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Gaussian
Presented By:
Mojdeh Yousefian
Ph.D student of medicinal chemistery
1
• Computational chemistry is a branch of chemistry that uses computer
simulation to assist in solving chemical problems.
• It uses methods of theoretical chemistry, incorporated into efficient
computer programs, to calculate the structures and properties of molecules.
• The results obtained from computation are complement information obtained
by chemical experiments.
• It can be used for drug design.
• It uses of the laws of quantum mechanics, classical mechanics, or a
combination of them to solve problems.
• Chossing the right method for the calculation depends on the type and
magnitude of the case and also the type of information that is required.
Computational chemistery
2
1. Ab initio
2. Density Functional Theory (DFT)
3. Semiempirical and empirical
4. Molecular mechanics
5. Methods for solids
6. Chemical dynamics
7. Molecular dynamics
Computational Chemistery Methods
3
There are many self-sufficient software packages
used by computational chemists. Some include
many methods covering a wide range, while others
concentrating on a very specific range or even a
single method.
Software Packages
• Biomolecular modelling programs: proteins, nucleic acid.
• Molecular mechanics programs.
• Quantum chemistry and solid state physics software supporting
several methods.
• Molecular design software
• Semi-empirical programs.
• Valence bond programs
4
Why are computational chemistry methods used?
• They are simple methods.
• They are less expensive than empirical methods.
• The reactions can be performed under cetrain conditions.
• They are safe.
• They are used when there isn’t any exprimental model for
system, or If are existed but is hard to access or create the
conditions.
5
Based computing softwares
1- based on quantom mechanics 2- based on molecular mechanics
Solving the schrodinger equation Newton’s law or classical physic
For small systems For very large systems
such as particle systems e.g such as protein with 80000
electron atoms
Point: Quantom mechanics is more accurate.
6
7
8
Take into consideration the
electron density
9
10
11
12
Gaussian is a computer program for computational chemistery initially released
in 1970 by John Popel and his research group at Carnegie-Mellon University as
Gaussian 70.
13
Gaussian is capable of predicting:
• Many properties of molecules and reactions.
• Molecular energies and structures.
• Bound and reaction energies.
• IR
• NMR
• Raman
• UV
• Reaction pathways
14
• Produce results that match closely with experimenral data
• Under Windows and linux
• Quicker than numerical models
• Do not require super computers
• Molecules in their ground and excited states can be calculated
15
• Computations can be carried out on molecules in the gas
phase or in solution, Not in solids.
16
Gaussview/Gaussian principal features and a sample
building exercise and calculation
• Gaussian calculations are best prepared using the Gaussview interface.
• Gaussview allow you to build the required molecule on your screen and
using menu pull-dowms you can load the file into the Gaussian program for
execution.
• After the Gaussian run has completed you can view the completed .log file
written by Gaussian and also you can use the binary. chk file to generate
various graphical surfaces.
17
Double clicking on the desktop icon starts the program as
shown below.
The blue empty window NEW is the builder window where
the required molecule is built.
18
To build a toluene
• click on the benzene ring icon on the main window.
• Place the cursor in the builder window and click.
• A benzene ring will appear as shown below.
19
• Then click on the atom type icon in the main window 6C.
• A periodic table will appear.
Click on C and select the tetrahedral atom type.
20
Now click on a H atom of the benzene ring in the builder menu and
the Toluene molecule should be built.
21
• You now can change the molecule display properties by going to the
VIEW menu and selecting DISPLAY FORMAT.
• A variety of formats Ball and Bond, Wireframe and Tube are available.
• Choose TUBE and note change in display window. Click OK to save
this display change.
22
• Calculations using the Gaussian program are set-up and run using the
CALCULATE menu.
• Upon opening the following is displayed
This allows various types of electronic structure calculations to be
performed using Gaussian. 23
GEOMETRY OPTIMIZATION
Geometry optimization is a name for the procedure that attempts to find the configuration
of minimum energy of the molecule. The procedure calculates the wave function and the
energy at a starting geometry and then proceeds to search a new geometry of a lower
energy.
This is repeated until the lowest energy geometry is found.
FREQUENCIES AND THERMOCHEMISTRY
calculate the vibrations of the molecule in question, along with other parameters that you
can choose to include or erase from the output.
