Open access peer-reviewed chapter

Vibrational Zero-Point Energy of Organosilicon Compounds

Written By

Mahmoud Rahal and Abdeslam El Hajbi

Submitted: January 23rd, 2019 Reviewed: May 23rd, 2019 Published: June 20th, 2019

DOI: 10.5772/intechopen.87021

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Abstract

In this chapter, the calculation of vibrational zero-point energies (ZPEs) of organosilicon compounds is reported. An empirical formula is used. This relationship was determined by relating vibrational zero-point energy to the nature and type of bonds forming the molecule. The calculated vibrational zero-point energies for several organosilicon derivatives belonging to different categories of compounds correlate well with the reported available values. In addition, the comparison of these results with the scaled values obtained using methods of quantum chemistry (AM1, ab initio, and by a similar empirical approach) indicates the reliability of our empirical model to reproduce vibrational zero-point energy of organosilicon compounds.

Keywords

  • zero-point energy (ZPE)
  • empirical ZPE
  • organosilicon compounds
  • theory-experiment correlation

1. Introduction

In the formulas of statistical mechanics, the vibrational zero-point energy (ZPE) constitutes the most significant term for the correction of the total energy of the molecules. ZPE (Figure 1) is a positive, additive, collective internal property and can be approximated by the harmonic formula:

Figure 1.

The Morse potential and harmonic oscillator potential.

ZPE=R2i=13N6hckνiE1

where the sum runs for the 3N-6 normal frequencies (νi) in the case of a nonlinear molecule of N atoms, R is the gas constant, k is the Boltzmann constant, c is the speed of light, and h is the Planck constant.

Thus, for a precise calculation of the enthalpies of formation, the use of a reliable method to determine vibrational zero-point energy appears necessary. The experimental determination of the ZPE requires the knowledge of all normal vibration mode frequencies by infrared and Raman method. In certain cases [1, 2], these methods involve experimental difficulties, and they are not feasible because of the existence of overtones and combination frequencies in the molecular spectra. Also, this experimental determination becomes even more difficult for the hazardous [3, 4, 5, 6] compounds which may be difficult to handle in air [7, 8, 9]. Otherwise, vibrational zero-point energy can be obtained by computing molecular vibrational frequencies with quantum chemistry methods [10, 11, 12, 13, 14]. However, such calculations can be very demanding in terms of computer time and disk space for large molecules and thus in daily practice; they are not usable by the chemist and technologist. Moreover, the theoretical vibrational frequencies are generally overestimated. The neglect of anharmonicity effects in the theoretical treatment constitutes the major source of this disagreement [15]. To solve this problem, we use an empirical correction factor which depends on the method, the basis set, the property to be determined (ZPE, Hvib(T), Svib (T), etc.), and sometimes the type of vibrations (low-frequency vibrations, high-frequency vibrations) [16]. For this reason and based on the fact that vibrational zero-point energy (ZPE) can be described with a good approximation by additivity rules [17, 18, 19], several researchers have sought to develop empirical rules to determine the vibrational ZPE.

Thus, to estimate ZPEs of molecules without using quantum chemistry methods, several empirical rules [20, 21, 22, 23, 24] have been developed in recent years. These additivity rules are classified into two categories: the first methods are based on the atomic contributions, while the second one are based on the contributions of bonds or groupings. The first category takes into account each of the atoms present in a given molecule. Thus, the studied property is evaluated as the sum of the atomic contributions. In the second approach, the molecule is divided into different fragments (bonds or groups). When a fragment is present in one molecule or another, the value of its contribution remains the same.

Using the first approach based on the additivity of atomic contributions, Flanigan et al. [20] have calculated the vibrational zero-point energy (ZPE) of hydrocarbons CnHm through the simple empirical relationship:

ZPE=2n+7mkcal/molE2

In 1985, using the least squares method, Schulman and Disch established a similar empirical relationship [25]. They determined the contributions of carbon and hydrogen atoms to estimate the vibrational zero-point energy of hydrocarbons. The relation thus obtained is written as follows:

ZPE=3.88n+7.12m6.19kcal/molE3

Then, this last formula has been extended to polyatomic molecular systems containing nitrogen, oxygen, chlorine, fluorine [26], bromine, sulfur [27], and silicon [28]. More recently, in order to obtain the ZPE of organophosphorus compounds, we have determined the increment of the phosphorus atom [29].

Eq. (3) takes now the form

ZPE=iNNiXi6.19kcal/molE4

where N is the number of kinds of atom in the molecule; Ni is the number of atoms of type i; Xi is the increment of the atom i.

In this context, Grice and Politzer [1] have also developed a simple linear relationship between the ZPE and molecular stoichiometry for several organic compounds.

In 2003, Ruzsinszky et al. [30] examined the relationship between ZPE values and partial charges calculated at the functional density theory (DFT) level. The results show that atomic partial charges can be used to estimate ZPEs with high accuracy. However, this method still requires to quantum chemical calculations to estimate the ZPE of the molecules.

The sum ZPE + H(T) − H(0) was studied by Fliszar et al. [13]. They found that this quantity obeyed to certain additivity rules, and they proved its correlation with the structural characteristics of the molecule, more precisely the number of atoms and the degree of branching in the case of hydrocarbons.

For the approach based on the contributions of bonds or groupings, Pitzer [31] was interested in the computation of the thermodynamic functions for gaseous hydrocarbons; he attributed an empirical value to each mode of vibration. In an n-paraffin study, Cottrell [32] found that the ZPE increases gradually with successive additions of the methylene group (CH2). Later, Pitzer and Catalano [33] assigned the constant 17.7 kcal/mol per unit of CH2 to calculate vibrational zero-point energy of these compounds.

