are described for each mole-	of the Si, Ge atoms in the calculations. By adding this sca-	53
54	cule. Compared with the experimental data all the calcula-	le factor into our harmonic frequencies, we are able to inc-	54
55	tions are consistent with the experiments, except for the	lude some effects of anharmonicity and should suffice the	55
56	obvious errors in the prediction of the CH3Cl angle value.	present calculations presented in this work.	56
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Table 1. Optimized Structures of XH3Y (X=C, Si and Ge; Y=F, Cl and Br) at the 1B3LYP, 2B1LYP, 3B3P86, 4MPW1PW91, 5B3PW91, 6MP2, 7MP4/6-311++G (3df, 3pd) level. Distances are in Â, angles are in degree.
XH3Y	parameter	1	2	3	4	5	6	7	Expt.
ch3f	C-F	1.389	1.388	1.379	1.376	1.380	1.383	1.388	1.3830a
	C-H	1.089	1.089	1.090	1.090	1.091	1.086	1.090	1.0870a
	H-C-F	108.7	108.7	110.0	109.0	109.0	108.7	108.6	110.20a
	H-C-H	110.2	110.2	110.0	109.9	110.0	110.2	110.3	108.73a
CH3Cl	C-Cl	1.793	1.793	1.776	1.774	1.778	1.771	1.783	1.785a
	C-H	1.084	1.083	1.085	1.085	1.086	1.083	1.087	1.090a
	H-C-Cl	108.3	108.3	108.6	108.6	108.6	108.6	108.4	110.75
	H-C-H	110.6	110.6	110.4	110.4	110.4	110.3	110.5	108.16
CH3Br	C-Br	1.958	1.958	1.938	1.935	1.940	1.929	1.943	1.9340a
	C-H	1.083	1.081	1.084	1.083	1.085	1.083	1.083	1.0823a
	H-C-Br	107.6	107.6	107.9	107.9	107.9	108.1	108.0	107.72a
	H-C-H	111.2	111.3	111.0	111.0	111.0	110.8	110.0	111.157a
SiH3F	Si-F	1.611	1.610	1.606	1.605	1.608	1.60	1.613	1.595a
	Si-H	1.476	1.474	1.477	1.478	1.479	1.470	1.471	1.476a
	H-Si-F	108.2	108.2	108.2	108.2	108.2	108.3	108.3	108.269a
	H-Si-H	110.7	110.7	110.7	110.7	110.7	110.6	110.6	110.64a
SiH3Cl	Si-Cl	2.068	2.068	2.088	2.054	2.058	2.053	2.058	2.051a
	Si-H	1.475	1.474	1.476	1.477	1.478	1.469	1.472	1.475a
	H-Si-Cl	108.5	108.5	108.5	108.5	108.6	108.6	108.6	108.295a
	H-Si-H	110.4	110.5	110.4	110.4	110.4	110.4	110.3	110.62a
SiH3Br	Si-Br	2.238	2.238	2.220	2.220	2.223	2.222	2.228	2.2123b
	Si-H	1.476	1.474	1.477	1.477	1.479	1.469	1.472	1.4743b
	H-Si-Br	108.4	108.4	108.4	108.4	108.5	108.4	108.4	108.161b
	H-Si-H	110.6	110.6	110.5	110.5	110.5	110.5	110.5	
GeH3F	Ge-F	1.760	1.757	1.748	1.747	1.752	1.791	1.798	1.7350b
	Ge-H	1.532	1.531	1.528	1.529	1.531	1.530	1.535	1.5220b
	H-Ge-F	105.9	106.0	105.9	106.0	106.0	105.6	105.5	105.92b
	H-Ge-H	112.8	112.7	112.7	112.7	112.7	113.1	113.1	
GeH3Cl	Ge-Cl	2.176	2.176	2.157	2.154	2.159	2.160	2.166	2.1447b
	Ge-H	1.531	1.530	1.527	1.528	1.530	1.530	1.534	1.5155b
	H-Ge-Cl	106.9	106.9	106.9	106.9	107.0	107.1	107.2	107.10b
	H-Ge-H	111.9	111.9	111.9	111.8	111.8	111.7	111.6	111.0b
GeH3Br	Ge-Br	2.334	2.334	2.311	2.311	2.316	2.314	2.322	2.297b
	Ge-H	1.531	1.530	1.527	1.528	1.530	1.530	1.536	1.527b
	H-Ge-Br	107.0	107.1	107.1	107.1	107.1	107.2	107.4	106.3b
	H-Ge-H	111.8	111.8	112.8	111.8	111.7	111.6	111.6	
a Taken from ref. 26. b Taken from ref. 27 and references therein.
