Correlation of Computational Modeling to Experimental IR and Raman Data of Structural Units found in Borosulfide and Borate Glass
Kyle Kruse
Abstract
Abinitio and semiempirical methods were used to obtain optimized geometries and vibrational frequencies for BO_{3}, BO_{4}, B_{3}O_{3}, B_{3}O_{6},_{ }B_{5}O_{10},_{ } BS_{3}, BS_{4}, B_{3}S_{6}, and B_{4}S_{9 }structural units. These units have been observed in borate and borosulfide glasses using techniques such as TOFMS, NMR, Raman, and FTIR. Theoretical results of calculations using various basis sets and levels of theory were compared to experimental IR and Raman data. Calculations upon similar borate and borosulfide units were compared to examine the effect of replacing oxygen atoms for sulfur atoms. The computed vibrational frequencies agree well with experimental IR values.
Introduction
Computational modeling is a process in which structures and reactions of a molecular input are predicted by computer simulation calculations. Each calculation is performed under different parameters based on the fundamental laws of physics. These parameters are comprised of different theoretical approximation methods and basis sets.
In the Gaussian program, both abinitio and semiempirical theoretical methods are applied to make approximations upon the calculations concerning the energy of manybody systems and to minimize unavoidable residual error while keeping the calculations plausible. The abinitio methods are purely based upon the first principles of quantum mechanical chemistry and include only empirical data. These abinitio calculations are not exact, but contain a small acknowledged error margin. Unlike the more accurate abinitio, a semiempirical calculation makes many approximations from experimental data. The semiempirical method is more commonly applied to larger molecules decreasing the complexity and the time of the calculation.
The two abinitio approximation methods used for geometry optimization and vibrational frequency calculations were the Density Functional Theory (DFT) and the HartreeFock Theory (HF). Overall, the DFT method provided vibrational modes with calculated frequencies that correlated better with experimental frequencies than the HF method did. What makes the Density Functional Theory different than other approximations is that this method takes into account the electron density, whereas many others are based on a complex manyelectron wavefunction^{[1]}. From these calculations, the selfconsistent field (SCF) energy and zero point energy were determined. These values are important since the SCF energy is the total energy of the system, and the zero point energy is the lowest possible energy that a quantum mechanical system can have. Zero point energy is also used to extrapolate the calculated quantities to zero Kelvin, refining the determination of the electronic energies.
For each calculation, there is a choice of basis set to apply to the computation. A basis set is a mathematical representation of the molecular orbitals within a molecule. Basis sets are often represented as a number with a hyphen followed by two or three more numbers. The number to the left of the hyphen indicates the number of Gaussian molecular orbitals and the hyphen represents a split valence set. The two or three numbers on the right side of the hyphen account for the basis functions corresponding to each atomic orbital. The more the number of atomic orbitals, the more accurate the calculation is due to fewer limitations on electron movement within a molecular orbital^{[2]}.
A computational program can calculate a number of different properties of a molecular unit. The most essential of these calculations is geometry optimization. Geometry optimization is the process of finding equilibrium between molecular structure and resultant energy, based on the observation of the molecular potential energy surface. The potential energy surface represents a link between bond distance and the energy associated with the nuclear positions. A structure is optimized when a global minimum is located, which indicates the lowest energy of repulsion and attraction between the atoms in the structure. The first derivative of the potential energy surface, also known as the gradient, helps the program find the global minimum by giving a description of the slope and indicating the direction in which the energy decreases most rapidly from the initial input. This optimization process is complete when the convergence criteria are met. These criteria consist of making the forces and the rootmeansquare of the forces as close to zero as possible and making the calculated displacement of the atoms and its rootmeansquare zero. With an optimized geometry, bond energies,
