[molpro-user] symmetry irreducible representation!

[Peter Knowles]

The spherical harmonic angular functions that are used are the plus and
imaginary minus combinations of Lz-quantized spherical harmonics, in
order to have real functions .. hence the notation d2+ d2- etc. Yes, one
should really write p0, p1+, p1- but everybody knows these as z, x and y
which is why they are printed that way.

Your second point seems to involve atoms not contained in the xy plane,
which can certainly generate combinations of px or py orbitals that are
A". I do not see the problem.

Peter

Wang Mingwei wrote:
> hello everyone,
> 
> In the molpro output, I find such interesting results. For example, when p-
> orbitals of one atom are referred, the px,py,pz symbols are used; but 
> conerning to the d-orbitals d0,d2+,d2-,d1+,d1- occur. I think these are two 
> different sets symbols. Why are they used at the same time?
> 
> Secondly, according to user's manual version 2002.6, under Cs symmetry 
> conditions z orbital belongs to A'' irreducible representation of Cs and 
> s,x,y to A'. But in my output, such following results are got:
> 
>  55.1 A'   10  2px           2.129386     0.010588
>             11  2px           0.594093     0.595167
>                               0.232524     0.462001
>   56.1 A'   10  2py           2.129386     0.010588
>             11  2py           0.594093     0.595167
>                               0.232524     0.462001
>   57.1 A'   10  2pz           2.129386     0.010588
>             11 -2pz           0.594093     0.595167
>                               0.232524     0.462001
>    1.2 A"    1  1s            0.356000    -0.291975
>              2 -1s            0.087200     0.553792
>                               0.031400     0.635339
>    2.2 A"    1  2pz           0.053000     0.700759
>              2  2pz           0.016000     0.389447
>    3.2 A"    1  2px           0.053000     0.700759
>              2 -2px           0.016000     0.389447
>    4.2 A"    1  2py           0.053000     0.700759
>              2 -2py           0.016000     0.389447
>    5.2 A"    1  3d1+         20.210000     0.029018
>              2  3d1+  
> 
> the input file:
>  memory,100,m
>  gprint,orbital,basis
>  geomtyp=xyz
>  geometry={
>  z;
>  11
>  This is geometry input for Ti2Cl9 with an xyz file
>  Ti,0.0000,0.0000,-1.6082
>  Ti,0.0000,0.0000,1.6082
>  Cl,0.0000,1.9044,0.0000
>  Cl,1.6492,-0.9522,0.0000
>  Cl,-1.6492,-0.9522,0.0000
>  Cl,0.0000,-2.0459,-2.7907
>  Cl,-1.7719,1.0229,-2.7907
>  Cl,1.7719,1.0229,-2.7907
>  Cl,-1.7719,1.0229,2.7907
>  Cl,0.0000,-2.0459,2.7907
>  Cl,1.7719,1.0229,2.7907
>  }
>   
>  basis
>  Ti=ecp1
>  Cl=STO-3G
>  end
> 
> hf;
> 
> Thanks a lot!
> ***********************
> Mingwei Wang
> College of Chemistry and Molecular Engineering
> Peking University
> Beijing, P. R. China
> ***********************
> mingwei at hpsv.pku.edu.cn
>