There are six different vibtrational frequencies according to the six normal vibrations for species of the C3v point group as depicted in Fig. 1. The first is the symmetric X-H stretch vp and the second is the Y-X-H umbrella motion v2. They are followed by the X-Y stretch is v3, and the degenerate modes are the asymmetric X-H stretch v4, the H-X-H scissor motion v5 and finally the Y-X-H rock v6. All computational normal modes obtained in this investigation were successfully assigned to one of the six types of vibrations. As a general rule, the calculated frequency values are consistent with the experimental results, although there are small variations with different methods used. It is difficult, however, to choose one computational method as the most suitable for calculating the vibrational spectra of all compounds. The advantages of
using certain methods in calculations of selected vibrational frequencies will be discussed later.
A very interesting property embedded in the molecular wavefunction is the vibrational assignment which has been developed in the valence coordinates most closely resembling normal coordinates.31 In this technique, Bowman and co-workers use successive contractions of the expansion set that keeps the hamiltonian matrices diagonally dominant. This allows the largest component of the eigenvector to be sufficient to assign rovibrational states for many species. Such calculations can be applied to assignment of lower energy vibrational transitions, photo-ionization spectra and improved description of Franck-Condon factors for simple molecules. However, it is difficult to apply such a scheme to our systems due to the in-
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Table 2a. Vibrational frequencies (cm ') of various species shown in Table 1 (X, Y are ligands from the table and modes shown in Figure 1) ,whe-re I is the intensities (in parentheses, KM/mol) and the values in EXP are the experimental values (where VS=Very Strong, S=Strong, M=Medium, W=Weak, VW=Very Weak), computed at the1B3LYP, 2B1LYP, 3B3P86, 4MPW1PW91, 5B3PW91, 6MP2, 7MP4/6-311++G (3df, 3pd) level
XH3Y		V1	I1	V2	I2	V3	I3	V4	I4	V5	I5	V6I6
						CH3F						
1I	3032.706	33.639	1493.811	5.088	1047.734	110.244	3111.68	28.576	1485.097	0.911	1192.920	1.026
2I	3044.911	33.474	1503.724	5.016	1053.839	111.754	3124.841	29.307	1494.857	1.032	1200.444	1.192
3I	3040.286	35.129	1488.878	5.737	1078.917	109.806	3127.575	27.397	1480.935	0.665	1194.225	0.838
4I	3051.952	34.021	1495.452	5.632	1088.562	110.936	3139.167	28.228	1488.823	0.725	1200.858	0.895
5I	3034.949	35.323	1487.639	5.534	1073.793	110.253	3121.566	28.536	1480.214	0.748	1193.286	0.835
6I	3087.626	32.204	1526.495	4.844	1084.246	105.480	3193.168	22.311	1510.283	1.357	1213.531	1.324
7I	3140.294	0.000	1495.132	0.000	1060.481	0.0000	3042.339	0.000	1510.556	0.000	1200.321	0.000
EXPia	2964	VS	1464	S	1048.6	S	3005.8	S	1466.5	M	1182.4	
						CH3Cl						
1I	3070.33	22.780	1384.861	11.195	717.452	25.909	3073.504	22.873	1483.535	6.134	1030.959	2.413
