Rep:Mod:Seagull

Structure comparison: BH₃, GaBr₃ and BBr₃

BH₃

The input of the computation was a distorted borane molecule: bond lenghts were set to 1.53000, 1.54000 and 1.55000 Angstrom. The bond angles were left at 120.000 degree.

First optimization

The molecule shape was optimized using B3LYP DFT method using the basis set 3-21G.

The energy converged to a minimum, which can be seen in the "Item" table of the output file:

 Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
-- Stationary point found.

Summary table:

BH3 optimization
File Name = SB_BH3_OPT
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 3-21G
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.46226429 a.u.
RMS Gradient Norm = 0.00008851 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 49.0 seconds.

As can be seen above, the energy of the optimized molecule is ca. -26.462 a.u.

Bond lengths and angles:

----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1947 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1948 -DE/DX = -0.0002 !
! R3 R(1,4) 1.1944 -DE/DX = -0.0001 !
! A1 A(2,1,3) 120.0157 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9983 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.986 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

Second optimization

Using the output of the first optimization as an input, the next B3LYP optimization was set, this time using 6-31G(d,p) basis set.

Output file: https://wiki.ch.ic.ac.uk/wiki/images/5/5e/SB_BH3_OPT_2.LOG

The energy converged, as seen in the "Item" table:

Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000039 0.000300 YES
Maximum Displacement 0.000354 0.001800 YES
RMS Displacement 0.000213 0.001200 YES
Predicted change in Energy=-3.185650D-08
Optimization completed.
-- Stationary point found.

Summary table:

BH3 optimization 2
File Name = SB_BH3_OPT_2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532357 a.u.
RMS Gradient Norm = 0.00004443 a.u.
Imaginary Freq =
Dipole Moment = 0.0006 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 35.0 seconds.

Energy: ca. -26.615 a.u.

Bond lengths and angles:

----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1922 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1924 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0491 -DE/DX = -0.0001 !
! A2 A(2,1,4) 119.9957 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9552 -DE/DX = 0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

GaBr₃

The input of the computation was gallium tribromide molecule with all bond lengths 2.39000 angstrom and bond angles 120.000 degree. The symmetry was restricted to D_3h. The molecule was optimized using B3LYP DFT method with LanL2DZ basis set.

Output files, available on D-Space: http://hdl.handle.net/10042/26087

"Item" table:

Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282685D-12
Optimization completed.
-- Stationary point found.

Summary table:

GaBr3 optimization
File Name = SB_GaBr3_opt
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000016 a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 28.0 seconds.

Bond lengths and angles:

 ----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3502 -DE/DX = 0.0 !
! R2 R(1,3) 2.3502 -DE/DX = 0.0 !
! R3 R(1,4) 2.3502 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

The Ga-Br bond lengths (R1 to R3 in the table, 2.35 angstrom) are around 4.5% larger than the bond lengths in gaseous GaBr₃ determined by electron diffraction (2.249 angstrom)^[1].

BBr₃

The input of the computation was a boron bromide molecule with all bond lengths equal to 2.02000 angstrom and bond angles the same as for the borane molecule after the second optimization. The molecule was optimized using B3LYP DFT method with basis set 6-31G(d,p) for boron atom and LanL2DZ for each bromine atom.

Output files, posted on D-space: http://hdl.handle.net/10042/26091

"Item" table:

Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.000127 0.001800 YES
RMS Displacement 0.000084 0.001200 YES
Predicted change in Energy=-4.254289D-09
Optimization completed.
-- Stationary point found.

Summary table:

BBr3 optimization
File Name = SB_BBr3_opt
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -64.43645434 a.u.
RMS Gradient Norm = 0.00001440 a.u.
Imaginary Freq =
Dipole Moment = 0.0008 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 35.4 seconds.