bond lengths, bond angles, and dihedral angles can be determined. For the proper calculation of any other parameters, geometry optimization must be completed to a basis level that is equivalent or higher than the parameter to be calculated^{[2]}.
Once the geometry is optimized, each structural unit undergoes a vibrational frequency calculation. This is a calculation of the modes of vibration, or direction and magnitude of nuclei movement in the ground and excited states. The number of modes of vibration for nonlinear molecules is found by the equation: 3n−6, where n is the number of atoms. A linear molecule has 3n−5 normal modes of vibration because the rotation about its molecular axis does not produce a change in dipole moment, preventing its observation.
The frequencies of the vibrations are approximated by the quantum harmonic oscillator equation:
E = (n+ ½)[hω/2π]
where n= energy level, h=Planck’s constant, and ω is the angular frequency. The energy of each vibration corresponds to a particular frequency at which the structure bends or stretches. These calculated frequencies of the vibrations are either located on the experimental infrared spectra if a change in the permanent dipole occurs or observed on Raman spectra if the polarizability changes during the vibration^{[2]}.
The general application of computational chemistry is to predict unobserved chemical and physical phenomena. The present research is centered on using computational chemistry to obtain a better understanding of glass structure, particularly borate and borosulfide glass. Glass structure is ambiguous because at the molecular level, glass consists of a continuous random network, where the building blocks of this network are fused together in an unsystematic pattern of cations and glassformers^{[3]}. The randomness of the glass structure is unique to the components that create its matrix.
Glass is usually composed of a glassformer and a modifier. Glassformers are exactly what their title insinuates substances that produce ‘good’ glasses. Many substances can produce glass, only a few can produce good glass. Typically, these glassformers are oxides. Examples of such substances are silicon oxide and boron oxide which are common components of everyday glass. The role of a modifier in glass is to alter the physical properties of the glassformer by integrating itself into the glass matrix. Examples of modifiers are cations like Pb^{2+}, Li^{+}, or Na^{+}.
The calculations are performed in an effort to gain insight on the randomness of borate and borosulfide matrices by visualizing the vibrational modes of their structural units under theoretical conditions. It is hoped that from gathered information, one could better understand and formulate predictions on the production and stabilization of the unique networks created by distinct components.
Experimental: Gaussian 2007
Structural units found in borate and borosulfide glasses were reconstructed in an open editor format with hydrogen atoms placed on the terminal oxygen or sulfur atoms to stabilize the molecule. In Gaussian 2007, each unit has its geometry optimized under a 6311+G(d,p) basis set with the exception of the B_{3}O_{3}H_{3} unit. The B_{3}O_{3}H_{3} geometry was optimized under a 6311+G(d,p) basis set and also, a 321G basis set for comparison to a calculation done in previous research^{[4]}.
Once the geometry of each unit was successfully optimized, vibrational frequency calculations were performed. Initial calculations for the BO_{3}H_{3} and B_{3}O_{6}H_{3} structural units were performed using both the restricted HartreeFock (RHF) method and Density Functional Theory (DFT) for comparison of the two approximation methods. The restricted HartreeFock approximation method is applied when all electrons are paired and the shells are considered closed, whereas the unrestricted HF method is used when electrons with unpaired spins are present, requiring different molecular orbitals to differentiate between unpaired electrons. Soon after these calculations were completed, the decision was made to only use the DFT approximation method. DFT was chosen over the HF method because calculations performed under the DFT method were displaying results that were closer to experimentally found IR values. The DFT method also is less demanding on the computer program than the HF method which allows for faster calculation time.