The empirical estimation of vibrational zero-point energies of halomethanes, ethylene, haloethylenes, methane isotopes, and benzene has been the subject of several studies by Bernstein [34, 35, 36]. He took into consideration the contributions of the internal coordinates and the interactions between them. A few years later, three empirical parameters were determined by Fujimoto and Shingu [37] to calculate the ZPEs of hydrocarbons with a precision similar to that of Bernstein, which are the contributions of C▬C bonds, C▬H bonds, and carbon chain.

In 1980, based on a system of harmonic oscillators, Oi and his collaborators published some papers [17, 18, 19] which describe the theoretical foundation showing the additivity of ZPE estimates.

Still in the framework of the estimates based on the contributions of the bonds or groupings, we established in 2001 an original empirical relation [38] which makes it possible to calculate the ZPE of the organic compounds. This rule was determined by linking the ZPE to the nature and type of bonds forming the molecular system. The established empirical formula is as follows:

ZPEemp.=iPNi×BCi2.09kcal/molE5

where P is the number of bonds in the molecule; Ni is the number of bonds of type i; BCi is the contribution of the bond i to the ZPE.

This established empirical relationship also makes it possible to calculate the vibrational zero-point energies of the aromatic derivatives with accuracy, provided that the empirical values are adjusted by the following equation:

ZPE=1.08.ZPEempirical1.07kcal/molE6

This adjustment can be explained by the fact that in aromatic compounds, the bonds in the aromatic nucleus are all identical because of the conjugation, whereas in our model it has been assumed that there are three C▬C single bonds and three C=C double bonds.

Eq. (5) was used to calculate the ZPEs of several organic compounds belonging to different classes of compounds (hydrocarbons, oxygen compounds, nitrogen compounds, chlorinated compounds, brominated compounds, fluorinated compounds, sulfur compounds, aromatic compounds, etc.). Thus, the contributions of the bonds C▬H, N▬H, O▬H, S▬H, C▬O, C▬C, C▬N, C▬S, N▬N, C▬F, C▬Cl, C=C, C=N, C=O, C=S, C☰C, and C☰N have been determined. To extend our model to brominated compounds, we have determined in 2004 the contribution of the C▬Br bond [39] and incorporated it into our empirical formula. The calculated vibrational zero-point energies for 38 compounds containing this bond (C▬Br) correlate well with experimental values. In addition, we have extended the field of application of this empirical model to organophosphorus compounds (III). The bond contributions of P▬F, P▬C, P▬H, P▬Cl, P▬S, P▬N, and P▬O were determined [29]. The results obtained for 101 chemical systems containing these bonds are in good agreement with experimental values. The estimated ZPEs were compared with the results obtained by application of quantum chemistry methods at the level ab initio (HF/6-31G*) and DFT(B3LYP/6-31G*), in all cases with satisfactory results.

More recently [40], to calculate vibrational zero-point energies (ZPEs) of organophosphorus compounds (V), we determined the contributions of the bonds P=O and P=S and incorporated them into our empirical formula. Comparison of the results obtained for more than 80 organophosphorus compounds (V) with the reported values and with those obtained by ab initio (HF/6-31G*) and DFT(B3LYP/6-31G*) shows the reliability of the empirical approach.

In this chapter, we describe the results obtained in the case of organosilicon compounds. We present the values obtained for the contributions of the Si▬H, Si▬C, Si▬Cl, Si▬O, and Si▬Si bonds which make it possible to calculate the vibrational zero-point energies of the silicon compounds. The results thus obtained are compared firstly with the available experimental values, secondly to the values obtained by the methods of the quantum chemistry at the semiempirical (AM1) and DFT(B3LYP/6-31G*) level, and finally to the results derived from a similar approach based on simple atom additivity.

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2. Computational methods

The theoretical calculations were performed at the semiempirical [41] and density functional theory [42, 43] levels using, respectively, the AM1 method and B3LYP [44, 45, 46] with 6-31G* basis set which were implemented in the Gaussian03W program [47, 48]. The molecular geometries were optimized without any symmetry constraints, and the harmonic frequencies were calculated to ensure that the structures really corresponded to a true local minimum energy on the potential energy surface in the first time and to determine the vibrational zero-point energies in the second time.

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3. Results and discussion

3.1 Estimation based on simple bond additivity

Using the least squares method, we have determined the contributions of the Si▬H, Si▬C, Si▬Cl, Si▬O, and Si▬Si bond by correlating, for a population of molecules, the values of the vibrational zero-point energies obtained experimentally and those obtained by Eq. (5). The values of the contributions obtained for the studied bonds and those already established [29, 38, 39, 40, 49] are given in Table 1.

BondBond contribution (BCi)Ref.
C▬H7.5877[38]
N▬H7.2013[38]
O▬H7.2964[38]
S▬H5.6921[38]
C▬O2.6985[38]
C▬C2.0751[38]
C▬N4.1409[38]
C▬S1.4403[38]
N▬N6.8372[38]
C▬F3.3078[38]
C▬Cl2.2051[38]
C=C2.6501[38]
C=N3.8852[38]
C=O3.9343[38]
C=S2.7319[38]
C☰C4.4125[38]
C☰N4.8169[38]
C▬Br1.9837[39]
Si▬H5.8011[49]
Si▬C0.3593[49]
Si▬Cl1.7690[49]
Si▬O1.3335[49]
Si▬Si−1.4548[49]
P▬H6.6486[29]
P▬C1.4190[29]
P▬O1.8406[29]
P▬Cl1.6717[29]
P▬N0.9873[29]
P▬F2.1507[29]
P▬S1.5424[29]
P=O2.4032[40]
P=S0.6131[40]

Table 1.

Bond contributions to ZPE (in kcal/mol).