2I	3082	23.260	1394.292	11.913	720.097	26.962	3085.068	23.307	1493.063	6.061	1037.636	2.307
3I	3080.45	22.438	1381.586	8.807	746.176	24.118	3081.847	22.184	1476.528	6.861	1032.360	2.736
4I	3092.04	23.196	1388.759	8.860	754.434	24.518	3093.002	23.282	1483.276	6.679	1038.550	2.681
5I	3075.28	23.134	1380.888	9.035	744.185	24.138	3076.592	23.032	1475.680	6.620	1031.851	2.743
6I	3108.1	22.010	1416.413	11.258	778.977	22.586	3108.840	22.004	1510.858	5.571	1059.318	2.358
7I	3071.089	0.000	1405.264	0.000	756.982	0.000	3174.764	0.000	1499.922	0.00	1048.810	0.000
EXPIa	2879.28	M	1354.9	S	732.1	S	3039.31	S	1452.1	M	1017.3	M
						CH3Br						
1I	3192.553	1.264	1331.354	18.483	591.795	12.174	3087.012	15.618	1476.512	5.940	963.025	3.704
2I	3205.113	1.315	1340.431	19.646	594.552	12.837	3099.315	16.149	1486.243	5.852	968.851	3.620
3I	3203.389	0.859	1329.709	14.710	619.852	10.791	3092.580	14.847	1469.810	6.631	966.334	4.145
4I	3214.590	1.054	1337.538	15.076	627.434	10.965	3104.095	16.120	1476.296	6.520	971.902	4.143
5I	3197.989	6.684	1329.283	15.183	617.251	10.826	3087.830	15.824	1469.212	6.369	965.883	4.109
6I	3235.335	0.701	1367.053	16.750	651.982	8.3	3116.225	15.749	1503.635	5.289	991.62	3.907
7I	3077.104	0.000	1354.874	0.000	628.485	0.000	3189.677	0.000	1492.876	0.000	978.613	0.000
EXPIa	2972	M	1305.9	S	611.1	S	3056.35	S	1442.7	M	954.7	
						SiH3F						
1I	2267.097	136.638	998.272	184.725	852.817	78.5363	2262.430	32.232	973.759	85.760	728.057	52.785
2I	2258.106	133.890	991.367	181.401	848.105	76.752	2251.946	31.558	967.474	83.385	723.057	51.402
3I	2263.168	126.275	983.627	178.356	858.770	69.776	2255.505	30.374	959.401	78.084	719.543	50.811
4I	2265.130	126.764	985.406	178.596	861.734	70.466	2258.402	30.457	961.022	78.321	721.196	51.567
5I	2252.988	127.602	981.240	175.730	853.381	71.041	2245.660	31.074	957.176	77.559	718.038	50.466
6I	2335.498	140.791	996.323	95.223	860.767	80.121	2332.776	34.513	996.496	95.214	739.474	57.270
7I	2303.199	0.000	979.119	0.000	850.669	0.0000	2308.866	0.000	1002.660	0.000	729.681	0.000
EXPIa	2206	-	990	S	872	M	2196	M	956	M	728.1	-
						SiH3Cl						
1I	2248.240	53.682	959.559	56.738	533.361	69.655	2259.531	96.168	952.550	251.673	657.685	22.826
2I	2259.045	54.838	966.278	58.513	534.863	71.207	2269.248	97.889	959.379	257.626	662.338	23.520
3I	2251.632	52.078	950.754	52.306	546.902	68.631	2264.017	89.129	943.423	238.490	654.623	22.446
4I	2253.710	52.210	952.440	52.182	550.618	69.020	2265.107	90.492	945.408	237.920	656.555	22.804
5I	2240.587	52.788	948.728	51.823	545.128	68.186	2252.787	91.257	941.936	236.074	653.750	22.343
6I	2321.753	58.447	986.898	64.669	561.387	74.668	2330.588	101.285	978.722	286.458	675.741	26.117
7I	2292.149	0.000	963.880	0.000	555.459	0.000	2302.334	0.000	970.810	0.000	666.318	0.000
EXPIa	2201	-	949	-	551	S	2195	S	954.4	S	664.0	M
						SiH3Br						
1I	2242.121	60.507	934.849	302.548	412.972	41.807	2256.275	85.214	957.868	52.290	629.298	14.267
2I	2253.500	60.829	941.516	309.309	414.344	42.619	2266.682	87.174	964.467	53.937	632.530	14.627