Using only the DFT approximation method, the geometry optimization and vibrational frequencies of the structural units of BO_{4}H_{4}, B_{5}O_{10}H_{4},_{ }BS_{3}H_{3}, BS_{4}H_{4}, B_{3}S_{6}H_{3}, and B_{4}S_{9}H_{4} were performed. Unfortunately, only a few experimental frequencies were found for the borosulfide units that correlate with the IR active calculated vibrational modes. This was not too troubling considering that the sole purpose of the observation of these borosulfide units was to compare them to the equivalent borates as an internal check or theoretical comparison upon the program itself to see how the substitution of sulfur for oxygen affects the placement of the vibrational modes in the predicted IR spectrum. Comparisons were achieved by looking at the placement of vibrational frequencies for ‘signature’ vibrational modes relative to particular geometries. For the trigonal planar BO_{3}/BS_{3} geometries, an umbrella motion is identified, in which is the central boron atom asymmetrically stretches in and out of the plane. The tetrahedral geometries of BO_{4}/BS_{4} have symmetrical stretching of nonhydrogen terminal atoms, and the ring structures of B_{3}O_{6}/B_{3}S_{6} have a breathing motion that the oxygen or sulfur atoms of the ring stretch symmetrically in and out appearing as if the structure is breathing.
In performing calculations on the BO_{4}H_{4} and BS_{4}H_{4} units, it was assumed that the structures have tetrahedral geometries because any other geometry would weaken the strength of the glass matrix. The optimized geometry of BS_{4}H_{4} was tetrahedral, but when the BO_{4}H_{4} is isolated in the program, the geometry was optimized as trigonal planar with the fourth oxygen atom being stretched out from the boron at a length twice as long as the other three BO bonds(Figure 6). Since this geometry appears to be unfavorable for a stable matrix structure, an attempt was made to place the BO_{4 }unit within a larger structure to observe if a surrounding matrixlike structure can stabilize the BO_{4} in a tetrahedral geometry. The four terminal oxygen atoms of BO_{4} were extended out by attaching a boron atom to each of them and creating rings off of the central BO_{4} unit. The geometry was held identical on each side of the molecule to produce a consistent structure. The final double ring structure had a molecular formula of B_{5}O_{10}H_{4} and the vibrational frequencies of the central BO_{4} unit were observed and compared to experimental data._{ }
As mentioned previously, geometry optimization and vibrational frequency calculations were performed for a B_{3}O_{3}H_{3} planar ring under a 6311+G(d,p) and a more basic 321G basis set. A 321G basis set was used for geometry optimization and vibrational frequency calculations to reconstruct the procedure done in previous research^{[4]}. In this procedure, a RHF/321G basis set was used upon a B_{3}O_{3}H_{3} unit and the vibrational frequencies were compared to experimental IR data. It was found that the calculated frequencies of a 321G basis are approximately 9% larger than experimental IR frequencies, which happens to be a typical error for this particular basis set. This was corrected by multiplying each calculated frequency by a value of 0.9. Once the calculations performed under a 321G basis set were completed, a RHF/6311+G(d,p) basis set was applied to observe how a higher basis set will match up with the same experimental IR frequencies. The error of this basis set is unknown, so no correction was made to the calculated vibrational frequencies.
The next structure observed is a proposed component in sodium borosulfide glasses^{[5]}. Sodium borosulfide glass contains a high 4coordinated boron to 3coordinated boron ratio. This structural unit, known as dithioborate, consists of possibly two 3coordinated and two 4coordinated boron atoms or four 4coordinated boron atoms depending if bonds to a central sulfur atom exist.
The final structure of B_{3}O_{7}H_{4}Li was not found in glass but calculations were done to simulate a glasslike situation. The B_{3}O_{7}H_{4}Li geometry calculation was performed with the sole purpose of observing how the program would react to the presence of a cation in the structure, as commonly found in glass with a modifier present.
The data collected from the successful calculations mentioned above include the total self consistent field (SCF) energy, zeropoint energy, the mode of vibration, and the wavelength at which each IR and Raman active mode occurred. No attempt to resolve the modes pertaining to hydrogen movement was made because the hydrogen atoms were placed in the structure for stabilization purposes only.
Results
Table 1 displays the energies, vibrational modes, and the theoretical and experimental frequencies associated with the isolated BO_{3}H_{3} unit determined by the two approximation methods.
Table 1
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
Experimental (cm^{1}) 
RHF 
251.3 
0.0522