To test the reliability of the extended empirical model, we applied it to 91 silicon compounds different from those used in the compilation of contributions. This group of molecules contains different classes such as silanes, siloxanes, chlorosilanes, silyl ethers, silanols, silyl chlorides, cyclic organosilicon, and aromatic organosilicon.

The ZPEs obtained are recorded in Table 2. These results show a very good agreement between the calculated and the experimental values. Indeed, the average error is of the order of 1.51 kcal/mol for the 91 molecular systems for which experimental or ab initio (HF/6-31G*) data are available. However, the ZPEs calculated for 3-phenyl-1,3-thiasilacyclohexane, 1-phenyl-1-silacyclohexane, 3-methyl-3-phenyl-1,3-thiasilacyclohexane, 1-methyl-1-phenyl-1-silacyclohexane, and (C6H5)3SiOH are underestimated.

CompoundZPE (kcal/mol)
Exp.Eq. (5)aAM1bB3LYP/6-31G*cEq. (4)dRef.
SiHCl39.299.027.268.544.08[50]
SiH3Cl17.0117.0814.5015.8813.88[51]
SiH2Cl213.3113.0511.0012.428.98[51]
SiH419.9021.1117.7118.8718.78[52]
C4H12Si (diethylsilane)90.6890.2687.3689.6591.26[52]
C6H16Si (triethylsilane)125.98124.83121.78124.68127.50[52]
C8H20Si (tetraethylsilane)161.23159.40156.08159.52163.74[52]
CH4SiCl2 (dichloromethylsilane)27.0927.6725.2726.6727.10[53]
CH5SiCl (chloromethylsilane)32.4834.4030.6233.6032.00[53]
CH6Si (methyl silane)37.2138.4435.5136.9936.90[54]
C3H6Si (1-silylpropyne)43.9642.8542.7143.6444.66[55]
CH2Br(CH3)2SiH (bromomethyl dimethyl silane)66.3367.4764.7566.8967.62[56]
H3SiSiH330.0831.2627.2729.6929.51[57]
C11H16Si (1-phenyl-1-silacyclohexane)151.56151.30e144.93145.51146.90[58]
C10H14SiS (3-phenyl-1,3-thiasilacyclohexane)134.31133.54e127.60137.91130.65[58]
C12H18Si (1-methyl-1-phenyl-1-silacyclohexane)169.58170.00e161.97162.84165.02[58]
C11H16SiS (3-methyl-3-phenyl-1,3-thiasilacyclohexane)152.32152.24e144.66146.27148.77[58]
H2ClSiSiH327.4827.2323.8926.3424.61[59]
HCl2SiSiH323.6323.2020.2922.6319.71[59]
H2ClSiSiH2Cl23.9423.2020.6422.9319.71[59]
Cl3SiSiH319.4719.1716.5318.6214.81[59]
HCl2SiSiHCl216.0915.1313.2915.439.91[59]
Cl3SiSiH2Cl15.9015.1313.1415.189.91[59]
Cl3SiSiHCl211.9511.109.5611.375.01[59]
Cl3SiSiCl37.777.075.857.310.11[59]
Si4H10 (n-butasilane)50.5051.5646.5450.8250.97[60]
Si5H12 (n-pentasilane)60.9361.7056.1461.2361.70[60]
Si6H14 (n-hexasilane)71.3971.8565.8071.8572.43[60]
Si7H16 (n-heptasilane)81.8582.0081.5782.4383.16[60]
Si8H18 (n-octasilane)92.5492.1585.1192.9093.89[60]
Si9H20 (n-nonasilane)102.75102.2994.71103.47104.62[60]
Si10H22 (n-decasilane)113.33112.44104.26114.00115.35[60]
C2H5SiCl (gauche vinyl silyl chloride)37.3137.0535.7537.1435.88[61]
C2H5SiCl (cis vinyl silyl chloride)37.3135.7034.1937.1435.88[61]
C2H6SiCl2 (2-chloroethylsilyl chloride C-gauche-Si-trans (Gt))46.7146.2743.9946.0045.22[62]
C2H6SiCl2 (2-chloroethylsilyl chloride C-trans-Si-trans (Tt))46.6246.2744.0146.0345.22[62]
C2H6SiCl2 (2-chloroethylsilyl chloride C-trans-Si-gauche (Tg))46.4646.2744.3046.0745.22[61]
C2H7SiCl (1-chloroethylsilane)49.7050.3047.4149.2750.12[63]
C2H7SiCl (gauche ethyl chlorosilane)51.3851.6549.1851.1150.12[64]
C2H7SiCl (trans ethyl chlorosilane)51.4251.6549.1951.1050.12[65]
H3SiOH24.2123.9421.7723.2222.18[66]
C3H6Cl2Si (1,1-dichlorosilacyclobutane)49.6551.8451.5552.3649.10[67]
C2H8Si (ethylsilane)54.7955.6952.7554.5455.02[68]
C3H9SiCl (chlorotrimethylsilane)68.1669.0566.1367.9168.24[69]
C3H10Si (trimethylsilane)71.9573.0870.2071.8673.14[69]
C4H12OSi (methoxytrimethylsilane)93.4194.0790.8192.9494.66[69]
(CH3)3SiOH (trimethylsilanol)75.3575.9173.3375.4773.14[69]
C3H10Si (gauche-n-propylsilane)72.2972.9470.0071.8973.14[70]
C3H10Si (anti-n-propylsilane)72.0772.9470.0071.7873.14[70]
C3H10Si (trans ethylmethylsilane)72.1473.0170.2172.0773.14[71]
C3H10Si (gauche ethylmethylsilane)72.2773.0170.3072.2073.14[71]
C4H10Si (cis methylsilylcyclopropane)76.8177.0974.0775.5177.02[72]
C4H10Si (gauche methylsilylcyclopropane)76.4477.0974.1075.4577.02[72]
C3H12Si2 (1,1,1-trimethyldisilane)82.5683.2379.6982.3883.87[73]
C5H12Si (cyclopentylsilane)94.6094.3493.2194.0595.14[74]
C6H14Si (cyclohexyl silane (chair-equatorial))112.15111.59110.54111.83113.26[75]
C6H14Si (cyclohexyl silane (chair-axial))112.93111.59110.54112.00113.26[75]
C3H8Si (allylsilane)57.7558.3456.2257.5158.90[76]
C3H8SiCl2 (anti dichloromethyldimethyl silane)62.4262.3159.7661.7863.34[77]
C3H8SiCl2 (gauche dichloromethyldimethyl silane)61.7362.3159.7861.7563.34[77]
C3H7SiCl (methylvinyl silyl chloride)54.4854.3852.9254.5554.00[78]
(H3Si)2CCH249.6551.2647.9257.0151.51**
((CH3)3Si)2CCH2152.56155.19151.46155.08160.23**
C5H12Si (1,1-dimethyl-1-silacyclobutane)93.3394.5593.4894.5795.14**
C3H8Si (silacyclobutane)59.0659.9159.2559.7158.90**
C4H10Si (1-methyl-silacyclobutane)76.3877.2376.5077.1877.02**
Cl3SiCH325.4426.3424.2825.8322.20**
Cl2Si(CH3)246.3647.6945.1747.1745.22**
(CH3)3SiCN71.8572.4570.9972.5973.95**
SiH3CN19.2720.4919.3619.9819.59**
Si(OH)434.5632.4332.1034.6432.38**
HSi(OH)330.7929.6028.8530.8828.98**
H3SiOSiH332.9035.3830.9333.1632.91**
Si(OH)3-O-Si(OH)355.8652.3651.1156.3953.31**
C2Si2H8O (1-oxa-2,5-disilacyclopentane)56.9056.9355.4157.4354.91**
(H2SiO)3 (cyclotrisiloxane)41.4040.7238.1241.4336.20**
(H2SiO)4 (cyclotetrasiloxane)54.9154.9951.1955.0550.33**
(C2H5O)4Si171.18174.09170.16172.95177.34**
CH3SiH2SiH2CH363.8365.9062.6565.3165.75**
H3SiSiH2SiH339.9441.4136.9240.1940.24**
(Me3Si)2SiH2143.61145.34141.84145.47148.96**
((CH3)3Si)3SiH205.33207.45204.16208.86214.05**
CH3OSi(CH3)391.4894.0790.7992.9494.66**
Et3SiOH126.18127.66125.19128.10130.90**
Ph3SiOH172.20176.01e174.18173.66177.46**
nbutyl3SiOH228.34231.16228.10231.39239.62**
(CH3)3SiOSi(CH3)3134.88139.31133.95137.52141.63**
(CH3)3SiOCOCH397.3497.3897.0098.80101.94**
C8H16SiO2 (4-trimethylsiloxy-3-penten-2-one)134.19137.23134.29135.98142.06**
(CH3)3SiOCOCF3 (trimethylsilyltrifluoroacetate)84.2285.1784.2784.8790.39**
C3H7SiCl (cis-cyclopropylchlorosilane)55.4755.8053.8755.0354.00[79]