Because the molecular frequencies depend on the second derivative of the energy with
respect to the nuclear positions, you should make sure that the theoretical model you
chose for the calculation computes second derivatives Ab initio and DFT theoretical
models are known to give the best results (based on experimental values). 24
• For an example choose Energy under the JOB TYPE sub-menu.
• Note one can also choose a variety of other jobs such as
geometry optimisation or vibrational frequency analysis.
25
• Under the METHOD sub-menu we can choose the type of calculation we wish to perform.
• This can be Hartree-Fock (HF) with or without some form of electron correlation
treatment, Semiempirical, e.g PM3 or AM1 or a Density Functional Theory (DFT)
Calculations using an appropriate density functional either local, gradient corrected or
hybrid type.
26
• For HF or DFT calculations we also have the opportunity of choosing an
appropriate basis set from a sub-menu.
• For our example calculation we will choose the HF method with the STO-G
basis set.
27
• We submit our calculation using the Submit button.
• You are asked for a file name to save the job.
Choose an appropriate/instructive name e.g. toluene_hf3g. Save the file and continue
with the submission.
• A new window will open where the progress of the run can be monitored.
28
• The output data is written to 2 types of results file a .log file which is a text listing of the
program steps and a .chk file which is a binary file that can be used to generate various
surface representations.
• Choose the .log file first and the toluene molecule will appear in a new window.
29
To view the .log file go to the RESULTS menu and choose VIEW FILE.
30
A window containing the file listing should appearas a Wordpad text file. Scroll down
through the file to see the information contained.
31
Displaying Molecular Orbitals, Electron Density and Electrostatic
Potentials
• Build the p-methylphenol molecule.
• Modify the molecule such that the OH group lies in the ring plane.
• This can be done using the dihedral angle modifier shown highlighted in the figure
below:
32
• For graphical representations of orbital and electron densities the checkpoint, .chk,
• file is required.
• using the CALCULATE menu.
• we need to save a copy of the .chk or checkpoint file in our working directory.
• We do this by opening the LINK 0 menu in the set-up box and clicking the checkpoint
file box.
33
By giving the .chk file an appropriate name we can retain it in our working directory
after job runs for analysis.
34
• Use the FILE/OPEN combination to obtain this using the .chk filter.
• Open the cresol.chk file saved in your working directory.
• The molecule appears in a separate window.
• To examine the orbital energy levels and the orbital electron densities use
EDIT/Mos.
35
• An orbital energy level diagram is produced and the occupied 1-21 in this case and
unoccupied orbitals are presented.
• The HOMO is molecular orbital 21 and the LUMO is molecular orbital 22.
36
• To get an electron density surface for any orbital simply click on the orbital or
combination of orbitals and highlight them.
• This is shown for the HOMO and LUMO below.
37
Select VISUALISE followed by UPDATE from the Surface window display and
after a few seconds an electron density contour of the HOMO and LUMO orbitals
will be displayed.
38
• To display other graphical surfaces the RESULTS/SURFACES menus must be
chosen from the main Gaussview window.
• An electron density contour plot can be obtained as shown below.
39
An electron density contour plot can be obtained as shown below.
40
• After submission the electron density plot is available in the “cubes available”.
• Under Surface Actions choose new surface and the electron density plot will be
displayed in a few seconds.
41
The display is a contour of electron density at a chosen value . This can be changed to
any desired value by typing the value in the “isovalue for new surfaces” text box.
42
• The “skin-like” nature of the representation is demonstrated by introducing z-clipping.
• This is performed by right-button clicking in the display window, selecting
DISPLAY FORMAT and then in the resulting new window selecting SURFACES.
• Moving the z-clip slider enables the interior of the display to be shown as
demonstrated below.
43
• Another useful graphical display is a mapped surface.
• Here two properties can be displayed at the same time providing additional
information.
1- a total electron density surface
2- the electrostatic potential
we first calculate the total
electron density default
contour and
map the electrostatic
potential onto this surface.
44
• Harmonic vibrational frequency calculations are also set up via the CALCULATE
menu.
• It is essential to perform the vibrational analysis using the exact same method that you have used
to perform a prior geometry optimisation.
• we could perform the vibrational analysis directly so long as we use the same calculation method
i.e AM1.
• Often it is best to perform the geometry optimisation and vibrational analysis in the same run
and this can be done most conveniently using the OPT+FREQ job-type in the CALCULATE
box.