733 
Umbrella motion 
650700 ^{[6]} 
926 
Stretching of BO 
N/A 

14861542 
Asymmetric stretch of B 
12001400 ^{[7]} 

DFT 
1247.6 
0.0484

667 
Umbrella motion 
650700 ^{[6]} 
873 
Stretching of BO 
N/A 

13911454 
Asymmetric stretch of B 
12001400 ^{[7]} 
*Table only contains IR active modes
The calculated frequencies of this free trigonal planar structure (Figure 3) agree well with its experimental vibrational modes even though theory did not account for the matrix structure. The frequencies and vibrational modes determined by the RHF and DFT methods display strong agreement to each other although the DFT frequencies relate more closely to experimental IR values and are an average of 7% lower than the RHF values. The higher frequencies calculated by RHF are most likely due to a consistent error introduced by the broad approximations associated with the normalized manybody system of the HartreeFock method.
Table 2 displays the energies associated with the calculations, the calculated frequencies, the corresponding vibrational modes, and the experimental frequencies associated with each vibrational mode.
Table 2
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
Experimental^{[5]} (cm^{1}) 
DFT 
1221.4 
0.032 
415 
Umbrella motion 
N/A 
430 
BS symmetrical stretching 
N/A 

767815 
B stretching, slight shifting 
~750 

1062 
B stretching shifting 
~850 
*Experimental values listed as “N/A” are frequencies involving motions that are not IR or Raman active
Experimentally, stretching was found for the 3coordinated boron at 750 and
850 cm^{1}. These values vary slightly from the calculated frequencies, which is most likely due to the fact that the calculation is done upon a loose structure that is not matrixembedded.
Table 4 contains the calculated energies and frequencies of IR and Raman active vibrational modes with correlating experimental vibrational frequencies.
Table 4
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
Experimental^{[5]} (cm^{1}) 
DFT 
1619.8 
0.042 
384 
BS symmetrical stretching 
N/A 
622653 
B asymmetrical stretching 
~650, ~750 
The tetrahedral BS_{4} contains bond angles of 109^{°} and bond lengths of 1.91 Å.
Experimentally, stretching of the BS_{4} unit was noticed at 650 and 750cm^{1}. The calculated vibrational frequency associated with the boron atom asymmetrical stretch was very close in value to the experimentally found vibrational frequency for this mode.
Table 3
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
Experimental (cm^{1}) 
DFT 
328.0 
0.0634 
651 
Umbrella motion 
N/A 
970 
O1 and O4 bending apart 
N/A 

1191 
B stretching in plane 
N/A 

1673 
strong B stretching in plane 
N/A 
The optimized geometry of the BO_{4} unit is a structure of little symmetry. Bond angles were found to be 142º separating oxygen atoms #2 and 3, 130 º between oxygen atoms #2 and 4, and 86º between oxygen atoms #3 and 4. The oxygen atom #3 is 3º behind the plane and #4 is 20º in front of the plane (Figure 5). BO bonds for oxygen atoms #1, 2, 3 and 4 are 1.53, 1.32, 1.32, and 2.54 Å, respectively. The bond to oxygen #4 is almost twice as long as the other bonds because the optimized geometry is attempting to expel the fourth oxygen since boron is most stable with only three bonds. Since these geometries are not of the same form, their vibrational frequencies of different vibrational modes cannot be compared.
Table 5 displays the energies associated with the calculations under DFT, the calculated frequencies for the vibrations, the modes of the vibrations, and the experimental frequency associated with each vibrational mode.
Table 5
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
Experimental (cm^{1}) 
DFT 
879.8 
0.11