3I	2248.585	58.506	925.677	285.551	426.408	41.170	2263.905	78.220	948.855	48.191	625.876	14.128
4I	2251.594	58.192	927.508	284.767	429.298	41.412	2266.042	78.566	950.109	48.035	627.288	14.165
5I	2236.190	59.154	924.521	283.036	425.261	40.902	2251.003	80.742	946.807	47.602	625.460	13.941
6I	2320.444	65.329	959.709	340.908	439.605	44.851	2332.252	89.058	982.719	59.105	645.396	17.028
7I	2290.032	0.000	966.547	0.000	434.576	0.000	2304.147	0.000	966.547	0.000	635.936	0.000
EXPIa	2200	-	930	S	430	M	2196	S	950.4	S	632.6	
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xh3y		V1	I1	V2	I2	V3	I3	V4	I4	V5	I5	V6I6
						GeH3F						
1I	2154.843	25.680	865.958	65.778	667.185	104.507	2166.739	122.048	865.958	65.778	628.143	36.201
2I	2164.580	32.297	876.224	65.426	673.228	106.758	2173.078	124.352	871.051	66.041	630.701	37.398
3I	2168.948	37.025	865.537	58.925	683.570	105.565	2182.164	105.478	870.726	58.160	627.839	36.340
4I	2177.874	30.321	868.845	60.893	686.758	107.461	2193.203	111.945	873.606	61.618	629.572	37.267
5I	2163.700	29.240	868.948	59.265	678.775	104.768	2174.969	118.148	863.965	59.813	626.978	36.258
6I	2235.889	22.971	892.957	75.686	738.329	154.334	2232.867	131.666	892.957	75.686	635.794	40.505
7I	2193.716	0.000	875.666	0.000	728.836	0.000	2199.086	0.000	877.538	0.000	623.501	0.000
EXPIb	2120.6	S	859.0	VS	689.1	S	2131.7	S	874.0	S	624.6	M
						GeH3Cl						
1I	2150.816	47.597	843.756	164.019	406.513	54.466	2164.156	98.140	871.551	46.105	591.816	15.681
2I	2157.763	51.052	851.401	168.007	407.99	55.547	2167.861	100.009	878.860	47.453	596.876	16.316
3I	2166.886	49.089	843.021	152.159	420.072	54.589	2185.186	92.325	870.053	42.671	595.831	15.701
4I	2173.003	50.688	847.562	154.920	423.685	55.482	2189.300	93.663	873.485	43.310	598.601	16.467
5I	2160.173	47.590	842.237	153.936	417.765	54.383	2175.691	94.380	870.031	42.894	594.969	15.819
6I	2231.680	57.714	873.858	199.143	608.571	20.791	2232.132	106.184	896.933	54.880	433.193	60.802
7I	2196.527	0.000	858.485	0.000	598.571	0.000	2199.906	0.000	881.248	0.000	428.853	0.000
EXPIb	2119.9	S	847.5	VS	421.7	S	2128.9	S	874.1	S	602.2	
						GeH3Br						
1I	2148.268	53.753	829.336	213.569	294.152	27.101	2163.497	90.527	871.769	43.215	569.974	10.049
2I	2153.914	59.216	837.249	219.436	295.125	27.614	2167.140	88.735	875.750	44.400	574.380	10.539
3I	2163.073	54.254	829.638	199.376	305.906	27.027	2185.006	83.239	870.208	39.299	570.518	10.331
4I	2173.380	52.990	832.306	202.993	307.277	27.614	2187.211	85.561	873.141	40.078	570.015	10.381
5I	2155.804	56.421	828.326	200.721	303.623	27.054	2169.929	84.383	868.348	39.451	569.100	10.343
6I	2225.913	62.544	861.330	251.476	314.744	30.247	2227.435	98.264	896.378	51.291	588.031	14.163
7I	2188.916	0.000	846.592	0.000	310.434	0.000	2191.258	0.000	881.017	0.000	578.270	0.000
EXPIb	2115.2	-	832.7	-	307.7	-	2126.7	-	870.9	-	578.2	-
a Taken from ref. 28.
b Taken from ref. 29.
creased level of complexity associated with such calculations. We do believe that by using high level ab initio methods with an extended basis set experimentally reliable calculations can be obtained.
