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Quantum chemical analysis of the vibrational frequencies and structure of tetrachlorodiborane
Journal of Molecular Structure (Theochem) 635 (2003) 211–219 www.elsevier.com/locate/theochem
Quantum chemical analysis of the vibrational frequencies and structure of tetrachlorodiborane James O. Jensen* US Army Edgewood Chemical and Biological Center, AMSSB-RRT-DP, Aberdeen Proving Ground, MD 21010-5424, USA Received 22 March 2003; accepted 2 June 2003
Abstract The normal mode frequencies and corresponding vibrational assignments of B2Cl4 are examined theoretically using the set of quantum chemistry codes. All normal modes were successfully assigned to one of six types of motion predicted by a group theoretical analysis (B – B stretch, B– Cl stretch, BCl2 scissors, BCl2 rock, BCl2 wag, and B– B torsion) utilizing the D2d symmetry of the molecule. The vibrational modes of the naturally isotopically substituted (1-10B and 2-10B) forms of B2Cl4 were also calculated and compared against experimental data. The barrier to rotation of the around the B– B bond is examined. Molecular orbitals are presented. Published by Elsevier B.V. GAUSSIAN 98
Keywords: Vibrations; Normal mode frequencies; Infrared spectra; Raman spectra; Boron chloride; Diboron tetra chloride; Tetrachlorodiborane
1. Introduction Tetrachlorodiborane (B2Cl4) was first reported in the literature in 1925 [1] and a number of papers have appeared on methods for synthesizing B2Cl4 [1 – 10]. B2Cl4 has proven to be a useful laboratory reagent [11 – 25] in the synthesis of novel boron containing compounds. The NMR spectroscopy [26,27], photoelectron spectroscopy [28], and mass spectrometry [29] of B2Cl4 have been reported. Due to its high symmetry and unusual bonding, B2Cl4 has been the subject of a number of theoretical studies [30 –41]. * Tel.: þ1-410-436-5665; fax: þ 1-410-436-1120. E-mail address: [email protected] (J.O. Jensen). 0166-1280/03/$ - see front matter Published by Elsevier B.V. doi:10.1016/S0166-1280(03)00458-5
Interpretation of an experimental infrared or Raman spectra of a complex molecule is a difficult task. An empirical set of rules often gets built up over a period of time [42]. For organic molecules these empirical rules are well established and have been an aid to scientists for decades. For inorganic compounds with much more variety in bonding types, the rules are far less established. One of the goals of this paper is to elucidate the typical vibrational frequencies for B – B and B – Cl type bonds, both stretching and bending. Natural occurring Boron consists of two isotopes, 10 B (19.6%) and 11B (80.4%). Isotopic effects are quite evident in the experimental spectrum of B2Cl4. The boron atoms are light enough such that the isotopic shifts are quite large and can be readily seen in the experimental spectrum.
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2. Computational methods
Fig. 1. Structure of B2Cl4.
Quantum chemical methods of normal mode analysis will be used to examine available experimental infrared and Raman data in detail. In this study the infrared and Raman spectra of B2Cl4 are examined using the GAUSSIAN 98 suite of quantum chemical codes [43]. High quality experimental data [44 – 51] on the vibrational modes of B2Cl4 exists in the literature. However, a detailed quantum chemical normal mode analysis has not been performed to date. A detailed quantum chemical study will aid in making definitive assignments to the fundamental normal modes of B2Cl4 and in clarifying the experimental data available for this molecule.