571 
Stretching of B 
~400^{[6]} 
665 
Breathing of ring 2 with O of BO_{4} 
~400, ~650^{[6]} 

780 
Stretching of O of BO_{4} in ring 1 
~800^{[6]} 

11891339 
Stretching of B in BO_{4 } 
~1220^{[7]} 
*Table only contains the vibrational modes associated with the movement of the BO_{4} unit.
As can be seen in Table 5, this mock glass structure holds the BO_{4} unit in a tetrahedral geometry and allows for the calculated vibrational frequencies to match up well with the approximated experimental values. Bond angles of the central BO_{4} unit of this structure are 112º between the oxygen atoms attached to ring 1 and 86º between the oxygen atoms attached to the bent ring or ring 2. BO bond lengths of BO_{4} are 1.45Å.
Table 6 shows the calculated frequencies from the previous research^{[4]}, the calculated frequencies for this research, the experimental frequencies, and the percent difference of the new calculations relative to the experimental data.
Table 6
Symmetries 
^{ [4]}Calculated Frequency 
^{ [4]}Calculated x0.9 
New Calculated Frequency 
New Calculated x0.9 
^{ [4]}Experimental Frequency 
% Difference EQ. 1 
A_{2}’’ 
1001 cm^{1} 
901cm^{1} 
1013cm^{1} 
912cm^{1} 
910cm^{1} 
2.20% 
A_{2}’’ 
399 
359 
434 
391 
(380) 
2.90 
E’ 
2803 
2523 
2901 
2611 
2613 
0.077 
E’ 
1532 
1379 
1473 
1326 
1403 
5.49 
E’ 
1325 
1193 
1309 
1178 
1200 
1.83 
E’ 
1072 
965 
1056 
950 
998 
4.81 
E’ 
567 
510 
555 
500 
530 
5.66 
A_{1}’ 
2823 
2523 
2924 
2631 
(2616) 
0.57 
A_{1}’ 
1060 
954 
1074 
967 
906 
6.73 
A_{1}’ 
884 
796 
851 
766 
(800) 
4.25 
E’’ 
990 
891 
984 
886 
1050 
15.6 
E’’ 
231 
208 
257 
231 
343 
32.7 
A_{2}’ 
1273 
1146 
1267 
1140 
1477 
22.8 
A2’ 
1224 
1102 
1185 
1067 
1197 
10.9 
*Experimental values in
parentheses are estimated.
*EQ. 1: % Difference = [(Exp. – Cal.)/Exp.] x100%
*Average % difference = 8.32
The calculated frequencies of the B_{3}O_{3}H_{3} structure correlate very well with the computed frequencies of the previous research^{[4]} performed on this structure. In relationship to the experimental values, the calculated frequencies differed by an average 8.32% (EQ. 1). The margin of variation would be lower if not for the few outliers of the E” and A_{2}’ symmetries which are only Raman active and were estimated from weak IR combination bands in the IR spectra^{[7]}. The geometry of this ring structure incorporates three trigonal planar BO_{3} units with bond angles of 120º and bond lengths of 1.36 Å.
Table 7 displays the calculated and experimental values for the B_{3}O_{3}H_{3} structural unit when performed under a more accurate RHF/6311+F(d,p) basis set.
Table 7
Symmetries 
Calculated Frequency 
^{ [7]}Experimental Frequency 
% Difference EQ. 1 
Symmetries 
Calculated Frequency 
^{ [4]}Experimental Frequency 
% Difference EQ. 1 
A_{2}’’ 
1014 cm^{1} 
910cm^{1} 
11.4% 
A_{1}’ 
2793 
(2616) 
6.77 
A_{2}’’ 
399 
(380) 
5.00 
A_{1}’ 
1048 
906 
15.7 
E’ 
2775 
2613 
6.20 
A_{1}’ 
882 
(800) 
10.3 
E’ 
1481 
1403 
5.56 
E’’ 
995 
1050 
5.24 
E’ 
1298 
1200 
8.17 
E’’ 
231 
343 
32.7 
E’ 
1043 
998 
4.51 
A_{2}’ 
1256 
1477 
14.96 
E’ 
572 
530 
7.92 
A2’ 
1162 
1197 
2.92 
The calculated frequencies collected under a RHF/6311+F(d,p) basis set are close in value to the experimental values. The calculated frequencies were approximately 9.8 % different than the experimental values, but unlike with the 321G basis set used for the previous calculations of this structural unit, the error of this more accurate basis set is unknown.
Table 8
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
Experimental (cm^{1}) 
RHF 
525.65 
0.0793 
485491 
Bending of B & O, rocking motion 
400650 ^{[6]} 
618 
Bending of B, ring flex 
400650 ^{[6]} 

731822 
Bending of B, umbrella motion 
400650 ^{[6]} 

876 
Asym. Stretch of O (breathing motion) 
796 ^{[7]} 

1313 
Symmetrical stretching of B 
12001400^{[7]} 

14691582 
Asymmetrical Stretch of B 
12001400 ^{ [7]} 

DFT 
528.36 
0.0738

454 
Bending of O, rocking motion 
400650 ^{[6]} 
582 
Bending of O, ring flex 
400650 ^{[6]} 

671740 
Bending of B, Umbrella motion 
400650 ^{[6]} 

804 
Asym. Stretch of O (breathing motion) 
796 ^{[7]} 

1220 
Symmetrical stretching of B 
12001400 ^{ [7]} 

1374 1492 
Asymmetrical stretching of B 
12001400 ^{ [7]} 
Calculated frequencies displayed an average of 3.78% difference to experimental IR frequencies when the RHF method was applied and 0.71% when the DFT method was used. Extending upon the previous structure, a geometry optimization and vibrational frequency calculation was performed on a B_{3}O_{6}H_{3} structural unit under both the restricted HartreeFock method and the DFT method. This structure is completely planar and symmetrical with bond angles of 120º angles and bond lengths of 1.36 Å.
Table 9
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
DFT 
2465.9 
0.0481 
297 
Bending, ring flex 
392  425 
Bending of B, umbrella motion 