The results suggest that it is difficult to choose the most reliable method for all studied systems. Several trends in results are, however, clear. In the geometry optimization, both DFT methods, MP2 and MP4 methods can
Fig. 1. Vibrational modes of the XH3Y molecules that belong to the C3v point group.
get very accurate results (except for the CH3Cl angles). Since MP2 and MP4 calculations are much more time consuming and have no obvious advantages for geometry optimization, we believe that DFT calculations are more favorable for geometry optimizations of these systems. For frequency analysis, in some cases the MP4 approach can give more accurate results than DFT methods (see for example v4 of CH3F, or v1 of CH3Br). In most cases DFT calculations are, however, also accurate and give better results than MP2 and MP4 calculations. For almost all frequency calculations MP2 results are the least accurate. Our calculations reveal that in many cases the accuracy of DFT methods is very high, with the average error of only 30 cm-1. This is, however, not true for the v1 vibration, where we usually obtain larger variations (of more than 50 cm-1).
Considering the applicability of different DFT methods, one can see that some of the functionals tend to be superior to the commonly used B3LYP method. Taking the frequency analysis of SiH3F as an example, the experimental value of v1 is 2206 cm-1, and the result of MPW1PW91 calcul1ation is 2252.988 cm-1 while the result of B3LYP calculation is 2267.097 cm-1. Similarly, B1LYP predicts v2 better than B3LYP, and MPW1PW91 predicts v3 better than B3LYP. Unfortunately it is impossible to find a single DFT method which will accurately predict all of the six vibrational frequencies. The differen-
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Table 2b. Scaled vibrational frequencies (cm ') by a factor of 0.9496 (which are represnted as the vSC values) for various species shown in Table 1 (X, Y are ligands from the table and modes shown in Figure 1) ,where I is the intensities (in parentheses, KM/mol) and the values in EXP are the experimental values computed at the1B3LYP, 2B1LYP, 3B3P86, 4MPW1PW91, 5B3PW91, 6MP2, 7MP4/6-311++G (3df, 3pd) level.
XH3Y
v41S
'I
3032.706 3044.911 3040.286 3051.952 3034.949 3087.626 3140.294
2879.857 2891.447 2887.055 2898.133 2881.987 2932.009 2982.023
EXPIa 2964
1493.811 1503.724 1488.878 1495.452 1487.639 1526.495 1495.132 1464
1418.522 1427.936 1413.838 1420.081 1412.661 1449.559 1419.777
1047.734 1053.839 1078.917 1088.562 1073.793 1084.246 1060.481 1048.6
CH3F
994.928
1000.725
1024.539
1033.698
1019.673
1029.600
1007.032
3111.68
3124.841
3127.575
3139.167 3121.566
3193.168 3042.339 3005.8
2954.851 2967.349 2969.945 2980.952 2964.239 3032.232 2889.005
1485.097 1494.857 1480.935 1488.823 1480.214 1510.283 1510.556 1466.5
1410.248 1419.516 1406.295 1413.786 1405.611 1434.164 1434.423
1192.920 1200.444 1194.225 1200.858 1193.286 1213.531 1200.321 1182.4
1132.796 1139.941 1134.036 1140.334 1133.144 1152.369 1139.824
1I 2I 3I 4I 5I 6I 7I
3070.33
3082
3080.45
3092.04
3075.28
3108.1
3071.089
2879.28
2915.585 2926.667 2925.195 2936.201 2920.285 2951.451 2916.306
1384.861 1394.292 1381.586 1388.759 1380.888 1416.413 1405.264 1354.9
1315.064 1324.020 1311.954 1318.766 1311.291 1345.026 1334.439
717.452 720.097 746.176 754.434 744.185 778.977 756.982 732.1
CH3Cl