45
• Alternatively the vibrational data can be displayed from the main Gaussview window
using the RESULTS/Vibrations menu combination.
• The vibrational frequency of all three modes and the Infa Red and Raman intensities
are given.
• Each vibrational mode can be animated by highlighting the mode and clicking the START
button.
46
In addition the calculated Infra Red and Raman spectra can be calculated and
displayed by clicking on the SPECTRUM button.
47
In addition DISPLACEMENT vectors can be displayed by
highlighting the show
displacement vectors button as shown above.
48
Gaussian Input File
‫عالمت‬ ‫با‬ ‫که‬ ‫دارد‬ ‫نام‬%‫شود‬ ‫می‬ ‫شروع‬. link 0 *‫قسمت‬ ‫اولین‬
*‫لینک‬‫فایل‬ ‫نام‬ ‫و‬ ‫آدرس‬ ‫مانند‬ ‫افزاری‬ ‫سخت‬ ‫منابع‬ ‫گیری‬ ‫کار‬ ‫به‬ ‫ی‬ ‫نحوه‬ ‫که‬ ‫است‬ ‫هایی‬ ‫واژه‬ ‫کلید‬ ‫حاوی‬ ‫صفر‬
‫کنند‬ ‫می‬ ‫مشخص‬ ‫را‬ ‫غیره‬ ‫و‬ ‫یو‬ ‫پی‬ ‫سی‬ ‫هسته‬ ‫تعداد‬ ،‫شود‬ ‫استفاده‬ ‫باید‬ ‫که‬ ‫ای‬ ‫حافظه‬ ‫میزان‬ ،‫اسکرچ‬ ‫های‬.
49
*‫خط‬‫عالمت‬ ‫با‬ ‫همواره‬ ‫دستور‬#‫می‬ ‫شروع‬‫شود‬.
*‫این‬‫افزاری‬ ‫نرم‬ ‫تنظیمات‬ ‫شامل‬ ‫همچنین‬ ‫و‬ ‫دهد‬ ‫انجام‬ ‫را‬ ‫ای‬ ‫محاسبه‬ ‫نوع‬ ‫چه‬ ‫که‬ ‫گوید‬ ‫می‬ ‫افزار‬ ‫نرم‬ ‫به‬ ‫خط‬
‫مربوط‬‫است‬ ‫محاسبه‬ ‫انجام‬ ‫به‬.
*‫است‬ ‫کار‬ ‫عنوان‬ ‫بعدی‬ ‫قسمت‬.
‫است‬ ‫کار‬ ‫از‬ ‫مختصر‬ ‫توصیفی‬ ‫شامل‬ ً‫ال‬‫معمو‬ ‫کار‬ ‫یک‬ ‫عنوان‬.
*‫آخرین‬‫است‬ ‫نظر‬ ‫مورد‬ ‫مولکول‬ ‫مشخصات‬ ‫شامل‬ ‫باال‬ ‫ورودی‬ ‫در‬ ‫قسمت‬.
50
G09’s input consists of the following parts
51
The first line : specifies the path to the file you just loaded.
Section: specifies the name of the checkpoint file (.Chk)
Route Section: specifies the basis set, the theoretical model and the type of
job you want to perform
Title Section: specifies the name of the job (for the user’s ease only)
Charge, Multipl.: specifies the charge and spin multiplicity of the current
molecule separated by a space.
Molecule Specification: specifies the atoms and their coordinates 52
53
WHAT INFORMATION DO YOU GET
OUT OF THIS CALCULATION?