Bond lengths and angles:

 ----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9339 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0108 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9978 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9914 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

Bond length comparison


compound	computed bond length [Å]	measured bond length [Å]^[1]
BH₃	1.192	1.190
BBr₃	1.934	1.893
GaBr₃	2.350	2.249

Knowing that the uncertainty of computed bond distances is ca. 0.01 A, we can say that for BH₃ and BBr₃ the computed values agree well with the experimental values. As stated above, the computed Ga-Br bond length is ca. 4.5 % larger than the experimental value. This can be caused by using a pseudopotential (LanLDZ) everywhere in the computation instead of the 6-31G(d,p) basis set.

BBr₃ vs BH₃

Bromine is an element with much different properties than hydrogen. In this case, they are both bonded to boron by a single covalent bond, however this bond is more polarized towards the "outer" atoms in BBr₃ (the electronegativity difference is 0.16 and 0.76 for BH₃ and BBr₃ respectively on the Pauling scale). The bromine atoms also differ by having 3 lone pairs. The bond lengths in BH₃ are slightly larger than the sum of covalent radii of H and B (1.15 A), while the bond lengths in BBr₃ are slightly smaller than the sum of the respective covalent radii (2.04 A). This can be interpreted in terms of donation of the electron density from Br lone pairs to the empty p orbital of the B atom and lack of such donation in BH₃.

BBr₃ vs GaBr₃

Boron and gallium are in the same group (13) and in their tribromides they both have an empty p orbital available to accept electron density from bromine atoms. Gallium is less electronegative than boron (1.81 vs. 2.04 on the Pauling scale), so the bonds in GaBr₃ are more polarized towards bromine. The experimental bond length in BBr₃ is 7.2% smaller than the sum of respective covalent radii (2.04 A) while the experimental bond length in GaBr₃ is 7.8% smaller than the sum of respective covalent radii (2.44 A). The slightly larger difference for GaBr₃ can be attributed to the larger polarity of the bond - the bond is less covalent and more ionic.

Displaying bonds in Gaussview

In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why? What is a bond?

IUPAC Gold Book^[2] defines (or rather: explains the concept of) a chemical bond in the following way:

chemical bond

When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds.

Gaussview software displays a bond between atoms if the distance between them is below certain value. However, at that distance the orbital overlap doesn't suddenly disappear and the energy of the system is still lower comparing to isolated atoms. Orbitals of correct symmetry will overlap regardless of the distance, but the energy of this interaction will be smaller at larger distances (it asymptotically tends to zero) and at some distance the interaction energy will be so small that we can neglect it. Because of this, one can't strictly say if bond at a certain distance still exists or already doesn't.

Frequency analysis of BH₃ and GaBr₃

BH₃

Borane molecule (input: bond lengths: 1.18000 A, bond angles: 120.000 degree, symmetry group restricted to D3h) was first optimized using B3LYP DFT method with 6-31G(d,p) basis set.

"Item" table:

 Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.008834D-10
Optimization completed.
-- Stationary point found.

Summary table:

BH3 optimization for frequency analysis (starting with pre-made BH3, symmetry restricted to D3h)
File Name = SB_BH3_OPT_3
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = 0.00000296 a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 1 minutes 1.0 seconds.

Bond lengths and angles:

 ----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------

The optimized molecule was then used for vibrational frequency analysis.

Output file:

https://wiki.ch.ic.ac.uk/wiki/images/4/45/SB_BH3_FREQ_2.LOG

Mass-weighted force constants:

Full mass-weighted force constant matrix:
Low frequencies --- -0.9431 -0.8608 -0.0055 5.7478 11.7258 11.7637
Low frequencies --- 1162.9963 1213.1826 1213.1853

Vibrational modes:


mode no.	form	wavenumber [cm^-1]	intensity [a.u.]	symmetry (D_3h point group)
1	The hydrogen atoms oscillate simultaneously perpendicular to the plane of the molecule. The boron atom oscillates in the same way, but with smaller amplitude and in opposite direction.	1163	93	A2"
2	Two hydrogen atoms oscillate at the same angle to the third bond (scissorring). The remaining two atoms vibrate with small amplitude in the opposite direction. All motions are in the plane of the molecule.	1213	14	E'
3	One hydrogen atom vibrates "sideways", while the remaining three atoms simultaneously rotate in the opposite direction. All motions are in one plane.	1213	14	E'
4	All three hydrogen atoms oscillate along the bonds in the plane of the molecule while boron remains stationary.	2582	0	A1'
5	Two hydrogen atoms oscillate along their bonds simultaneously to/away and from/away boron. Boron atom vibrates opposite to them. All motions within the plane of the molecule.	2715	126	E'
6	Two hydrogen atoms vibrate along the bods simultaneously to/to and away/away from the boron atom. At the same time, the third hydrogen oscillates in the reverse direction along its bond.	2715	126	E'