The vibrational frequencies of B2Cl4 were calculated at the Hartree – Fock, DFT (B3LYP) [52,53] and MP2 [54] levels of theory using the 6-311G basis set. The calculations utilized the D2d symmetry of the B2Cl4 molecule (see Fig. 1). The computations were performed using the GAUSSIAN 98 program package [43]. Each of the vibrational modes was assigned to one of six types of motion (B – B stretch, B – Cl stretch, BCl2 scissors, BCl2 rock, BCl2 wag, and B – B torsion) by means of visual inspection using the Gaussview program [55]. The choice of internal coordinates is always somewhat arbitrary. However, the above set is complete and matches well the observed motion using the Gaussview program. The symmetry of the B2Cl4 molecule was also helpful in making vibrational assignments. The symmetries of the vibrational modes were determined by using standard procedure [56] of decomposing the traces of the symmetry operations into the irreducible representations of the D2d group. The symmetry analysis for the vibrational modes of B2Cl4 is presented in some detail in order to better describe the basis for the assignments. For the B – Cl stretching modes the four B –Cl bonds were used as the basis of the analysis. The sd operator has a trace of two. All other operators except
Table 1 Normal modes of B2Cl4 calculated at the Hartree– Fock level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Experimental frequencyc
Correctedd frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1185 420 182 28 760 309 857 528 108
Infrared inactive
1 5 1 3 1 3 3 0 2
B –B stretch B –Cl stretch BCl2 scissors B –B torsion B –Cl stretch BCl2 scissors B –Cl stretch BCl2 wag BCl2 rock
1122 401 176 25 728 289 915 512 104
1122 417 173 25 755 294 851 512 104
B1 B2 E
a b c d
Inactive 207 6 387 19 3
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Ref. [46]. Raw calculated frequencies multiplied by the correction factors in Table 4.
J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219
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Table 2 Normal modes of B2Cl4 calculated at the DFT (B3LYP) level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Experimental frequencyc
Correctedd frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1126 401 173 27 722 293 897 493 100
IR inactive
17 8 2 5 2 4 7 1 2
B –B stretch B –Cl stretch BCl2 scissors B –B torsion B –Cl stretch BCl2 scissors B –Cl stretch BCl2 wag BCl2 rock
1122 401 176 25 728 289 915 512 104
1122 405 173 25 729 294 905 512 104
B1 B2 E
a b c d
Inactive 169 4 337 10 1
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Ref. [46]. Raw calculated frequencies multiplied by the correction factors in Table 4.
Table 3 Normal modes of B2Cl4 calculated at the MP2 level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Experimental frequencyc
Correctedd frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1171 420 179 25 762 306 970 510 98
IR inactive
7 7 2 5 1 4 4 1 2
B–B stretch B–Cl stretch BCl2 scissors B–B torsion B–Cl stretch BCl2 scissors B–Cl stretch BCl2 wag BCl2 rock
1122 401 176 25 728 289 915 512 104
1122 399 173 25 725 295 923 512 104
B1 B2 E
a b c d
Inactive 164 4 369 8 1
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Ref. [46]. Raw calculated frequencies multiplied by the correction factors in Table 4.
E have a trace of zero. Thus the four B– Cl stretching modes possess the symmetries A1, B2, and E. For the two BCl2 scissoring modes the C2 and sd operators each have a trace of two. All other operators expect E have a trace of zero. Thus the two BCl2 scissoring modes possess the symmetries A1 and B2. For the two BCl2 wagging modes the C2 operator has a trace of minus two. All other operators expect E have a trace of zero. Thus the two BCl2 wagging modes possess the E symmetry. For the two BCl2 rocking modes the C2 operator has a trace of minus two. All other operators expect E have a trace of zero.
Table 4 Correction factors for B2Cl4
B–B stretch B–Cl stretch BCl2 wag BCl2 scissors BCl2 rock B–B torsion
Hartree–Fock
DFT (B3LYP)
MP2
0.9468 0.9934 0.9697 0.9512 0.9630 0.8929
0.9964 1.0095 1.0385 1.0018 1.0400 0.9259
0.9582 0.9511 1.0039 0.9638 1.0612 1.0000
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Fig. 2. Normal modes of B2Cl4.