430 
Asym. Stretch of S (breathing motion) 

476 
Stretching of S in ring 

867 
Asymmetrical stretching of B 

921 
Symmetrical stretching of B 
*No experimental data worthy of comparison was found.
The optimized geometry of this structure contains bond lengths of 1.82 Å, ring BSB angles of 110º and SBS bond angles of 130º. The terminal SBS angles are 115º. The one noteworthy vibrational mode is the asymmetrical stretching of the sulfur atoms. This motion is also described as the breathing motion. Under the DFT method, this motion occurs for this borosulfide unit at 430cm^{1}.
The geometry optimization and vibrational frequency calculations were performed under the DFT method and collected data are displayed in Table 10.
Table 10
Theory 
SCF energy (Hartree) 
Zeropoint energy (Hartree) 
Calculated Frequency (cm^{1}) 
Mode 
Experimental Frequency (cm^{1}) 
DFT 
3685.3

0.065

314 
Breathing motion of ring; symmetrical stretching 
N/A 



568597 
Stretching of 4 coord. B in plane 
~650^{[5]} 



647660 
Slight stretching of 3 coord. B 
~650^{[5]} 



735 
Stretching of 4 coord. B out of plane 
~750^{[5]} 



10121045 
Stretching of 3 coord. B in plane 
~850^{[5]} 



1028 
Stretching of 4 coord. B in plane 
~750^{[5]} 
Accuracy of calculations on this particular structural unit were difficult to determine since the structure is a proposed structure and there is insufficient experimental data for comparison.
Geometry optimization calculations of B_{3}O_{7}H_{4}Li structural units were also attempted, but were unsuccessful. This unit has not been identified in glass but calculations were done to simulate glasslike situations. The B_{3}O_{7}H_{4}Li geometry calculation was performed to observe how the program would react to the presence of a cation in the structure, as commonly found in glass with a modifier. The geometry contorted itself into unfavorable geometry with the presence of the Li^{+} ion (Figure 12).
Conclusion & Discussion
Geometry optimization and vibrational frequency calculations were performed on BO_{3}, B_{3}O_{3}, B_{3}O_{6},_{ }and B_{5}O_{10} structural units found in boron oxide glasses, and BS_{3}, BS_{4}, B_{3}S_{6}, and B_{4}S_{9 }structural units present in borosulfide glasses. With the exception of the B_{3}O_{3}H_{3} unit, all calculations were performed under a 6311+G(d,p) basis set and using either HartreeFock or Density Functional Theory approximation methods. For calculations concerning the BO_{3}H_{3} and B_{3}O_{6}H_{3}, both approximation theories were applied and the DFT method proved to provide better correlation of calculated vibrational frequencies to experimentally collected data as seen in Tables 1 and 8 for these structures.
Geometry optimization calculations were completed for the simple borate units of BO_{3}H_{3} and BO_{4}H_{4}. The calculations were successful for both units but the optimized geometry of the BO_{4} unit was not as expected. The BS_{4} geometry takes on a principle tetrahedral geometry and the BO_{4} resembles a trigonal planar geometry. The 4coordinated boron structure continuously reverted to a trigonal planar geometry (Figures 5 and 6) with the fourth oxygen atom being stretched out from the central boron since boron prefers to be 3coordinated. In performing calculations on the BO_{4}H_{4} unit, it was assumed that the structure has a tetrahedral geometry because any other geometry would weaken the strength of the glass matrix. It is not known for sure why a substitution of sulfur for oxygen results in a tetrahedral structure, but the heavier and larger sulfur atoms are most likely the cause.
In an attempt to hold the BO_{4} structure in the tetrahedral geometry, the structure of B_{5}O_{10}H_{4} (Figure 7) was constructed. The double ring structure successfully held the unit within the tetrahedral geometry and the vibrational frequencies of this encased unit matched well with the experimental IR data as shown in Table 5.
The calculated vibrational frequency data collected from the isolated BS_{3} and BS_{4} units were compared to borate units of the same geometry. Both structures are perfectly planar with bond angles of 120^{°}. The bond lengths of the BS_{3}H_{3} structure were 1.82 Angstroms whereas bond lengths found in the BO_{3}H_{3} structure were 1.37Å. The greater bond lengths of the borosulfide structure are due to the greater repulsion between the larger sulfur atoms and the central boron atom. Since both the BO_{3} and BS_{3 }have an optimized geometry of trigonal planar, they both have similar vibrational modes. For comparison, signature vibrational modes of particular geometries are observed. For these trigonal planar structures, the umbrella motion vibrational mode occurred about 300 wavenumbers apart at 733cm^{1} for BO_{3 }and at 415cm^{1 }for BS_{3}. The difference in the locations of these modes in the IR spectrum was expected since the heavier sulfur atoms vibrate at a lower energy and lower frequency as compared to the lighter oxygen atoms which vibrate at higher energy and frequency.