681.292 683.804 708.569 716.411 706.678 739.717 718.830
3073.504 3085.068 3081.847 3093.002 3076.592 3108.840 3174.764 3039.31
2918.599 2929.581 2926.522 2937.115 2921.532 2952.154 3014.756
1483.535 1493.063 1476.528 1483.276 1475.680 1510.858 1499.922 1452.1
1408.765 1417.813 1402.111 1408.519 1401.306 1434.711 1424.326
1030.959 1037.636 1032.360 1038.550 1031.851 1059.318 1048.810 1017.3
978.999
985.339
980.329
986.207
979.846
1005.928
995.950
1I 2I
CH3Br
3192.553 3205.113 3203.389 3214.590 3197.989 3235.335 3077.104 2972
3031.648 3043.575 3041.938 3052.575 3036.810 3072.274 2922.018
1331.354 1340.431 1329.709 1337.538 1329.283 1367.053 1354.874 1305.9
1264.254 1272.873 1262.692 1270.126 1262.287 1298.154 1286.588
591.795 594.552 619.852 627.434 617.251 651.982 628.485 611.1
561.969 564.587 588.611 595.811 586.142 619.122 596.809
3087.012 3099.315 3092.580 3104.095 3087.830 3116.225 3189.677 3056.35
2931.427 2943.110 2936.714 2947.649 2932.203 2959.167 3028.917
1476.512 1486.243 1469.810 1476.296 1469.212 1503.635 1492.876 1442.7
1402.096 1411.336 1395.732 1401.891 1395.164 1427.852 1417.635
963.025
968.851
966.334
971.902
965.883
991.62
978.613
954.7
914.489 920.021 917.631 922.918 917.202 941.642 929.291
1I 2I 3I 4I 5I 6I 7I
2267.097 2258.106 2263.168 2265.130 2252.988 2335.498 2303.199 2206
2152.835 2144.297 2149.104 2150.967 2139.437 2217.789 2187.118
998.272	947.959	852.817
991.367	941.402	848.105
983.627	934.052	858.770
985.406	935.742	861.734
981.240	931.786	853.381
996.323	946.108	860.767
979.119	929.771	850.669
990		872
959.559	911.197	533.361
966.278	917.578	534.863
950.754	902.836	546.902
952.440	904.437	550.618
948.728	900.912	545.128
986.898	937.158	561.387
963.880	915.300	555.459
949		551
934.849	887.733	412.972
941.516	894.064	414.344
925.677	879.023	426.408
927.508	880.762	429.298
924.521	877.925	425.261
959.709	911.340	439.605
966.547	917.833	434.576
930		430
SiH3F
809.835 3
805.361 815.488 818.303 810.371 817.384 807.795
2262.430 2251.946 2255.505 2258.402 2245.660 2332.776 2308.866 2196
2148.404 2138.448 2141.828 2144.579 2132.479 2215.204 2192.499
973.759	924.682	728.057	691.363
967.474	918.713	723.057	686.615
959.401	911.047	719.543	683.278
961.022	912.586	721.196	684.848
957.176	908.934	718.038	681.849
996.496	946.273	739.474	702.205
1002.660	952.126	729.681	692.905
956		728.1	
952.550	904.541	657.685	624.538
959.379	911.026	662.338	628.956
943.423	895.874	654.623	621.630
945.408	897.759	656.555	623.465
941.936	894.462	653.750	620.801
978.722	929.394	675.741	641.684
970.810	921.881	666.318	632.736
954.4		664.0	
957.868	909.591	629.298	597.581
964.467	915.858	632.530	600.650
948.855	901.033	625.876	594.332
950.109	902.224	627.288	595.673
946.807	899.088	625.460	593.937
982.719	933.190	645.396	612.868
966.547	917.833	635.936	603.885
950.4		632.6	
1I 2I 3I 4I
SiH3Cl
2248.240 2259.045 2251.632 2253.710 2240.587 2321.753 2292.149 2201
2134.929 2145.189 2138.150 2140.123 2127.661 2204.737 2176.625
506.480 507.906 519.338 522.867 517.654 533.093 527.464
2259.531 2269.248 2264.017 2265.107 2252.787 2330.588 2302.334 2195
2145.651 2154.878 2149.911 2150.946 2139.247 2213.126 2186.296
1I 2I 3I 4I 5I 6I 7I
SiH3Br
2242.121 2253.500 2248.585 2251.594 2236.190 2320.444 2290.032 2200
2129.118 2139.924 2135.256 2138.114 2123.486 2203.494 2174.614
392.158 393.461 404.917 407.661 403.828 417.449 412.673