Thus the two BCl2 rocking modes possess the E symmetry. The single B – B stretching mode possesses A1 symmetry, and the single B– B torsion possesses B1 symmetry. By combining the results of the Gaussview program [55] with the symmetry considerations,
vibrational frequency assignments were made with a high degree of confidence. There is always some choice in defining internal coordinates for a normal mode analysis study. However, the set of coordinates listed above complete and matches well the motions observed using the Gaussview program.
J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219 Table 5 Geometric parameters of B2Cl4. Distances are presented in pm and angles in degrees. All calculations utilized the standard 6-311G** basis set
B –B B –Cl Cl–B –Cl a
Hartree–Fock
DFT (B3LYP)
MP2
Experimenta
170.5 175.3 119.5
168.6 175.6 119.4
169.1 174.1 120.0
170.2 175.0 118.65
Ref. [59].
3. Results Tables 1 – 3 contain the calculated vibrational frequencies for B2Cl4 at the Hartree –Fock, B3LYP, and MP2 levels of theory, respectively. Correction factors for the different types of vibrational modes
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were calculated, following a procedure that was previously proposed [57]. The correction factors are obtained by taking the average of the ratios between the computed and experimental frequencies for a particular type of motion. There is very little variation in the ratios for all of the modes within a motion type. This indicates that the procedure should lead to reliable predictions. The computed correction factors at the Hartree – Fock, B3LYP and MP2 levels of theory are presented in Table 4. These correction factors were used to generate the predicted frequencies in the last column of Tables 1– 3. Fig. 2 presents a view of the normal modes of B2Cl 4 using the NCAPLOT utility in SPIROVIB2 [58]. The corrected DFT frequencies for the 0-10B form of B2Cl4 are presented also. Table 5 contains the geometric parameters [51,59 –62] for B2Cl4. Due to the symmetry of this molecule ðD2d Þ;
Fig. 3. Occupied molecular orbitals of B2Cl4. Atomic core orbitals have been omitted.
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Fig. 3 (continued )
the geometry is completely specified by two bond lengths and one bond angle. Fig. 3 presents selected molecular orbitals [63] of B2Cl4 using the Chem3D program. The orbitals in Fig. 3 are the occupied
orbitals from the Hartree – Fock calculation. The atomic core orbitals have been omitted. The calculated barrier to rotation [49,59,64,65] around the B – B bond is presented in Table 6.
Table 6 Transition barrier height calculated at three levels of theory using the standard 6-311Gp p basis set
Energy ground ðD2d Þ Energy transition state ðD2h Þ Zero point energy ðD2d Þ Zero point energy ðD2h Þ ZPE ðD2d Þ corrected DE (Hartree) DE (kJ/mole) a b
Ref. [59]. Ref. [49].
Hartree–Fock
DFT (B3LYP)
MP2
Experimenta
Experimentb
21887.56704 21887.56248 0.01383 0.01385 0.01377 0.00465 12.21
21890.76958 21890.76578 0.01303 0.01308 0.01297 0.00390 10.25
21888.28070 21888.27717 0.01371 0.01376 0.01366 0.00352 9.25
– – – – – – 7.74
– – – – – – 7.12
J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219 Table 7 Change in symmetry due to isotopic substitution of boron atoms (0-10B ! 1-10B ! 2-10B) in B2Cl4 D2d (0-10B, 2-10B)
C2v (1-10B)
A1 ! B1 ! B2 ! E!