Table 2.

Comparison of computed (empirical Eq. (5), AM1, B3LYP/6-31G*, empirical Eq. (4)) zero-point energy with experimental values.

Values determined by our model.


Values scaled by 0.95 [80].


Values scaled by 0.96 [80].


Values computed by Schulman-Disch extended empirical formula.


Values adjusted by Eq. (6).


Values calculated with HF/6-31G* and scaled by 0.89 [80].


This is due to the presence of the aromatic ring in these organosilicon compounds [29, 38, 39, 40]. Nevertheless, the adjustment of empirical ZPE values by Eq. (6) leads to a decrease of the mean error which becomes 1.02 kcal/mol (i.e., 1.98%).

The curve of correlation between the experimental and empirical values (Figure 2) appears very satisfactory, the slope is close to unity (0.99), the correlation coefficient is equal to 0.9994, and standard deviation is 1.2. The statistical data concerning the regression curves ZPEexp = aZPEtheor + b and ZPEexp = aZPEtheor are summarized in Table 3. The use of this data for the adjustment of the empirical values of vibrational zero-point energies (ZPEs) reduces the mean error to 0.9 kcal/mol.

Figure 2.

Correlation between experimental ZPEs and empirical values calculated using Eq. (5).

Calculation methodLinear model
ZPEexp = aZPEtheorZPEexp = b + aZPEtheor
aR2abR2
Proposed empirical model (Eq. (5))0.993 ± 0.0020.99980.990.2720.9994
AM11.025 ± 0.0030.99920.952.2120.9982
DFT (B3LYP/6-31G*)0.999 ± 0.0020.99960.950.3040.9986
Schulman-Disch extended model (Eq. (4))0.984 ± 0.00380.99860.953.5450.9972

Table 3.

Coefficients a, b, and R2 in equations ZPEexp = b + aZPEtheor in both cases b = 0 and b ≠ 0.