1. Atomic coordinates of optimized molecule
2. Optimized parameters: atomic distances and angles
3. HOMO/LUMO eigenvalues (hartree)
4. Mulliken atomic charges (short)
5. Dipole moments
6. Single Point energy
7. Harmonic frequnecies (wavenumbers)
8. Reduced masses (amu)
9. Force constants
10. IR intensities
11. Raman intensities (not default)
12. Thermochemistry
(a) Temperature
(b) Pressure
(c) Isotopes used
(d) Molecular mass
(e) Thermal energy: E (Thermal)
(f) Constant volume molar heat capacity (CV)
(g) Entropy (S)
(h) Free Energy (sum of electronic and thermal Free Energies)
(i) Enthalpy (sum of electronic and thermal Enthalpies)
54
55

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Gaussian presentation

  • 1. Gaussian Presented By: Mojdeh Yousefian Ph.D student of medicinal chemistery 1
  • 2. • Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. • It uses methods of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules. • The results obtained from computation are complement information obtained by chemical experiments. • It can be used for drug design. • It uses of the laws of quantum mechanics, classical mechanics, or a combination of them to solve problems. • Chossing the right method for the calculation depends on the type and magnitude of the case and also the type of information that is required. Computational chemistery 2
  • 3. 1. Ab initio 2. Density Functional Theory (DFT) 3. Semiempirical and empirical 4. Molecular mechanics 5. Methods for solids 6. Chemical dynamics 7. Molecular dynamics Computational Chemistery Methods 3
  • 4. There are many self-sufficient software packages used by computational chemists. Some include many methods covering a wide range, while others concentrating on a very specific range or even a single method. Software Packages • Biomolecular modelling programs: proteins, nucleic acid. • Molecular mechanics programs. • Quantum chemistry and solid state physics software supporting several methods. • Molecular design software • Semi-empirical programs. • Valence bond programs 4
  • 5. Why are computational chemistry methods used? • They are simple methods. • They are less expensive than empirical methods. • The reactions can be performed under cetrain conditions. • They are safe. • They are used when there isn’t any exprimental model for system, or If are existed but is hard to access or create the conditions. 5
  • 6. Based computing softwares 1- based on quantom mechanics 2- based on molecular mechanics Solving the schrodinger equation Newton’s law or classical physic For small systems For very large systems such as particle systems e.g such as protein with 80000 electron atoms Point: Quantom mechanics is more accurate. 6
  • 7. 7
  • 8. 8
  • 9. Take into consideration the electron density 9
  • 10. 10
  • 11. 11
  • 12. 12
  • 13. Gaussian is a computer program for computational chemistery initially released in 1970 by John Popel and his research group at Carnegie-Mellon University as Gaussian 70. 13
  • 14. Gaussian is capable of predicting: • Many properties of molecules and reactions. • Molecular energies and structures. • Bound and reaction energies. • IR • NMR • Raman • UV • Reaction pathways 14
  • 15. • Produce results that match closely with experimenral data • Under Windows and linux • Quicker than numerical models • Do not require super computers • Molecules in their ground and excited states can be calculated 15
  • 16. • Computations can be carried out on molecules in the gas phase or in solution, Not in solids. 16
  • 17. Gaussview/Gaussian principal features and a sample building exercise and calculation • Gaussian calculations are best prepared using the Gaussview interface. • Gaussview allow you to build the required molecule on your screen and using menu pull-dowms you can load the file into the Gaussian program for execution. • After the Gaussian run has completed you can view the completed .log file written by Gaussian and also you can use the binary. chk file to generate various graphical surfaces. 17
  • 18. Double clicking on the desktop icon starts the program as shown below. The blue empty window NEW is the builder window where the required molecule is built. 18
  • 19. To build a toluene • click on the benzene ring icon on the main window. • Place the cursor in the builder window and click. • A benzene ring will appear as shown below. 19
  • 20. • Then click on the atom type icon in the main window 6C. • A periodic table will appear. Click on C and select the tetrahedral atom type. 20