A1 A2 A1 B1 þ B2
4. Discussion Natural occurring boron consists of two isotopes, B (19.6%) and 11B (80.4%). In Tables 1 – 3 the most abundant isotope (11B) was used in all cases for both the calculations and predictions. Naturally occurring a B2Cl4 exist as a mixture of 64.6% 0-10B, 31.5% 1-10B, and 3.8% 2-10B. Boron is a relatively light atom and isotopic shifts are evident in the spectrum of many naturally occurring boron compounds. Also the substitution of 10B for 11B in B2Cl4 causes a change in the point group of the molecule. Changes in the point group (D2d (0- 10 B) ! C2v (1- 10B) ! D2d (2-10B)) along with the changes in the atomic masses create a complicated pattern of frequency shifting and 10
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splitting. These changes in point groups are presented in Table 7. The predicted spectra of B2Cl4 with 1-10B and 2-10B substitutions are shown in Tables 8 and 9, respectively. Calculations were performed using at the DFT level of theory using the B3LYP functional. The correction factors in Table 4 were used to calculate the predicted frequencies, which matched quite well with experimental data. In Tables 1 – 3 and 9 normal modes intensities have not been corrected for degeneracies. It is appropriate to multiply the IR and Raman intensities of modes of E symmetry by two.
5. Summary and conclusions A normal mode analysis of B2Cl4 was completed with good results. Normal modes were calculated at the Hartree – Fock, DFT (B3LYP) and MP2 levels of theory using the standard 6-311G** basis. Computed vibrational modes were compared against available experimental information that exists in the literature. All normal modes were successfully assigned to one of six types of motion (B –B stretch, B – Cl stretch, BCl2 scissors, BCl2 rock, BCl2 wag, and B –B torsion) predicted by a group theoretical analysis.
Table 8 Normal modes of the 1-10B form of B2Cl4 calculated at the DFT (B3LYP) level of theory using the standard 6-311G** basis set Symmetry Normal mode Newa symmetry Calculated frequency IRb intensity Ramanc activity Assignment A1
B1 B2 E
n1 n2 n3 n4 n5 n6 n7 n8 n9
a
A1 A1 A1 A2 A1 A1 B1 B2 B2 B1 B1 B2
1154 401 173 27 734 294 933 897 513 493 100 100
1 0 0 Inactive 175 4 365 335 11 10 1 1
17 8 2 5 2 4 7 7 1 1 2 2
Correctedd frequency
B–B stretch 1150 B–Cl stretch 405 BCl2 scissors 173 B–B torsion 25 B–Cl stretch 741 BCl2 scissors 295 B–Cl stretch 942 B–Cl stretch 905 BCl2 wag 533 BCl2 wag 512 BCl2 rock 104 BCl2 rock 104
C2v . Normal modes of B1 symmetry are defined to be those that are symmetric with respect to the Cl– 10B –Cl plane and anti-symmetric with respect to the Cl– 11B– Cl plane. Normal modes of B2 symmetry are defined to be those that are symmetric with respect to the Cl– 11B–Cl plane and anti-symmetric with respect to the Cl– 10B –Cl plane. This follows the normal convention based on moments of inertia. b Units of IR intensity are km/mol. c ˚ 4/amu. Units of Raman scattering activity are A d Raw calculated frequencies multiplied by the correction factors in Table 4.
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Table 9 Normal modes of 2-10B form of B2Cl4 calculated at the DFT (B3LYP) level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Correctedc frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1179 402 173 27 747 295 994 513 101
IR inactive
18 8 2 5 1 4 7 1 2
B–B stretch B–Cl stretch BCl2 scissors B–B torsion B–Cl stretch BCl2 scissors B–Cl stretch BCl2 wag BCl2 rock
1175 406 173 25 754 296 1003 533 105
B1 B2 E
a b c
Inactive 183 4 364 11 1
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Raw calculated frequencies multiplied by the correction factors in Table 4.
The vibrational modes of the 1-10B and 2-10B forms of B2Cl4 were also calculated and compared against experimental data. A complex pattern of frequency shifts and splittings was predicted. The molecular orbitals and rotational barrier of B2Cl4 were also examined.
Acknowledgements The author would like to express appreciation to the Joint Science and Technology Panel for Chemical and Biological Defense (JSTPCBD), for support of this work as part of the Joint Service Wide Area Detection Program.