3.2 Estimation based on simple atom additivity

In order to be able to compare the results obtained by the application of the empirical formula based on bond contribution additivity (Eq. (5)) to those obtained by the approach based on atomic contribution additivity, we have grouped in Table 2 the values of vibrational zero-point energies computed with the extended rule of Schulman and Disch (Eq. (4)). The increment of the silicon atom was calculated by AbdulHussain and Fleifel [28]. The value of this increment is shown in Table 4, with those previously published [25, 26, 27, 28, 29] for the atoms H, C, O, N, Cl, F, Br, S, and P. Note that the formula of Schulman and Disch was established on the basis that the structural isomers of organic compounds have almost the same value of ZPE. However, the difference can reach 4 kcal/mol [9]. The results obtained by the method based on the additivity of the atomic contributions show, for the 91 silicon compounds, an average error of 2.53 (6.9%). The correlation between the experimental and calculated values by the Schulman-Disch extended formula is shown in Figure 3. The statistical parameters obtained in this case are a correlation coefficient of 0.9972, a slope of 0.95, and a standard deviation of 2.45. Using the regression curves (Table 3) for adjusting the calculated values permits to reduce the mean error to 1.68 (4.0%) if the intercept is different from 0 (b ≠ 0) to 2.28 (7.0%) if b = 0. These results are slightly less good than those obtained by our approach.

AtomIncrementRef.AtomIncrementRef.
H7120[25]Cl2220[26]
C3880[25]S1870[27]
N4050[26]Br1600[27]
O3400[26]Si−3510[28]
F3270[26]P0.035[29]

Table 4.

Atom contributions to ZPE (in kcal/mol).

Figure 3.

Correlation between experimental ZPEs and empirical values calculated using Eq. (4).

3.3 Quantum chemical calculations

To compare the results obtained by our empirical relationship with those obtained by quantum chemistry methods, we have calculated vibrational zero-point energies for the same organosilicon compounds using semiempirical (AM1) and DFT(B3LYP/6-31G*) methods. Results are summarized in Table 2. To correct calculated ZPEs, the scaling factors of Scott and Radom [80] are used.

Based on these results, the values calculated at the DFT(B3LYP/6-31G*) level are closer to the experimental data than those obtained at the semiempirical (AM1) level. The mean error is 2.50 (5.45%) for AM1, compared to 1.08 (1.86%) for DFT(B3LYP/6-31G*). The correlations obtained between the experimental values and those calculated by using AM1 and DFT methods are represented, respectively, in Figure 4a and b. Examination of this correlations shows that these methods are able to calculate accurately the zero-point vibration energies of the organosilicon compounds with a small advantage for the DFT method. For the adjustment of calculated ZPEs, the use of the regression line of the form ZPEexp = aZPEtheor (Table 3) permits to reduce the mean error of 2.5–1.83 kcal/mol for AM1 and from 1.08 to 1.06 kcal/mol for DFT(B3LYP/6-31G*). When the intercept is different from zero, the average error decreases from 2.5 to 1.37 kcal/mol for AM1 and from 1.08 to 1.00 for DFT(B3LYP/6-31G*).

Figure 4.

(a) Correlation between experimental and theoretical (AM1) ZPE and (b) correlation between experimental and theoretical (B3LYP/6-31G*) ZPE.

As a result, the four estimates of vibrational zero-point energy of the organosilicon compounds (our empirical model, Schulman-Disch extended empirical formula, AM1, and DFT) are correct. But the empirical approaches have the advantage of simplicity and speed. In addition, the approach based on bond contributions additivity has also the advantage of providing different values of ZPE for the function isomers. Furthermore, the adjustment of calculated values, empirically or using quantum methods, with the ZPEexp = b + aZPEtheor model makes the four estimates comparable.

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4. Conclusions and outlook

In this chapter, we reported the extension of our empirical relationship established in 2011 for the computation of zero-point vibrational energies (ZPE) of organosilicon compounds. The bond contributions of Si▬H, Si▬C, Si▬Cl, Si▬O, and Si▬Si were determined. The application of the proposed empirical model to more than 90 organosilicon shows the reliability of this model. The results derived from this model are compared with those obtained by quantum chemistry methods (semiempirical (AM1) and DFT (B3LYP/6-31G*)) on the one hand and to those obtained by similar empirical approach on the other hand. As a result, the empirical model provides a simple, fast, and accurate way to estimate the vibrational zero-point energies of organosilicon compounds.

Establishing these empirical rules is becoming increasingly important. Indeed, thermodynamic data play an important role in the understanding and design of chemical processes. Experimental methods require appropriate equipment, sufficient product purity, time, and cost of experience. The use of such techniques becomes difficult for toxic compounds. In addition, the large difference between the number of synthesized compounds and the available experimental data continues to increase. In such situation, the practical approach is to use predictive models to estimate the properties of compounds from the molecular structures. In this outlook, we propose to extend the field of application of the proposed empirical model to other compounds such as organoborons, organomagnesians, etc., and to establish similar approaches to estimate other thermodynamic quantities such as enthalpy of formation (ΔH0f), entropy (S0), and heat capacity (C).

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List of abbreviations

ZPEzero-point vibrational energy
AM1Austin model 1 (developed by Michael Dewar and collaborators in 1985)
Hvib(T)vibrational enthalpy of the molecule
Svib(T)entropy due to vibrational motion
H(T)−H(0)thermal correction
HF/6-31G*Hartree-Fock theory in combination with the 6-31G(d) basis set
DFTdensity functional theory
B3LYP/6-31G*Becke’s three parameter exchange function (B3) with Lee-Yang-Parr correlation function (LYP) functional coupled with 6-31G* basis set
Eqnequation