  • 21. Now click on a H atom of the benzene ring in the builder menu and the Toluene molecule should be built. 21
  • 22. • You now can change the molecule display properties by going to the VIEW menu and selecting DISPLAY FORMAT. • A variety of formats Ball and Bond, Wireframe and Tube are available. • Choose TUBE and note change in display window. Click OK to save this display change. 22
  • 23. • Calculations using the Gaussian program are set-up and run using the CALCULATE menu. • Upon opening the following is displayed This allows various types of electronic structure calculations to be performed using Gaussian. 23
  • 24. GEOMETRY OPTIMIZATION Geometry optimization is a name for the procedure that attempts to find the configuration of minimum energy of the molecule. The procedure calculates the wave function and the energy at a starting geometry and then proceeds to search a new geometry of a lower energy. This is repeated until the lowest energy geometry is found. FREQUENCIES AND THERMOCHEMISTRY calculate the vibrations of the molecule in question, along with other parameters that you can choose to include or erase from the output. Because the molecular frequencies depend on the second derivative of the energy with respect to the nuclear positions, you should make sure that the theoretical model you chose for the calculation computes second derivatives Ab initio and DFT theoretical models are known to give the best results (based on experimental values). 24
  • 25. • For an example choose Energy under the JOB TYPE sub-menu. • Note one can also choose a variety of other jobs such as geometry optimisation or vibrational frequency analysis. 25
  • 26. • Under the METHOD sub-menu we can choose the type of calculation we wish to perform. • This can be Hartree-Fock (HF) with or without some form of electron correlation treatment, Semiempirical, e.g PM3 or AM1 or a Density Functional Theory (DFT) Calculations using an appropriate density functional either local, gradient corrected or hybrid type. 26
  • 27. • For HF or DFT calculations we also have the opportunity of choosing an appropriate basis set from a sub-menu. • For our example calculation we will choose the HF method with the STO-G basis set. 27
  • 28. • We submit our calculation using the Submit button. • You are asked for a file name to save the job. Choose an appropriate/instructive name e.g. toluene_hf3g. Save the file and continue with the submission. • A new window will open where the progress of the run can be monitored. 28
  • 29. • The output data is written to 2 types of results file a .log file which is a text listing of the program steps and a .chk file which is a binary file that can be used to generate various surface representations. • Choose the .log file first and the toluene molecule will appear in a new window. 29
  • 30. To view the .log file go to the RESULTS menu and choose VIEW FILE. 30
  • 31. A window containing the file listing should appearas a Wordpad text file. Scroll down through the file to see the information contained. 31
  • 32. Displaying Molecular Orbitals, Electron Density and Electrostatic Potentials • Build the p-methylphenol molecule. • Modify the molecule such that the OH group lies in the ring plane. • This can be done using the dihedral angle modifier shown highlighted in the figure below: 32
  • 33. • For graphical representations of orbital and electron densities the checkpoint, .chk, • file is required. • using the CALCULATE menu. • we need to save a copy of the .chk or checkpoint file in our working directory. • We do this by opening the LINK 0 menu in the set-up box and clicking the checkpoint file box. 33
  • 34. By giving the .chk file an appropriate name we can retain it in our working directory after job runs for analysis. 34
  • 35. • Use the FILE/OPEN combination to obtain this using the .chk filter. • Open the cresol.chk file saved in your working directory. • The molecule appears in a separate window. • To examine the orbital energy levels and the orbital electron densities use EDIT/Mos. 35
  • 36. • An orbital energy level diagram is produced and the occupied 1-21 in this case and unoccupied orbitals are presented. • The HOMO is molecular orbital 21 and the LUMO is molecular orbital 22. 36
  • 37. • To get an electron density surface for any orbital simply click on the orbital or combination of orbitals and highlight them. • This is shown for the HOMO and LUMO below. 37
  • 38. Select VISUALISE followed by UPDATE from the Surface window display and after a few seconds an electron density contour of the HOMO and LUMO orbitals will be displayed. 38