Computed IR spectrum:

There are only 3 peaks observed (rather than 6) because:

a) modes 2 and 3 have wavenumbers so close that they appear as one peak

b) vibrational mode 4 is not associated with change of the dipole moment of the molecule (the dipole moment is zero all the time during the vibration), hence it is not excited by IR radiation. In other words, the transition is forbidden by the selection rule saying that the dipole moment must change during the vibration.

c) modes 5 and 6 have virtually the same wavenumbers, so they appear as one peak

GaBr₃ and comparison with BBr₃

The optimized molecule of GaBr₃ (using B3LYP DFT and LanLDZ basis set - see above) was used as an input for vibrational frequency analysis.

Output files, posted on DSpace: http://hdl.handle.net/10042/26124

Mass-weighted force constants:

Full mass-weighted force constant matrix:
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982

computed IR spectrum:

Vibration modes, compared to the corresponding modes of BH₃:


mode no.	form	wavenumber [cm^-1]	intensity [a.u.]	wavenumber [cm^-1]	intensity [a.u.]	symmetry (D_3h point group)
		BH₃		GaBr₃
1	The H/Br atoms oscillate simultaneously perpendicular to the plane of the molecule. The central atom oscillates in the same way in opposite direction.	1163	93	100	9	A2"
2	Two H/Br atoms oscillate at the same angle to the third bond (scissoring). The remaining two atoms vibrate in the opposite direction. All motions are in the plane of the molecule.	1213	14	76	3	E'
3	One H/Br atom vibrates "sideways", while the remaining three atoms simultaneously rotate in the opposite direction. All motions are in one plane.	1213	14	76	3	E'
4	All three H/Br atoms oscillate along the bonds in the plane of the molecule while central atom remains stationary.	2582	0	197	0	A1'
5	Two H/Br atoms oscillate along their bonds simultaneously to/away and from/away boron. Central atom vibrates opposite to them. All motions within the plane of the molecule.	2715	126	316	57	E'
6	Two H/Br atoms vibrate along the bods simultaneously to/to and away/away from the central atom. At the same time, the third H/Br atom oscillates in the reverse direction along its bond.	2715	126	316	57	E'

Both molecules, being made of 4 atoms have 6 vibrational modes (in general: non-linear, n-atomic molecule has 3n-6 modes). Because of the same symmetry of both molecules, the type of modes (symmetry labels) are identical. In both spectra, modes 1 - 3 have lower energy than modes 4 - 6. This is predictible, since modes 1-3 involve mainly bond bending while modes 4-6 involve mainly bond stretching. However, there are two important differences in the vibrations of these two species:

a) The wavenumbers are much smaller for GaBr₃. The energy of a vibrational mode in a polyatomic molecule is given by a series of energy terms having ientical form to the energy of a (quantum) harmonic oscillator^[3]. The energy (given as wavenumber) of transition for harmonic oscillator is:

$ν = \frac{1}{2 π c} \sqrt{\frac{k}{m}}$

In case of polyatomic molecule^[3], k is the "effective" force constant of given mode - it's influenced by strength of bonds oscillating in that mode. In the same fashion, m is the "effective" mass in the mode, a quantity influenced by the masses of atoms oscillating in that mode. In our case, the masses of all atoms were increased very much, so there is no surprize that all transition wavenumbers are much smaller.

b) Modes 1 and 3 are ordered in the opposite way - in GaBr₃ mode 1 is no longer the lowest energy transition. This is can be interpreted in terms of simple comparison of atomic radii - gallium atom (covalent radius: 122 A) is not much larger than boron atom (84 A) but bromine atoms (120 A) are much larger than hydrogen atoms (31 A). In mode 1, all three H/Br atoms are simultaneously getting close to each other, so for larger Br atoms the effective force constant (k in the above equation) associated with this mode will be much larger.