References

  1. 1. Grice ME, Politzer P. Use of molecular stoichiometry to estimate vibrational-energy. Chemical Physics Letters. 1995;244:295-298
  2. 2. Irikura KK. Experimental vibrational zero-point energies: Diatomic molecules. Journal of Physical and Chemical Reference Data. 2007;36:389-397
  3. 3. Pilcher G. In: Hartley FR, editor. The Chemistry of Organophosphorus Compounds, Vol. 1. New York: John Wiley & Sons; 1990. p. 127
  4. 4. Mollendal H, Konovalov A, Guillemin JC. Synthesis and microwave spectrum of (2-chloroethyl)phosphine (ClCH2CH2PH2). The Journal of Physical Chemistry. A. 2009;113:12904-12910
  5. 5. Durham HD, Ecobichon DJ. An assessment of the neurotoxic potential of fenitrothion in the hen. Toxicology. 1986;41:319-332
  6. 6. Ecobichon DJ, Davies JE, Doull J, Ehrich M, Joy R, McMillan D, et al. In: Baker SR, Wilkinson CF, editors. Neurotoxic Effects of Pesticides, in the Effects of Pesticides on Human Health, Vol. 18. Princeton, NJ: Princeton Scientific; 1990. p. 131
  7. 7. Dorofeeva OV, Ryzhova ON, Zverev VG. Computational study of the thermodynamic properties of organophosphorus(V) compounds. Journal of Molecular Structure (THEOCHEM). 2007;811:267-279
  8. 8. Dorofeeva OV, Moiseeva NF. Computational study of the thermochemistry of organophosphorus (III) compounds. The Journal of Physical Chemistry. A. 2006;110:8925-8932
  9. 9. Sidell FR. Soman and sarin: Clinical manifestations and treatment of accidental poisoning by organophosphates. Clinical Toxicology. 1974;7:1-17
  10. 10. Smeyers YG, Villa M. Influence of the vibrational zero-point energy correction on the amine inversion barrier and the far-infrared spectrum of methylamine. Chemical Physics Letters. 2000;324:273-278
  11. 11. Sana M, Leroy G, Peeters D, Wilante C. The theoretical study of the heats of formation of organic compounds containing the substituents CH3, CF3, NH2, NF2, NO2, OH and F. Journal of Molecular Structure (THEOCHEM). 1988;164:249-274
  12. 12. Dykstra CE, Shuler K, Young RA, Bai Z. Anharmonicity effects on zero point energies of weakly bound molecular clusters. Journal of Molecular Structure (THEOCHEM). 2002;591:11-18
  13. 13. Fliszar S, Poliquin F, Badilescu I, Vauthier E. Structure dependent regularities of zero-point plus heat content energies in organic molecules. Canadian Journal of Chemistry. 1988;66:300-303
  14. 14. Tajti A, Szalay PG, Császár AG, Kállay M, Gauss J, Valeev EF, et al. HEAT: High accuracy extrapolated ab initio thermochemistry. The Journal of Chemical Physics. 2004;121:11599-11613
  15. 15. Zahedi-Tabrizi M, Tayyari F, Moosavi-Tekyeh Z, Jalali A, Tayyari SF. Structure and vibrational assignment of the enol form of 1,1,1-trifluoro-2,4-pentanedione. Spectrochimica Acta A. 2006;65:387-396
  16. 16. Merrick JP, Moran D, Radom L. An evaluation of harmonic vibrational frequency scale factors. The Journal of Physical Chemistry. A. 2007;111:11683-11700
  17. 17. Oi T, Popowics A, Ischida T. Additivity of vibrational zero-point energy. The Journal of Physical Chemistry. 1986;90:3080-3088
  18. 18. Oi T, Ischida T. Correlation of zero-point energy with molecular structure and molecular forces. Development of the approximation. The Journal of Physical Chemistry. 1983;87:1067-1073
  19. 19. Oi T, Ischida T. Correlation of zero-point energy with molecular structure and molecular forces. III: Approximation for H/D isotope shifts and linear frequency sum rule. The Journal of Physical Chemistry. 1984;88:2057-2061
  20. 20. Flanigan MC, Kormornicki A, McIver JW Jr. In: Segal GA, editor. Electronic Structure Calculation. New York: Plenum Press; 1977
  21. 21. Császár AG, Furtenbacher T. Zero-cost estimation of zero-point energies. The Journal of Physical Chemistry. A. 2015;119:10229-10240
  22. 22. Barić B, Maksić ZB, Vianello R. On the atomic additivity of zero point vibrational energy in molecules. Journal of Molecular Structure (THEOCHEM). 2004;672:201-207
  23. 23. Arimoto S. Preliminary considerations towards a theoretical foundation of the zero energy additivity rules. Physics Letters A. 1985;113A:126-132
  24. 24. Bernstein HJ. The physical properties of molecules in relation to their structure. I. Relations between additive molecular properties in several homologous series. The Journal of Chemical Physics. 1952;20:263-269
  25. 25. Schulman JM, Disch RL. A simple formula for the zero-point energies of hydrocarbons. Chemical Physics Letters. 1985;113:291-293
  26. 26. Ibrahim MR, Fataftah ZA. Estimation of zero-point energies of compounds containing N, O, Cl and F atoms. Chemical Physics Letters. 1986;125:149-154
  27. 27. Ibrahim MR, Fataftah ZA. Estimation of zero-point energies of bromo and thio compounds. Chemical Physics Letters. 1987;136:583-587
  28. 28. AbdulHussain NS, Fleifel IA. Vibrational zero-point energies of non-aromatic silicon compounds. Journal of Basrah Researches. 2012;38:106-113
  29. 29. Rahal M, Bouabdallah I, Malek F, El Hajbi A. A simple way to predict vibrational zero point energy of organophosphorus(III) compounds. Computational and Theoretical Chemistry. 2015;1068:13-20