  • 39. • To display other graphical surfaces the RESULTS/SURFACES menus must be chosen from the main Gaussview window. • An electron density contour plot can be obtained as shown below. 39
  • 40. An electron density contour plot can be obtained as shown below. 40
  • 41. • After submission the electron density plot is available in the “cubes available”. • Under Surface Actions choose new surface and the electron density plot will be displayed in a few seconds. 41
  • 42. The display is a contour of electron density at a chosen value . This can be changed to any desired value by typing the value in the “isovalue for new surfaces” text box. 42
  • 43. • The “skin-like” nature of the representation is demonstrated by introducing z-clipping. • This is performed by right-button clicking in the display window, selecting DISPLAY FORMAT and then in the resulting new window selecting SURFACES. • Moving the z-clip slider enables the interior of the display to be shown as demonstrated below. 43
  • 44. • Another useful graphical display is a mapped surface. • Here two properties can be displayed at the same time providing additional information. 1- a total electron density surface 2- the electrostatic potential we first calculate the total electron density default contour and map the electrostatic potential onto this surface. 44
  • 45. • Harmonic vibrational frequency calculations are also set up via the CALCULATE menu. • It is essential to perform the vibrational analysis using the exact same method that you have used to perform a prior geometry optimisation. • we could perform the vibrational analysis directly so long as we use the same calculation method i.e AM1. • Often it is best to perform the geometry optimisation and vibrational analysis in the same run and this can be done most conveniently using the OPT+FREQ job-type in the CALCULATE box. 45
  • 46. • Alternatively the vibrational data can be displayed from the main Gaussview window using the RESULTS/Vibrations menu combination. • The vibrational frequency of all three modes and the Infa Red and Raman intensities are given. • Each vibrational mode can be animated by highlighting the mode and clicking the START button. 46
  • 47. In addition the calculated Infra Red and Raman spectra can be calculated and displayed by clicking on the SPECTRUM button. 47
  • 48. In addition DISPLACEMENT vectors can be displayed by highlighting the show displacement vectors button as shown above. 48
  • 49. Gaussian Input File ‫عالمت‬ ‫با‬ ‫که‬ ‫دارد‬ ‫نام‬%‫شود‬ ‫می‬ ‫شروع‬. link 0 *‫قسمت‬ ‫اولین‬ *‫لینک‬‫فایل‬ ‫نام‬ ‫و‬ ‫آدرس‬ ‫مانند‬ ‫افزاری‬ ‫سخت‬ ‫منابع‬ ‫گیری‬ ‫کار‬ ‫به‬ ‫ی‬ ‫نحوه‬ ‫که‬ ‫است‬ ‫هایی‬ ‫واژه‬ ‫کلید‬ ‫حاوی‬ ‫صفر‬ ‫کنند‬ ‫می‬ ‫مشخص‬ ‫را‬ ‫غیره‬ ‫و‬ ‫یو‬ ‫پی‬ ‫سی‬ ‫هسته‬ ‫تعداد‬ ،‫شود‬ ‫استفاده‬ ‫باید‬ ‫که‬ ‫ای‬ ‫حافظه‬ ‫میزان‬ ،‫اسکرچ‬ ‫های‬. 49
  • 50. *‫خط‬‫عالمت‬ ‫با‬ ‫همواره‬ ‫دستور‬#‫می‬ ‫شروع‬‫شود‬. *‫این‬‫افزاری‬ ‫نرم‬ ‫تنظیمات‬ ‫شامل‬ ‫همچنین‬ ‫و‬ ‫دهد‬ ‫انجام‬ ‫را‬ ‫ای‬ ‫محاسبه‬ ‫نوع‬ ‫چه‬ ‫که‬ ‫گوید‬ ‫می‬ ‫افزار‬ ‫نرم‬ ‫به‬ ‫خط‬ ‫مربوط‬‫است‬ ‫محاسبه‬ ‫انجام‬ ‫به‬. *‫است‬ ‫کار‬ ‫عنوان‬ ‫بعدی‬ ‫قسمت‬. ‫است‬ ‫کار‬ ‫از‬ ‫مختصر‬ ‫توصیفی‬ ‫شامل‬ ً‫ال‬‫معمو‬ ‫کار‬ ‫یک‬ ‫عنوان‬. *‫آخرین‬‫است‬ ‫نظر‬ ‫مورد‬ ‫مولکول‬ ‫مشخصات‬ ‫شامل‬ ‫باال‬ ‫ورودی‬ ‫در‬ ‫قسمت‬. 50
  • 51. G09’s input consists of the following parts 51
  • 52. The first line : specifies the path to the file you just loaded. Section: specifies the name of the checkpoint file (.Chk) Route Section: specifies the basis set, the theoretical model and the type of job you want to perform Title Section: specifies the name of the job (for the user’s ease only) Charge, Multipl.: specifies the charge and spin multiplicity of the current molecule separated by a space. Molecule Specification: specifies the atoms and their coordinates 52
  • 53. 53
  • 54. WHAT INFORMATION DO YOU GET OUT OF THIS CALCULATION? 1. Atomic coordinates of optimized molecule 2. Optimized parameters: atomic distances and angles 3. HOMO/LUMO eigenvalues (hartree) 4. Mulliken atomic charges (short) 5. Dipole moments 6. Single Point energy 7. Harmonic frequnecies (wavenumbers) 8. Reduced masses (amu) 9. Force constants 10. IR intensities 11. Raman intensities (not default) 12. Thermochemistry (a) Temperature (b) Pressure (c) Isotopes used (d) Molecular mass (e) Thermal energy: E (Thermal) (f) Constant volume molar heat capacity (CV) (g) Entropy (S) (h) Free Energy (sum of electronic and thermal Free Energies) (i) Enthalpy (sum of electronic and thermal Enthalpies) 54
  • 55. 55