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Quantum chemical analysis of the vibrational frequencies and structure of tetrachlorodiborane James O. Jensen* US Army Edgewood Chemical and Biological Center, AMSSB-RRT-DP, Aberdeen Proving Ground, MD 21010-5424, USA Received 22 March 2003; accepted 2 June 2003
Abstract The normal mode frequencies and corresponding vibrational assignments of B2Cl4 are examined theoretically using the set of quantum chemistry codes. All normal modes were successfully assigned to one of six types of motion predicted by a group theoretical analysis (B – B stretch, B– Cl stretch, BCl2 scissors, BCl2 rock, BCl2 wag, and B– B torsion) utilizing the D2d symmetry of the molecule. The vibrational modes of the naturally isotopically substituted (1-10B and 2-10B) forms of B2Cl4 were also calculated and compared against experimental data. The barrier to rotation of the around the B– B bond is examined. Molecular orbitals are presented. Published by Elsevier B.V. GAUSSIAN 98
Keywords: Vibrations; Normal mode frequencies; Infrared spectra; Raman spectra; Boron chloride; Diboron tetra chloride; Tetrachlorodiborane
1. Introduction Tetrachlorodiborane (B2Cl4) was first reported in the literature in 1925 [1] and a number of papers have appeared on methods for synthesizing B2Cl4 [1 – 10]. B2Cl4 has proven to be a useful laboratory reagent [11 – 25] in the synthesis of novel boron containing compounds. The NMR spectroscopy [26,27], photoelectron spectroscopy [28], and mass spectrometry [29] of B2Cl4 have been reported. Due to its high symmetry and unusual bonding, B2Cl4 has been the subject of a number of theoretical studies [30 –41]. * Tel.: þ1-410-436-5665; fax: þ 1-410-436-1120. E-mail address: [email protected] (J.O. Jensen). 0166-1280/03/$ - see front matter Published by Elsevier B.V. doi:10.1016/S0166-1280(03)00458-5
Interpretation of an experimental infrared or Raman spectra of a complex molecule is a difficult task. An empirical set of rules often gets built up over a period of time [42]. For organic molecules these empirical rules are well established and have been an aid to scientists for decades. For inorganic compounds with much more variety in bonding types, the rules are far less established. One of the goals of this paper is to elucidate the typical vibrational frequencies for B – B and B – Cl type bonds, both stretching and bending. Natural occurring Boron consists of two isotopes, 10 B (19.6%) and 11B (80.4%). Isotopic effects are quite evident in the experimental spectrum of B2Cl4. The boron atoms are light enough such that the isotopic shifts are quite large and can be readily seen in the experimental spectrum.
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2. Computational methods
Fig. 1. Structure of B2Cl4.
Quantum chemical methods of normal mode analysis will be used to examine available experimental infrared and Raman data in detail. In this study the infrared and Raman spectra of B2Cl4 are examined using the GAUSSIAN 98 suite of quantum chemical codes [43]. High quality experimental data [44 – 51] on the vibrational modes of B2Cl4 exists in the literature. However, a detailed quantum chemical normal mode analysis has not been performed to date. A detailed quantum chemical study will aid in making definitive assignments to the fundamental normal modes of B2Cl4 and in clarifying the experimental data available for this molecule.
