The document discusses frequency calculations in Gaussian09 which can (1) predict IR and Raman spectra by calculating vibrational frequencies and intensities, (2) compute force constants for geometry optimizations, (3) identify the nature of stationary points on a potential energy surface by analyzing imaginary frequencies, and (4) compute zero-point vibrational energy and thermal corrections. It then provides examples of frequency calculations on files modeling the reaction of benzene and hydrogen, reporting frequencies, intensities, force constants, identification of stationary points, and thermal corrections. While two of the files could not be fully optimized, the optimized file for benzene and hydrogen was found to have the lowest summed electronic and zero-point energy, no imaginary frequencies, and is thus a

1. Frequency CaIculations
Presented by
Nguyen Duy The

2. Introduction
 Running frequency calculations using Gaussian09, frequency
calculations can serve a number of different purposes:
 To predict the IR and Raman spectra of molecules (frequencies and
intensities). (Content 1)
 To compute force constants for a geometry optimization. (Content 2)
 To identify the nature of stationary points on the potential energy
surface. (Content 3)
 To compute zero-point vibration and thermal energy corrections to
total energies as well as other thermodynamic quantities of interest
such and the enthalpy and entropy of the system (Content 4)

3. Object: Benzen + Hydro ( C6H6 + H2)
• Files 1(F1) : th1benzen.cml + Benzen1.com + Benzen1.log
▫ F1.1: file structure after optimizating by Avogadro.
▫ F1.2: Input file for gaussian09
▫ F1.3: file log after running
• Files 2(F2): th2benzen.cml + Benzen2.com + Benzen2.log
• Files 3(F3): th3benzen.cml + Benzen3.com + Benzen3.log
Link: https://github.com/nguyenthe123/BTMaterialsScience

4. Object: File .cml of C6H6 + H2
F1.1 F2.1 F3.1

5. Chú ý: Các file .com tương ứng F2.1, F3.1 đều không thể
opt trên Gaussian09 do đó chỉ thực hiện được với file
F1.1.

6. Object: File .com of C6H6 + H2
# RHF/6-31G(d) Freq Pop=full Opt
Benzen Hydro 1
0 1
C 1.2016810000 0.3925400000 -0.0654360000
C 0.3261360000 0.5145560000 -1.7171510000
C -1.5466010000 0.5931780000 -1.7782590000
C -2.5348880000 0.5494680000 -0.1884670000
C -1.6557910000 0.4277120000 1.4555860000
C 0.2085270000 0.3493880000 1.5174730000
H -0.6431300000 1.0452900000 -0.1023190000
H -0.6893590000 -0.1027310000 -0.1626210000
H 2.2809920000 0.3465040000 -0.0164380000
H 0.9048330000 0.5393040000 -2.6319480000
H -2.0625750000 0.6638000000 -2.7271990000
H -3.6145720000 0.5941180000 -0.2107910000
H -2.2241290000 0.4023970000 2.3732440000
H 0.7087820000 0.2791060000 2.4720000000

7. Content 1: Frequencies and intensities
Spectral line 1 2 3 4 5 6 7 8 9 10 11
Frequencies
(Hz)
198.871
5
332.665
5
518.59
89
558.85
46
609.46
52
745.35
44
836.65
33
865.761
5
908.54
88
997.21
48
1019.
8460
IR Int (cm^-1) 0.2629 0.5802 5.0308 0.0606 0.2734 59.809
1
21.630
3
1.2090 0.4553 5.2517 0.596
3
Spectral line 12 13 14 15 16 17 18 19 20 21 22
Frequencies 1081.74
02
1105.88
42
1110.6
029
1143.
4718
1159.9
245
1277.5
267
1304.
9732
1307.502
0
1387.3
516
1484.8
350
1508.3
326
IR Int 6.2349 0.1908 0.6175 0.140
3
2.5474 0.0026 1.891
4
4.9045 5.2512 0.6725 2.7036

