Vibrations of CH4: Finding A1 Coordinates

[physicist888]

somone could help me to know how to find the normal vibration coordinate of the A1 representation in terms of the coordinates x,y and z of each atomes ( given: we take the carbone atome as a center of the x,y and z axis ).

 

[Rajini]

its really simple if u use some quantum mechanical software like Gaussian, Molpro, etc...but i think its not very easy to computer using hand...If u want to know pls. refer this book..
Molecular Vibrations by Wilson, Decius and Cross..this is a good book for normal mode analysis...
PS: Nowadays no one using their brain to calculate by such coordinates...Just read and understand the theory..and use computational software...its easy...For e.g., CH4 has 5*3-6=9 Normal modes.

 

[physicist888]

i know that it has 9 normal modes. I've write the normal mode representation in terms of the basis representations, and I've found it equal to A1 + E + T1 + 3T2 , that's mean that there's one mode of symetry A1, and to solve my exercise i should find the normal mode coordinate Q in terms of x,y and z as I've asked before.
the mode of symetry A1 is the stretching out of all the CH . I've calcule the projections , and I've found a result. i don't know if its right or not. and i need to be sure about my answer. i hope you could give me a hand with that.

 

[Rajini]

hi

Hi I am not very familiar.I just started working with such things...so thought of helping u with my low level of knowledge...first of all i don't understand by basis representations...But interested to learn from u..how u calculated it...if u have some time..pls reply me...
In ur case..for CH4 (Methane)..i.e., it has Td group. With normal modes A1+A2+E2+3T1+3T2. Again i don't know whether its correct or not!just check it...btw now its holydays..but if this is not so urgent...we can or i can try to make some calculation..off course with softwares...let u know...
Rajini

 

[physicist888]

man, there're now E2 in the group Td. I've did the calculation and I am sure about it.
the normal representation = A1 + E + T1 + 3T2 .
ive calcule the normal mode Q in terms of x1,y1,z1, x2,y2... which are the coordinates of the hydrogen atoms. but I am not sure about it. i just want to be sure, and i don't have a lot of time for that. so if you could give me a hand, really ill appreciate that.
and about teaching you about the calculation, no prob i will.

 

[Rajini]

hi..can u tell me in brief...what does A1, A2, symmetry means...does it same as Ag, Au..today i will try to find out normal modes for ur CH4..

 

[physicist888]

hey..im always waiting your results...hope youll reply me soon

 

[Rajini]

normal coordinates:
1 2 3
A' A" A'
Frequencies -- 1310.4290 1310.4755 1310.7241
Red. masses -- 1.1791 1.1791 1.1790
Frc consts -- 1.1930 1.1930 1.1934
IR Inten -- 11.9592 11.9658 11.9521
Atom AN X Y Z X Y Z X Y Z
1 6 0.12 -0.01 -0.00 0.00 -0.00 0.12 0.01 0.12 0.00
2 1 -0.60 0.00 0.00 -0.00 -0.00 -0.60 -0.05 0.09 -0.00
3 1 0.03 -0.17 0.00 0.00 0.00 -0.60 -0.23 -0.54 -0.00
4 1 -0.45 0.17 -0.25 -0.27 -0.19 -0.14 0.06 -0.51 -0.21
5 1 -0.45 0.17 0.25 0.27 0.19 -0.14 0.06 -0.51 0.21
4 5 6
A" A' A'
Frequencies -- 1531.2293 1531.2985 3025.1364
Red. masses -- 1.0078 1.0078 1.0078
Frc consts -- 1.3922 1.3924 5.4341
IR Inten -- 0.0000 0.0000 0.0001
Atom AN X Y Z X Y Z X Y Z
1 6 -0.00 -0.00 0.00 0.00 -0.00 -0.00 0.00 0.00 -0.00
2 1 0.00 -0.00 0.50 0.50 -0.01 -0.00 0.01 0.50 -0.00
3 1 0.00 0.00 -0.50 0.17 0.47 0.00 0.47 -0.17 -0.00
4 1 -0.28 0.41 -0.00 -0.34 -0.23 -0.29 -0.24 -0.16 0.41
5 1 0.28 -0.41 -0.00 -0.34 -0.23 0.29 -0.24 -0.16 -0.41
7 8 9
A" A' A'
Frequencies -- 3146.3090 3146.3337 3146.8136
Red. masses -- 1.1016 1.1016 1.1016
Frc consts -- 6.4249 6.4249 6.4271
IR Inten -- 20.9966 20.9909 20.9555
Atom AN X Y Z X Y Z X Y Z
1 6 0.00 0.00 0.09 0.09 0.00 -0.00 0.00 -0.09 0.00
2 1 0.00 -0.00 0.02 0.02 -0.03 -0.00 0.01 0.86 0.00
3 1 -0.00 0.00 0.02 -0.75 0.29 -0.00 -0.30 0.09 0.00
4 1 0.34 0.23 -0.57 -0.18 -0.14 0.35 0.13 0.07 -0.23
5 1 -0.34 -0.23 -0.57 -0.18 -0.14 -0.35 0.13 0.07 0.23

 

[Rajini]

the above are the normal coordinates...total 9. first 3 are A', A'' and A' and their freq. are respectively (1310.429, etc)...the coordinates for A' is 0.12 -0.01 and -0.00. Pls. try to understand it...if u want a clear file..then send me ur email...for 5 atoms with 5 diff. corredinates..
have fun

 

[physicist888]

actualy its hard to understand it like this. here you are my email, and I am connected on msn at the moment, so maybe be we could have a conversation about that. land__life@hotmail.com

 

[Rajini]

is that what u r looking for!