2256.275 2266.682 2263.905 2266.042 2251.003 2332.252 2304.147 2196
2142.559 2152.441 2149.804 2151.833 2137.552 2214.706 2188.018
SC
SC
SC
SC
SC
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6
I
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4
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EXPra
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I
EXP a
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EXP a
I
EXP a
I
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xh3y		V1	v1SC	V2	v2SC	V3	v3SC	v4	v41SC	v5	v5SC	v6 v6SC
						GeH3F						
■'I	2154.843	2046.239	865.958	822.314	667.185	633.559	2166.739	2057.535	865.958	822.314	628.143	596.485
2I	2164.580	2055.485	876.224	832.062	673.228	639.297	2173.078	2063.555	871.051	827.150	630.701	598.914
3I	2168.948	2059.633	865.537	821.914	683.570	649.118	2182.164	2072.183	870.726	826.841	627.839	596.196
4I	2177.874	2068.109	868.845	825.055	686.758	652.145	2193.203	2082.666	873.606	829.576	629.572	597.842
5I	2163.700	2054.650	868.948	825.153	678.775	644.565	2174.969	2065.351	863.965	820.421	626.978	595.378
6I	2235.889	2123.200	892.957	847.952	738.329	701.117	2232.867	2120.331	892.957	847.952	635.794	603.750
7I	2193.716	2083.153	875.666	831.532	728.836	692.103	2199.086	2088.252	877.538	833.310	623.501	592.077
EXPIb	2120.6		859.0		689.1		2131.7		874.0		624.6	
GeHjCl
1I	2150.816	2042.415	843.756	801.231	406.513	386.025	2164.156	2055.083	871.551	827.625	591.816	561.988
2I	2157.763	2049.012	851.401	808.490	407.99	387.427	2167.861	2058.601	878.860	834.565	596.876	566.793
3I	2166.886	2057.675	843.021	800.533	420.072	398.900	2185.186	2075.053	870.053	826.202	595.831	565.801
4I	2173.003	2063.484	847.562	804.845	423.685	402.331	2189.300	2078.959	873.485	829.461	598.601	568.432
5I	2160.173	2051.300	842.237	799.788	417.765	396.710	2175.691	2066.036	870.031	826.181	594.969	564.983
6I	2231.680	2119.203	873.858	829.816	608.571	577.899	2232.132	2119.633	896.933	851.728	433.193	411.360
7I	2196.527	2085.822	858.485	815.217	598.571	568.403	2199.906	2089.031	881.248	836.833	428.853	407.239
EXPIb	2119.9		847.5		421.7		2128.9		874.1		602.2	
						GeH3Br						
1I	2148.268	2039.995	829.336	787.537	294.152	279.327	2163.497	2054.457	871.769	827.832	569.974	541.247
2I	2153.914	2045.357	837.249	795.052	295.125	280.251	2167.140	2057.916	875.750	831.612	574.380	545.431
3I	2163.073	2054.054	829.638	787.824	305.906	290.488	2185.006	2074.882	870.208	826.350	570.518	541.764
4I	2173.380	2063.842	832.306	790.358	307.277	291.790	2187.211	2076.976	873.141	829.135	570.015	541.286
5I	2155.804	2047.151	828.326	786.578	303.623	288.320	2169.929	2060.565	868.348	824.583	569.100	540.417
6I	2225.913	2113.727	861.330	817.919	314.744	298.881	2227.435	2115.172	896.378	851.201	588.031	558.394
7I	2188.916	2078.595	846.592	803.924	310.434	294.788	2191.258	2080.819	881.017	836.614	578.270	549.125
EXPIb	2115.2		832.7		307.7		2126.7		870.9		578.2	
a Taken from ref. 28. b Taken from ref. 29.
ces between the results for different DFT methods are, on the other hand, not very large and, compared with experimental values, rather small. Thus, we believe that any of the five tested DFT methods is a reliable tool to perform vibrational analysis of monohalogenated species. The IR intensities are predicted accurately, although for some systems there is not a single method reproducing ideally all the experimental data.