The vibrational frequencies of B2Cl4 were calculated at the Hartree – Fock, DFT (B3LYP) [52,53] and MP2 [54] levels of theory using the 6-311G basis set. The calculations utilized the D2d symmetry of the B2Cl4 molecule (see Fig. 1). The computations were performed using the GAUSSIAN 98 program package [43]. Each of the vibrational modes was assigned to one of six types of motion (B – B stretch, B – Cl stretch, BCl2 scissors, BCl2 rock, BCl2 wag, and B – B torsion) by means of visual inspection using the Gaussview program [55]. The choice of internal coordinates is always somewhat arbitrary. However, the above set is complete and matches well the observed motion using the Gaussview program. The symmetry of the B2Cl4 molecule was also helpful in making vibrational assignments. The symmetries of the vibrational modes were determined by using standard procedure [56] of decomposing the traces of the symmetry operations into the irreducible representations of the D2d group. The symmetry analysis for the vibrational modes of B2Cl4 is presented in some detail in order to better describe the basis for the assignments. For the B – Cl stretching modes the four B –Cl bonds were used as the basis of the analysis. The sd operator has a trace of two. All other operators except
Table 1 Normal modes of B2Cl4 calculated at the Hartree– Fock level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Experimental frequencyc
Correctedd frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1185 420 182 28 760 309 857 528 108
Infrared inactive
1 5 1 3 1 3 3 0 2
B –B stretch B –Cl stretch BCl2 scissors B –B torsion B –Cl stretch BCl2 scissors B –Cl stretch BCl2 wag BCl2 rock
1122 401 176 25 728 289 915 512 104
1122 417 173 25 755 294 851 512 104
B1 B2 E
a b c d
Inactive 207 6 387 19 3
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Ref. [46]. Raw calculated frequencies multiplied by the correction factors in Table 4.
J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219
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Table 2 Normal modes of B2Cl4 calculated at the DFT (B3LYP) level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Experimental frequencyc
Correctedd frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1126 401 173 27 722 293 897 493 100
IR inactive
17 8 2 5 2 4 7 1 2
B –B stretch B –Cl stretch BCl2 scissors B –B torsion B –Cl stretch BCl2 scissors B –Cl stretch BCl2 wag BCl2 rock
1122 401 176 25 728 289 915 512 104
1122 405 173 25 729 294 905 512 104
B1 B2 E
a b c d
Inactive 169 4 337 10 1
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Ref. [46]. Raw calculated frequencies multiplied by the correction factors in Table 4.
Table 3 Normal modes of B2Cl4 calculated at the MP2 level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Experimental frequencyc
Correctedd frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1171 420 179 25 762 306 970 510 98
IR inactive
7 7 2 5 1 4 4 1 2
B–B stretch B–Cl stretch BCl2 scissors B–B torsion B–Cl stretch BCl2 scissors B–Cl stretch BCl2 wag BCl2 rock
1122 401 176 25 728 289 915 512 104
1122 399 173 25 725 295 923 512 104
B1 B2 E
a b c d
Inactive 164 4 369 8 1
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Ref. [46]. Raw calculated frequencies multiplied by the correction factors in Table 4.
E have a trace of zero. Thus the four B– Cl stretching modes possess the symmetries A1, B2, and E. For the two BCl2 scissoring modes the C2 and sd operators each have a trace of two. All other operators expect E have a trace of zero. Thus the two BCl2 scissoring modes possess the symmetries A1 and B2. For the two BCl2 wagging modes the C2 operator has a trace of minus two. All other operators expect E have a trace of zero. Thus the two BCl2 wagging modes possess the E symmetry. For the two BCl2 rocking modes the C2 operator has a trace of minus two. All other operators expect E have a trace of zero.
Table 4 Correction factors for B2Cl4
B–B stretch B–Cl stretch BCl2 wag BCl2 scissors BCl2 rock B–B torsion
Hartree–Fock
DFT (B3LYP)
MP2
0.9468 0.9934 0.9697 0.9512 0.9630 0.8929
0.9964 1.0095 1.0385 1.0018 1.0400 0.9259
0.9582 0.9511 1.0039 0.9638 1.0612 1.0000
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J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219
Fig. 2. Normal modes of B2Cl4.
Thus the two BCl2 rocking modes possess the E symmetry. The single B – B stretching mode possesses A1 symmetry, and the single B– B torsion possesses B1 symmetry. By combining the results of the Gaussview program [55] with the symmetry considerations,
vibrational frequency assignments were made with a high degree of confidence. There is always some choice in defining internal coordinates for a normal mode analysis study. However, the set of coordinates listed above complete and matches well the motions observed using the Gaussview program.