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?

Because for different basis sets, the energy minimum will be at different positions of the atoms.

What is the purpose of carrying out a frequency analysis?

There are at least two important purposes:

a) We want to verify that the structure of a molecule is indeed optimized. If it is optimized, position of all atoms corresponds to an energy minimum and therefore force constants associated with all modes will be positive.

b) We want to simulate the vibrational (IR or Raman) spectrum of a compound.

What do the "Low frequencies" represent?

They correspond to the motions of the center of mass of the molecule. In any normal mode, the center of mass doesn't move, so in a good simulation, the values of these "low frequencies" will be close to zero.

Molecular orbitals of BH₃

Optimized borane molecule (the same as used for the frequency analysis, see above) was used for energy computation (using B3LYP DFT method, 6-31G(d,p) basis set) in order to plot molecular orbitals.

Output files:

Checkpoint file: https://wiki.ch.ic.ac.uk/wiki/images/4/48/SB_BH3_MO_2.chk

Log file: https://wiki.ch.ic.ac.uk/wiki/images/1/18/SB_BH3_MO_2.LOG

The computed MO boundary surfaces can be compared with graphical representations of orbitals predicted by of group theory:

There is a very good agreement between the predictions and computed boundary surfaces - all the major features (shape of the orbitals, position and orientation of the nodal planes) agree. The size of the boundary surfaces is arbitrary, because they are plotted as a set of points with some fixed electron probability density (the ones shown above were plotted for density set to 0.02).

NBO analysis of NH₃

Ammonia molecule was first optimized with B3LYP DFT method (basis set 6-13G(d,p), "nosymm" keyword). The input molecule had all bond lengths of 1.00000 A and bond angles 109.471 A.

Output file:

https://wiki.ch.ic.ac.uk/wiki/images/6/61/SB_NH3_OPT.LOG

"Item" table:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000024     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000079     0.001800     YES
 RMS     Displacement     0.000053     0.001200     YES
 Predicted change in Energy=-1.629717D-09
 Optimization completed.
    -- Stationary point found.

Summary table:

NH3 optimization
File Name = SB_NH3_OPT
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = 0.00000885 a.u.
Imaginary Freq = 
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time:       0 days  0 hours  0 minutes 49.0 seconds.

The optimized molecule was then used in frequency analysis to confirm that energy minimum was achieved.

Output file: https://wiki.ch.ic.ac.uk/wiki/images/d/db/SB_NH3_FREQ.LOG

Mass-weighted force constants:

Full mass-weighted force constant matrix:
 Low frequencies ---  -30.7764   -0.0011   -0.0006    0.0013   20.3142   28.2484
 Low frequencies --- 1089.5557 1694.1237 1694.1868

Vibration wavenumbers obtained: 1090, 1694, 1694, 3461, 3589, 3590 cm^-1. Therefore, the molecule shape is optimized (there are no negative numbers).

The optimized ammonia molecule was then used for energy computation (using B3LYP DFT method, 6-31G(d,p) basis set) for natural bond orbitals (NBO) analysis.

Output files: Checkpoint file: https://wiki.ch.ic.ac.uk/wiki/images/e/e9/SB_NH3_MO.chk Log file: https://wiki.ch.ic.ac.uk/wiki/images/3/3e/SB_NH3_MO.LOG

Charge distribution visualization (color range: bright red: -1.125, bright green: 1.125):

The calculated charge is -1.125 on nitrogen atom and 0.375 on each hydrogen atom.

Reaction energy of NH₃BH₃ formation

In order to calculate the reaction energy of association of ammonia and borane to form NH₃BH₃, a molecule of NH₃BH₃ was optimized using B3LYP DFT method with 6-31G(d,p) basis set.