  30. 30. Ruzsinszky A, Kristyan S, Margitfalvi JL, Csonka GI. Rapid estimation of zero-point energies of molecules using Hartree-Fock atomic partial charges. The Journal of Physical Chemistry. A. 2003;107:1833-1839
  31. 31. Pitzer KS. Thermodynamics of gaseous hydrocarbons: Ethane, propane, propylene, n-butane, isobutane, 1-butene, cis and trans 2-butenes, isobutene, and neopentane (tetramethylmethane). The Journal of Chemical Physics. 1937;5:473-479
  32. 32. Cottrell TL. Binding energies in hydrocarbons. Journal of the Chemical Society. 1948;0:1448-1453
  33. 33. Pitzer KS, Catalano E. Electronic correlation in molecules. III. The paraffin hydrocarbons. Journal of the American Chemical Society. 1956;78:4844-4846
  34. 34. Bernstein HJ, Pullin ADE. A sum rule for the vibrational frequencies of homologs. The Journal of Chemical Physics. 1953;21:2188-2195
  35. 35. Bernstein HJ. Constitutive nature of the heat capacity of gases. The Journal of Chemical Physics. 1956;24:911-912
  36. 36. Bernstein HJ. Bond and interaction contributions for calculating the heat of formation, diamagnetic susceptibility, molar refraction and volume, and thermodynamic properties of some substituted methanes. The Journal of Physical Chemistry. 1965;69:1550-1564
  37. 37. Shingu H, Fujimoto T. Empirical correlation between molecular structure and zero-point energies in hydrocarbons. The Journal of Chemical Physics. 1959;31:556-557
  38. 38. Rahal M, Hilali M, El Hamadi A, El Mouhtadi M, El Hajbi A. Calculation of vibrational zero-point energy. Journal of Molecular Structure (THEOCHEM). 2001;572:73-80
  39. 39. Rahal M, El Hajbi A. Vibrational zero-point energies of bromo compounds. Journal of Molecular Structure (THEOCHEM). 2004;668:197-200
  40. 40. Rahal M, Bouabdallah I, El Bouzaidi RD, Malek F, El Hajbi A. Vibrational zero point energy of organophosphorus (V) compounds. Vibrational Spectroscopy. 2016;86:173-180
  41. 41. Dewar MJS, Zoebisch EG, Healy EF, Stewart JJP. Development and use of quantum mechanical molecular models. 76. AM1: A new general purpose quantum mechanical molecular model. Journal of the American Chemical Society. 1985;107:3902-3909
  42. 42. Parr RG, Wang W. Density-Functional Theory of Atoms and Molecules. Oxford University Press: New York; 1994
  43. 43. Neumann R, Nobes RH, Handy NC. Exchange functionals and potentials. Molecular Physics. 1996;87:1-36
  44. 44. Becke AD. Density-functional exchange-energy approximation with correct asymptotic behavior. Physics Review. 1988;A38:3098-30100
  45. 45. Becke AD. Density-functional thermochemistry. III. The role of exact exchange. The Journal of Chemical Physics. 1993;98:5648-5652
  46. 46. Lee C, Yang W, Paar RG. Development of the Colle-Salvetti correlation energy formula into a functional of the electron density. Physics Review. 1988;B37:785-786
  47. 47. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, et al. Gaussian 03, Revision C.02. Pittsburgh, PA: Gaussian Inc.; 2003
  48. 48. Rahal M, El Mouhalhal N, El Hajbi A. Détermination des grandeurs thermodynamiques par les méthodes semi-empiriques (AM1, PM3 ET MNDO). Annales de Chimie Science des Materiaux. 2006;31:103-112
  49. 49. Rahal M, Bouabdallah I, El Hajbi A. Rapid estimation of vibrational zero-point energies of silicon compounds. Computational and Theoretical Chemistry. 2013;1017:182-187
  50. 50. Smith JG. The millimetre wave spectrum of trichlorosilane. Journal of Molecular Spectroscopy. 1986;120:110-117
  51. 51. Zhang Q, Wang S, Gu Y. Direct ab initio dynamics studies of the reactions of H with SiH4-nCln (n = 1–3). The Journal of Physical Chemistry. A. 2002;106:3796-3803
  52. 52. Keister JW, Tomperi P, Baer T. Thermochemistry of gaseous ethylsilane cations. Journal of the American Society for Mass Spectrometry. 1998;9:597-605
  53. 53. Gamil GA, Panikar SS, El Defrawy AM, Kalasinsky VF, Durig JR. Vibrational spectra, r0 structural parameters, barriers to internal rotation, and <i> ab initio calculations of ClCH2SiH3, Cl2CHSiH3, ClCH2SiF3 and Cl2CHSiF3. Journal of Molecular Structure. 2009;922:93-102
  54. 54. Shimanouchi T. Tables of Molecular Vibrational Frequencies, Consolidated volume 1. Washington, DC: National Bureau of Standards; 1972. NSRDS NBS-39
  55. 55. Khaikin LS, Grikina OE, Sipachev VA, Traetteberg M. The structure and spectra of 1-silylpropyne: Scaled quantum-chemical forcefields and vibrational effects. Journal of Molecular Structure. 2001;567:85-99
  56. 56. Aleksa V, Klaeboe P, Nielsen CJ, Tanevska V, Guirgis GA. The conformations of bromomethyl dimethyl silane and bromomethyl dimethyl silane-d1 as studied by vibrational spectroscopy and by ab initio calculations. Vibrational Spectroscopy. 1998;17:1-30
  57. 57. Bethke GW, Wilson MK. Vibrational spectrum of disilane. The Journal of Chemical Physics. 1957;26:1107-1117
  58. 58. Shainyan BA, Kleinpeter E. Conformational preferences of Si-Ph, H and Si-Ph, Me silacyclohexanes and 1,3-thiasilacyclohexanes. Additivity of conformational energies in 1,1-disubstituted heterocyclohexanes. Tetrahedron. 2012;68:114-125
  59. 59. Swihart MT, Carr RW. Thermochemistry and thermal decomposition of the chlorinated disilanes (Si2HnCl6-n, n=0–6) studied by ab initio molecular orbital methods. The Journal of Physical Chemistry. A. 1997;101:7434-7445