The geometry optimization and vibrational frequency calculations of the B_{3}O_{3}H_{3} structural unit were completed under a RHF/6311+G(d,p) and a RHF/321G basis set. Calculations were performed under a RHF/321G basis set to compare calculated frequencies to prior research done under the same parameters. A consistent error was identified in the 321G basis set^{[4]}, but more investigation is needed to determine the error associated with the RHF/6311+G(d,p). Overall, the calculated frequencies correlated well with the computed frequencies from the previous research, and both basis sets matched well with the experimental IR frequencies.
Extending upon the previous structure of the B_{3}O_{3}H_{3}, a geometry optimization and vibrational frequency calculation was performed on a B_{3}O_{6}H_{3} structural unit where terminal oxygen atoms were added to the boron atoms of the ring. This structure is completely planar and symmetrical with bond angles of 120º. Both approximation methods worked well. The calculated vibrational frequencies outside the experimental range varied by an average of 3.78% under the RHF method and the vibrational frequencies calculated under the DFT approximations matched very well with a difference of 0.71%.
The vibrational frequencies of the B_{3}O_{6}H_{3} were compared to that of B_{3}S_{6}H_{3}. These ring structures contain one signature vibrational mode known as the breathing motion where the oxygen or sulfur atoms of the ring stretch symmetrically in and out of plane. Under the DFT method, this particular mode occurred at 804cm^{1 } for B_{3}O_{6}H_{3} and at 430cm^{1} for the B_{3}S_{6}H_{3 }unit. The other vibrational modes followed the trend with the vibrational modes of borosulfides appearing at a few hundred wavenumbers less than the borate vibrational modes. Similar to the BO_{3} and BS_{3} comparison, the vibrational modes of the borosulfide structures are expected to occur at wavenumbers lower than the vibrational borate modes due to the heavier sulfur atoms.
The final structure observed is a proposed component dithioborate in sodium borosulfide glasses^{[5]}. The calculations upon this structure were performed to determine the stability and feasibility of the structure. The geometry optimization of this unit was a success although there was not sufficient experimental data.
The dithioborate structure had very high calculation time on a regular PC. Since calculations on structures larger than dithioborate would be difficult to obtain with the present resources, dithioborate is observed to represent the best glass matrixlike structure.
Geometry optimization calculations of B_{3}O_{7}H_{4}Li structure was attempted with no success. This structure has not been documented in glass but represents a glasslike situation. Glass typically has a cation present within its structure that often acts as a modifier. In a B_{3}O_{7}H_{4} ring structure, a lithium ion was added to the center and the optimized geometry output stretched one of the bonds as seen in Figure 12. The unfavorable geometry with the presence of the Li^{+} ion is possibly due to the introduction of a new mass inside the ring where the ring was not allowed to expand. Further investigation is needed to examine if the program is accepting of the cation or if there are other factors at play.
Overall, the theoretical IR frequencies compared well to the experimental IR data with some slight variances. The slight variances observed between the calculated frequencies and the experimental data are most likely due to the fact that the calculations are done upon loose structures that are not matrixembedded. It is believed that the calculated values would reflect the experimental values more closely when the units are placed within larger structures simulating a glass matrix. However, from the calculations performed, it was noticed that the program had more difficulty obtaining accurate data for structural units containing bulkier atoms, such as sulfur rather than oxygen. This occurrence is understandable considering that the approximation methods have to take into account another molecular orbital for the sulfur atom. To observe structures containing atoms of large size would most likely not be beneficial since the complexity of the larger molecular inputs leads to larger approximations as a whole.
In the attempt to replicate experimental data through theory, more work is still needed to determine why there are some discrepancies between the different theoretical methods and the experimentally collected data.
This introductory work with theoretical calculations will hopefully open the door for observations for new glass structures. Glass consisting of different components is being produced and examined on a consistent basis by the addition of different modifiers and dopants. It is anticipated that this research can help in the prediction of glass structures with beneficial properties such as stability, strength or thermal properties.
Acknowledgments
Thanks to NSFREU program for funding research (REU 0649007), Coe College for hosting the research experience and providing guidance in the study, and the chemistry department of McKendree University for all their help.
References
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