The last question concerns the necessity of using a large, 6-311++G(3df,3pd) basis set. Table 3 shows the relative error in frequency assignments using different computational approaches and basis sets for the CH3Cl system. Clearly, the larger basis set improves the results obtained at the B3LYP level of theory. The results for the lar-
gest basis set are also more accurate then in the case of more sophisticated ab-initio methods using smaller basis sets. Thus we believe that DFT calculations can provide us with more reliable results than high level ab-initio methods for the frequency analysis of small organic molecules, and a large basis set of 6-311++G (3df,3pd) is crucial for the improvement of accuracy.
4. Conclusions
From theoretical studies we provide the geometrical structures, vibrational frequencies as well as IR intensities of monohalogenated carbon family species using five
Table 3. Av values (Av = vcalculated-ve dmental) for the frequency analysis of CH3Cl at different levels of theory.
	B3LYP	B3LYP	B3LYP	MP4	CISD	QCISD	CCSD
	6-311++(3df,3pd)	6-31G*	6-311+G(3df,2p)	6-311G*	6-31G*	6-311G**	6-311G*
Av,	191	216 a	191 a	193 a	288 a	218 a	209 a
Av„	30	59 a	26 a	80 a	120 a	83 a	89 a
Av3	-14.7	-11.1 a	-17.1 a	30 a	58 a	41 a	38 a
AV^	34	156 a	125 a	137 a	229 a	156 a	149 a
Av5	31	49 a	34 a	51 a	102 a	44 a	58 a
AV6	14	28 a	12 a	44 a	74 a	43 a	51 a
a Taken from ref. 26.
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DFT methods (B3LYP, B1LYP, B3P86, MPW1PW91, B3PW91) and two high level of ab-initio methods (MP2, MP4) at 6-311++G (3df,3pd) level of theory. DFT methods are shown to be as accurate as MP2 and MP4 methods in geometry optimization. The advantages of DFT methods over MP2 and MP4 approaches in frequency analysis are presented. In comparison with the available data, we conclude that for the frequency analysis of a small organic systems there is no need to use high level ab-initio methods, since DFT methods with large basis set of 6-311++G (3df,3pd) can provide more reliable results.
Other attempts to estimate the anharmonicity have been attempted. Recently, a Car-Parrinello simulation of a Mannich base, (4,5-dimethyl-2(N,N-dimethylaminemet-hyl)phenol) was performed. This system has been shown to be troublesome due to the internal hydrogen bonding network32. Mavri and co-workers proposed a package that uses ab initio or DFT calculated points and fits them to calculate accurate expectation values, and IR spectra33. The advantage to such a technique is that it accounts for anharmonicity effects. Future prospects in this work include the use of such models to study the systems described herein.
While we have only considered fundamental modes there is some knowledge available on the overtones and hot transitions for certain species34 from a theoretical perspective. Experimentally, there is very little knowledge known about the hot transitions and overtones in molecules of this type. However, other investigations have shown that hot transitions and overtones can be adequately accounted for (in correlation to experiments) by using DFT methods and gaussian basis sets35. To the best of our knowledge limited information on these data points are available for the compounds investigated herein.
The results from all tested DFT methods are all similar. At this point it is difficult to choose a method, which would be the most accurate in all cases. A benchmark study of various density functionals to evaluate the performance of more density functional techniques for the frequency analysis of the discussed systems is in process.
5. Acknowledgments
Special thanks are extended to DGSCA as well as UNAM for valuable resources.
6. References
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7.	C. R. Zobel and A. B. F. Duncan, J. Am. Chem. Soc. 1955,	6 77, 2611-2615.	7
8.	H. Adachi, J. Electron. Spectrosc. Relat. Phenom. 1979, 16,	8 277-284.	9
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16	Povzetek
17	Z metodami gostotnostnega funkcionala B3LYP, B1LYP, B3P86, MPW1PW91 in B3PW91 kot tudi z MP2 in MP4 z	17
18	uporabo baznega seta 6-311++G (3df,3pd) smo izračunali geometrijske parametre, valovna števila infrardečih nihanj in	18
19	njihove intenzitete za molekule XH3Y (X=C, Si, Ge in Y=F, Cl, Br). Izračune smo primerjali z opaženimi vrednostmi iz	19
20	literature. Prednosti DFT metod so razvidne iz primerjav izračunanih in opaženih vrednosti. V članku predlagamo naju-	20
21	streznejše metode in bazne sete.	21
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