8. Content 1: Frequencies and intensities
Spectral line 23 24 25 26 27 28 29 30 31 32 33
Frequencies 1541.2
218
1570.77
33
1621.76
40
1636.8
527
1828.36
36
1880.0
548
3164.4
235
3171.75
93
3237.09
54
3238.26
90
3341.5
353
IR Int 1.9241 0.7326 0.9334 0.5977 2.1806 0.6317 17.047
4
70.0087 58.7152 2.8076 0.9271
Spectral line 34 35 36
Frequencies 3349.0890 3366.1518 3376.865
1
IR Int 9.7631 69.4005 26.2481

9. Content 1: Frequencies and intensities

10. Content 2: Force constant
Spectral line 1 2 3 4 5 6 7 8 9 10 11
Force
constant
0.0416 0.1462 0.4564 0.3847 1.2006 0.4234 0.6445 0.6917 1.4794 1.3349 1.677
9
Spectral line 12 13 14 15 16 17 18 19 20 21 22
Force
constant
1.8313 0.9113 1.0380 1.400
6
1.4663 0.9950 1.1320 1.1336 1.3443 1.6563 2.1752
Spectral line 23 24 25 26 27 28 29 30 31 32 33
Force
constant
2.1923 2.3991 1.6842 1.7523 14.331
9
11.300
6
6.3553 6.3256 6.7125 6.7778 7.1392
Spectral line 34 35 36
Force
constant
7.1857 7.3377 7.3909

11. Content 2: Force constant

12. Content 3: Stationary Points
• There are two pieces of information from the output which are critical
to characterizing a stationary point:
 The number of imaginary frequencies.
 The normal mode corresponding to the imaginary frequency.
lmanginary Frequencies are listed in the output of a frequency calculation
as negative numbers. By definition, a structure which has n imaginary
frequencies is an nth order saddle point

13. Content 3: Stationary Points
From: Exploring Chemistry with Electronic Structure Methods - James B. Foresman
Aleen Frisch

14. Content 3: Stationary Points
F1.3 F2.3 F3.3
The number of imaginary
frequencies
0

15. Content 4: The Zero-point and Thermal Energy-corrected
The zero-point energy is a correction to the electronic energy of the molecule or hamal mayy cdon. to account for
the effects of molecular vibrations which persist even at 0 K.
From: Exploring Chemistry with Electronic Structure Methods - James B. Foresman
Aleen Frisch

16. F1.3 F2.3 F3.3
Zero-point vibrational energy 345650.2 (Joules/Mol)
82.61238 (Kcal/Mol)
238397.0 (Joules/Mol)
56.97825 (Kcal/Mol)
237582.3 (Joules/Mol)
56.78352 (Kcal/Mol)
Zero-point correction 0.131651 (Hartree/Particle) 0.090801 (Hartree/Particle) 0.090490 (Hartree/Particle)
Thermal correction to Energy 0.136509 0.097207 0.096498
Thermal correction to Enthalpy 0.137454 0.098151 0.097443
Thermal correction to Gibbs Free
Energy
0.103571 0.061294 0.061095
(E0) Sum of electronic and zero-point
Energies
-231.700246 -193.443437 -230.767603
(E) Sum of electronic and thermal
Energies
-231.695388 -193.437031 -230.761595
(H) Sum of electronic and thermal
Enthalpies
-231.694444 -193.436087 -230.760651
(G) Sum of electronic and thermal
Free Energies
-231.728327 -193.472944 -230.796998
Content 4: The Zero-point and Thermal Energy-corrected

17. Nhận xét: Mặc dù không thể opt 2 file F2 và F3 xong có
thể tạm nhận xét năng lượng E0 của F1 là bé hơn so với
trường hợp E0 khi chưa opt. Và số điểm ảo của tần số
cũng không có => Minimum => Có xu hướng về cấu trúc
này trong tự nhiên.

18. Frequency CaIculations
Presented by
Nguyen Duy The