[molpro-user] Is it a bug about LZZ expection ?

[Peter Knowles]

This is no bug, but just a consequence of the form of the angular momentum operators.  Try the following input:

basis,cc-pV5Z(s)
geometry={
He,-1,0,0,0
He,-1,0,0,3
H,-1,0,10000,10000
}
rhf
{mcscf;expec2,lxx,lyy,lzz}
table,lxlx,lyly,lzlz

and see the results (2/3,1/3,1/3)*10^8.  It all comes from the distant H atom; the angular momentum operator is Lz=i(yd/dx-xd/dy) and this will be dominated by yd/dx at this geometry. Thus L_z^2 is approximately -y^2 d^2/dx^2. For the hydrogen atom, the expectation of d^2/dx^2 is exactly -1/3.

Peter

On 16 Jul 2013, at 03:42, mingkai <fumingkai at iccas.ac.cn> wrote:

> Dear molpro users,
>      Recently,our lab focuses on the renner-teller effect on CH2. Holding Cs geometry，C-H1 being 2 bohr , C-H2 being 16 Bohr, we just change the angle of HCH.  The C-H2 is so long that we think that taking CH2 as linear CH1 and atomic H2 is ok. The LZZ result of the lowest three states when the angle is 180 lists as follows.
> 
>    LZZ1                   LZZ2                  LZZ3    
>  1.00000000    4.00000000   2.59868127D-10 
>   It refers to Π， Δ，Σ respectively. For CH2 is so long that we think just changing HCH will not cause huge different of LZZ. However 
> it seems that the LZZ becomes extremely  large when the angle nears 90.
>      HCH        LZZ1              LZZ2                LZZ3                        
>     180    1.00000000       4.00000000     2.59868127D-10      
>     170    3.57222517       6.57222516     2.57222517D+00   
>     160   10.97873819      13.97873817   9.97873819D+00    
>     150    22.32615781     25.32615778   2.13261578D+01    
>     140    36.24574583     39.24574579   3.52457459D+01     
>     130    51.05850592     54.05850591   5.00585061D+01     
>    
>     110    76.32441184     79.32441192   7.53244121D+01     
> 
>     90      86.30120183     89.30120200   8.53012023D+01     
> 
>     80     83.72797802     86.72797820    8.27279784D+01     
>   
>     60     64.97312513     67.97312525    6.39731254D+01     
> 
>     40     36.24176110     39.24176110    3.52417612D+01    
> 
>     20    10.97738207     13.97738204     9.97738205D+00     
> 
>     10    3.57190386       6.57190385       2.57190385D+00      
> 
>   1. I wonder why LZZ become so large when angle approachs 90. For the CH2 is so long that we think LZZ will not    change so much when only angle varies. Who can tell me any possible explanation.
> 
>   2.Here is another interesting phenomenon that seems prove our before assumption.Whatever angle change, the difference of “LZZ1” column and “LZZ2” column always be 3,namely difference between Π and Δ . And difference of “LZZ2” column and “LZZ3” column always be 4 ,namely difference between Σ and Δ.It looks like that some original point just do some translation.For we always focus C atom as origin of coordinates, how does the regular difference come? Is it a Molpro bug or we missing some useful principle?
> 
> We eagerly waiting for your advice. Any suggestion will be appreciated.
> 
> Best regard
> 
> -kai 
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--
Prof. Peter J. Knowles             
School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, UK
Telephone +44 29 208 79182 Email KnowlesPJ at Cardiff.ac.uk 
WWW http://www.cardiff.ac.uk/chemy/contactsandpeople/academicstaff/knowles.html