J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219 Table 5 Geometric parameters of B2Cl4. Distances are presented in pm and angles in degrees. All calculations utilized the standard 6-311G** basis set
B –B B –Cl Cl–B –Cl a
Hartree–Fock
DFT (B3LYP)
MP2
Experimenta
170.5 175.3 119.5
168.6 175.6 119.4
169.1 174.1 120.0
170.2 175.0 118.65
Ref. [59].
3. Results Tables 1 – 3 contain the calculated vibrational frequencies for B2Cl4 at the Hartree –Fock, B3LYP, and MP2 levels of theory, respectively. Correction factors for the different types of vibrational modes
215
were calculated, following a procedure that was previously proposed [57]. The correction factors are obtained by taking the average of the ratios between the computed and experimental frequencies for a particular type of motion. There is very little variation in the ratios for all of the modes within a motion type. This indicates that the procedure should lead to reliable predictions. The computed correction factors at the Hartree – Fock, B3LYP and MP2 levels of theory are presented in Table 4. These correction factors were used to generate the predicted frequencies in the last column of Tables 1– 3. Fig. 2 presents a view of the normal modes of B2Cl 4 using the NCAPLOT utility in SPIROVIB2 [58]. The corrected DFT frequencies for the 0-10B form of B2Cl4 are presented also. Table 5 contains the geometric parameters [51,59 –62] for B2Cl4. Due to the symmetry of this molecule ðD2d Þ;
Fig. 3. Occupied molecular orbitals of B2Cl4. Atomic core orbitals have been omitted.
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J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219
Fig. 3 (continued )
the geometry is completely specified by two bond lengths and one bond angle. Fig. 3 presents selected molecular orbitals [63] of B2Cl4 using the Chem3D program. The orbitals in Fig. 3 are the occupied
orbitals from the Hartree – Fock calculation. The atomic core orbitals have been omitted. The calculated barrier to rotation [49,59,64,65] around the B – B bond is presented in Table 6.
Table 6 Transition barrier height calculated at three levels of theory using the standard 6-311Gp p basis set
Energy ground ðD2d Þ Energy transition state ðD2h Þ Zero point energy ðD2d Þ Zero point energy ðD2h Þ ZPE ðD2d Þ corrected DE (Hartree) DE (kJ/mole) a b
Ref. [59]. Ref. [49].
Hartree–Fock
DFT (B3LYP)
MP2
Experimenta
Experimentb
21887.56704 21887.56248 0.01383 0.01385 0.01377 0.00465 12.21
21890.76958 21890.76578 0.01303 0.01308 0.01297 0.00390 10.25
21888.28070 21888.27717 0.01371 0.01376 0.01366 0.00352 9.25
– – – – – – 7.74
– – – – – – 7.12
J.O. Jensen / Journal of Molecular Structure (Theochem) 635 (2003) 211–219 Table 7 Change in symmetry due to isotopic substitution of boron atoms (0-10B ! 1-10B ! 2-10B) in B2Cl4 D2d (0-10B, 2-10B)
C2v (1-10B)
A1 ! B1 ! B2 ! E!
A1 A2 A1 B1 þ B2
4. Discussion Natural occurring boron consists of two isotopes, B (19.6%) and 11B (80.4%). In Tables 1 – 3 the most abundant isotope (11B) was used in all cases for both the calculations and predictions. Naturally occurring a B2Cl4 exist as a mixture of 64.6% 0-10B, 31.5% 1-10B, and 3.8% 2-10B. Boron is a relatively light atom and isotopic shifts are evident in the spectrum of many naturally occurring boron compounds. Also the substitution of 10B for 11B in B2Cl4 causes a change in the point group of the molecule. Changes in the point group (D2d (0- 10 B) ! C2v (1- 10B) ! D2d (2-10B)) along with the changes in the atomic masses create a complicated pattern of frequency shifting and 10
217
splitting. These changes in point groups are presented in Table 7. The predicted spectra of B2Cl4 with 1-10B and 2-10B substitutions are shown in Tables 8 and 9, respectively. Calculations were performed using at the DFT level of theory using the B3LYP functional. The correction factors in Table 4 were used to calculate the predicted frequencies, which matched quite well with experimental data. In Tables 1 – 3 and 9 normal modes intensities have not been corrected for degeneracies. It is appropriate to multiply the IR and Raman intensities of modes of E symmetry by two.