Output file:

https://wiki.ch.ic.ac.uk/wiki/images/f/f8/SB_NH3BH3_OPT.LOG

"Item" table:

Item               Value     Threshold  Converged?
 Maximum Force            0.000139     0.000450     YES
 RMS     Force            0.000063     0.000300     YES
 Maximum Displacement     0.000771     0.001800     YES
 RMS     Displacement     0.000338     0.001200     YES
 Predicted change in Energy=-2.028054D-07
 Optimization completed.
    -- Stationary point found.

Summary table:

NH3BH3 optimization
File Name = SB_NH3BH3_OPT
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22469007 a.u.
RMS Gradient Norm = 0.00006839 a.u.
Imaginary Freq = 
Dipole Moment = 5.5653 Debye
Point Group = C1
Job cpu time:       0 days  0 hours  1 minutes 50.0 seconds.

The optimized molecule was then used in frequency analysis to confirm that energy minimum was achieved.

Output file:

https://wiki.ch.ic.ac.uk/wiki/images/5/5e/SB_NH3BH3_FREQ.LOG

Mass-weighted force constants:

 Full mass-weighted force constant matrix:
 Low frequencies ---   -0.0011   -0.0008    0.0003   19.0327   23.6880   42.9723
 Low frequencies ---  266.5858  632.3792  639.4620

Vibration wavenumbers obtained: 267, 632, 639, 640, 1069, 1197, 1204, 1204, 1330, 1676, 1676, 2470, 2530, 2530, 3462, 3579, 3579 cm^-1. All numbers are positive, so energy minimum is achieved.

From the energy values of the optimized NH₃, BH₃ and NH₃BH₃ molecules it is possible to obtain the energy of association of NH₃ and BH₃:

$Δ E = E_{N H 3 B H 3} - (E_{N H 3} + E_{B H 3})$

$E_{N H 3 B H 3} = - 83.22469007 a . u .$

$E_{N H 3} = - 56.55776856 a . u .$ (value obtained from the optimization for the NBO analysis above)

$E_{B H 3} = - 26.61532357 a . u .$ (value obtained from the second optimization for the structure comparison)

$Δ E = - 0.051576877 a . u . \approx - 135 k J / m o l$

References

↑ ^1.0 ^1.1 CRC Handbook of Chemistry and Physics, CRC Press, 93rd edn., 2012, pp. 9-19
↑ DOI:10.1351/goldbook.CT07009
↑ ^3.0 ^3.1 P. W. Atkins and J. de Paula, in Atkin’s Physical Chemistry, Oxford University Press, 10th edn., 2010, pp. 471 – 427.

[HCP_bonds-1] 1.0 ^1.1 CRC Handbook of Chemistry and Physics, CRC Press, 93rd edn., 2012, pp. 9-19

[Goldbook_bond-2] DOI:10.1351/goldbook.CT07009

[Atkins_p472-3] 3.0 ^3.1 P. W. Atkins and J. de Paula, in Atkin’s Physical Chemistry, Oxford University Press, 10th edn., 2010, pp. 471 – 427.

[1]

[2]

[3]

Structure comparison: BH3, GaBr3 and BBr3

BH3

First optimization

Second optimization

GaBr3

BBr3

Bond length comparison

BBr3 vs BH3

BBr3 vs GaBr3

Displaying bonds in Gaussview

In some structures Gaussview does not draw in the bonds where we expect, does this mean there is no bond? Why? What is a bond?

Frequency analysis of BH3 and GaBr3

BH3

GaBr3 and comparison with BBr3

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?

What is the purpose of carrying out a frequency analysis?

What do the "Low frequencies" represent?

Molecular orbitals of BH3

NBO analysis of NH3

Reaction energy of NH3BH3 formation

References

Structure comparison: BH₃, GaBr₃ and BBr₃

BH₃

GaBr₃

BBr₃

BBr₃ vs BH₃

BBr₃ vs GaBr₃

Frequency analysis of BH₃ and GaBr₃

BH₃

GaBr₃ and comparison with BBr₃

Molecular orbitals of BH₃

NBO analysis of NH₃

Reaction energy of NH₃BH₃ formation