  60. 60. Ye CC, Xie LF, Ju XH. Theoretical study of on thermodynamic properties and stabilities of n-silanes. Phosphorus, Sulfur and Silicon and the Related Elements. 2011;186:1948-1961
  61. 61. Durig JR, Nashed YE, Qtaitat MA, Guirgis GA. Spectra and structure of silicon containing compounds. XXVI. Raman and infrared spectra, ro structural parameters, conformational stability, vibrational assignment, and ab initio calculations of vinyl silyl chloride. Journal of Molecular Structure (THEOCHEM). 2000;525:191-208
  62. 62. Pana C, Guirgis GA, Durig JR. Infrared and raman spectra, conformational analysis, ab initio calculations and vibrational assignment of 2-chloroethylsilyl chloride. Journal of Molecular Structure. 2005;742:199-213
  63. 63. Mohamed TA, Guirgis GA, Nashed YE, Durig JR. Spectra and structure of silicon containing compounds. Vibrational Spectroscopy. 2002;30:111-120
  64. 64. Guirgis GA, Nashed YE, Durig JR. Raman and infrared spectra, conformational stability, ab initio calculations and vibrational assignments for 2-chloroethyl silane. Journal of Molecular Structure. 1999;510:13-34
  65. 65. Mohamed TA, Guirgis GA, Nashed YE, Durig JR. Spectra and structure of silicon-containing compounds. XXV. Raman and infrared spectra, r0 structural parameters, vibrational assignment, and ab initio calculations of ethyl chlorosilane-Si-d2. Structural Chemistry. 1999;10:333-348
  66. 66. Lü R, Qiu G, Liu C. Theoretical study of ethanethiol adsorption on HZSM-5 zeolite. Journal of Natural Gas Chemistry. 2005;14:119-124
  67. 67. Abdulaziz AA, Jaan L. Structure, vibrational spectra, and DFT and ab initio calculations of silacyclobutanes. Organometallics. 2008;27:3435-3443
  68. 68. Mohamed TA, Guirgis GA, Nashed YE, Durig JR. Spectra and structures of silicon-containing compounds. XXIV. Raman and infrared spectra, r0 structural parameters, vibrational assignment, barriers to internal rotation, and ab initio calculations of ethylsilane. Structural Chemistry. 1998;9:255-264
  69. 69. Montejo M, Ureña FP, Márquez F, González JJL. The vibrational spectra of (CH3)3SiX (S=H, F, Br) molecules, revisited transferable scale factor sets for methylsilane derivatives. Spectrochimica Acta Part A. 2005;62:1058-1069
  70. 70. Durig JR, Pana C, Guirgis GA. Spectra and structure of silicon containing compounds. XXXII. Raman and infrared spectra, conformational stability, vibrational assignment and ab initio calculations of n-propylsilane-d0 and Si-d3. Spectrochimica Acta Part A. 2003;59:979-1002
  71. 71. Duriga JR, Pana C, Guirgis GA. Spectra and structure of silicon containing compounds. XLII. Conformational stability, ab initio calculations, r0 structural parameters, and vibrational assignments for ethylmethylsilane and ethylmethylsilane-Si-d2. Journal of Molecular Structure. 2004;88:95-109
  72. 72. Durig JR, Panikar SS, Guirgis GA, Gounev TK, Ward RM, Peeblesc RA, et al. Conformational stability, r0 structural parameters, barriers to internal rotation, vibrational spectra and ab initio calculations of c-C3H5SiH2CH3. Journal of Molecular Structure. 2009;923:1-12
  73. 73. Mohamed TA. Structural parameters, barriers to internal rotation, normal coordinate analysis and quantum mechanics calculations of 1,1,1-trimethyldisilane. Journal of Molecular Structure (THEOCHEM). 2003;635:161-172
  74. 74. Durig JR, Zhao W, Zhu X, Geyer TJ, Dakkouri M. Spectra and structure of small ring compounds. LXV. Raman and infrared spectra, conformational stability, and vibrational assignment of cyclopentylsilane. Journal of Molecular Structure. 1995;351:31-49
  75. 75. Zheng C, Subramaniam S, Kalasinsky VF, Durig JR. Raman and infrared studies supported by ab initio calculations for the determination of conformational stability, silyl rotational barrier and structural parameters of cyclohexyl silane. Journal of Molecular Structure. 2006;785:143-159
  76. 76. Guirgis GA, Nashed YE, Gounev TK, Durig JR. Conformational stability, structural parameters, vibrational frequencies, and Raman and infrared intensities of allylsilane. Structural Chemistry. 1998;9:265-277
  77. 77. Guirgis GA, Zhengb C, Nashed YE, Mohamed TA, Durig JR. Spectra and structure of silicon containing compounds XXXV infrared and Raman spectra, vibrational assignment, conformational stability and ab initio calculations of dichloromethyldimethyl silane. Journal of Molecular Structure. 2003;649:7-24
  78. 78. Durig JR, Hur SW, Guirgis GA. Infrared and Raman spectra, conformational stability, vibrational assignment and ab initio calculations of methylvinyl silyl chloride. Spectrochimica Acta Part A. 2003;59:2449-2471
  79. 79. Kalincsák F, Pongor G. Extension of the density functional derived scaled quantum mechanical force field procedure. Spectrochimica Acta Part A. 2002;58:999-1011
  80. 80. Scott AP, Radom L. Harmonic vibrational frequencies: An evaluation of Hartree-Fock, Moller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. The Journal of Physical Chemistry. 1996;100:16502-16513

Written By

Mahmoud Rahal and Abdeslam El Hajbi

Submitted: January 23rd, 2019 Reviewed: May 23rd, 2019 Published: June 20th, 2019