5. Summary and conclusions A normal mode analysis of B2Cl4 was completed with good results. Normal modes were calculated at the Hartree – Fock, DFT (B3LYP) and MP2 levels of theory using the standard 6-311G** basis. Computed vibrational modes were compared against available experimental information that exists in the literature. All normal modes were successfully assigned to one of six types of motion (B –B stretch, B – Cl stretch, BCl2 scissors, BCl2 rock, BCl2 wag, and B –B torsion) predicted by a group theoretical analysis.
Table 8 Normal modes of the 1-10B form of B2Cl4 calculated at the DFT (B3LYP) level of theory using the standard 6-311G** basis set Symmetry Normal mode Newa symmetry Calculated frequency IRb intensity Ramanc activity Assignment A1
B1 B2 E
n1 n2 n3 n4 n5 n6 n7 n8 n9
a
A1 A1 A1 A2 A1 A1 B1 B2 B2 B1 B1 B2
1154 401 173 27 734 294 933 897 513 493 100 100
1 0 0 Inactive 175 4 365 335 11 10 1 1
17 8 2 5 2 4 7 7 1 1 2 2
Correctedd frequency
B–B stretch 1150 B–Cl stretch 405 BCl2 scissors 173 B–B torsion 25 B–Cl stretch 741 BCl2 scissors 295 B–Cl stretch 942 B–Cl stretch 905 BCl2 wag 533 BCl2 wag 512 BCl2 rock 104 BCl2 rock 104
C2v . Normal modes of B1 symmetry are defined to be those that are symmetric with respect to the Cl– 10B –Cl plane and anti-symmetric with respect to the Cl– 11B– Cl plane. Normal modes of B2 symmetry are defined to be those that are symmetric with respect to the Cl– 11B–Cl plane and anti-symmetric with respect to the Cl– 10B –Cl plane. This follows the normal convention based on moments of inertia. b Units of IR intensity are km/mol. c ˚ 4/amu. Units of Raman scattering activity are A d Raw calculated frequencies multiplied by the correction factors in Table 4.
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Table 9 Normal modes of 2-10B form of B2Cl4 calculated at the DFT (B3LYP) level of theory using the standard 6-311G** basis set Symmetry
Normal mode
Calculated frequency
IRa intensity
Ramanb activity
Assignment
Correctedc frequency
A1
n1 n2 n3 n4 n5 n6 n7 n8 n9
1179 402 173 27 747 295 994 513 101
IR inactive
18 8 2 5 1 4 7 1 2
B–B stretch B–Cl stretch BCl2 scissors B–B torsion B–Cl stretch BCl2 scissors B–Cl stretch BCl2 wag BCl2 rock
1175 406 173 25 754 296 1003 533 105
B1 B2 E
a b c
Inactive 183 4 364 11 1
Units of IR intensity are km/mol. ˚ 4/amu. Units of Raman scattering activity are A Raw calculated frequencies multiplied by the correction factors in Table 4.
The vibrational modes of the 1-10B and 2-10B forms of B2Cl4 were also calculated and compared against experimental data. A complex pattern of frequency shifts and splittings was predicted. The molecular orbitals and rotational barrier of B2Cl4 were also examined.
Acknowledgements The author would like to express appreciation to the Joint Science and Technology Panel for Chemical and Biological Defense (JSTPCBD), for support of this work as part of the Joint Service Wide Area Detection Program.
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