Interactive evaluation of second quantized expectation values 1


Enter your operators:2



Examples

Input corresponding expression comment
A1*VN*T2 $ \langle$$ \Phi_{I}^{A}$|$ \hat{V}_{N}^{}$$ \hat{T}_{2}^{}$|$ \Phi$$ \rangle$ a simple example
A1*(FN+VN)*(I+T1+T2) $ \langle$$ \Phi_{I}^{A}$|($ \hat{F}_{N}^{}$ + $ \hat{V}_{N}^{}$)(1 + $ \hat{C}$)|$ \Phi$$ \rangle$, $ \hat{C}$ = $ \hat{C}_{1}^{}$ + $ \hat{C}_{2}^{}$ CI type singles projection
exp(-(T1+T2))*(FN+VN)*exp(T1+T2) $ \langle$$ \Phi$| e-$\scriptstyle \hat{T}$($ \hat{F}_{N}^{}$ + $ \hat{V}_{N}^{}$)e$\scriptstyle \hat{T}$|$ \Phi$$ \rangle$, $ \hat{T}$ = $ \hat{T}_{1}^{}$ + $ \hat{T}_{2}^{}$ linked CCSD energy projection
A2*exp(-(T1+T2))*(FN+VN)*exp(T1+T2) $ \langle$$ \Phi_{{IJ}}^{{AB}}$| e-$\scriptstyle \hat{T}$($ \hat{F}_{N}^{}$ + $ \hat{V}_{N}^{}$)e$\scriptstyle \hat{T}$|$ \Phi$$ \rangle$, $ \hat{T}$ = $ \hat{T}_{1}^{}$ + $ \hat{T}_{2}^{}$ linked CCSD doubles projection
A2*(FN+VN)*exp(T1+T2) $ \langle$$ \Phi_{{IJ}}^{{AB}}$|($ \hat{F}_{N}^{}$ + $ \hat{V}_{N}^{}$)e$\scriptstyle \hat{T}$|$ \Phi$$ \rangle$, $ \hat{T}$ = $ \hat{T}_{1}^{}$ + $ \hat{T}_{2}^{}$ unlinked CCSD doubles projection
A4*exp(-(T1+T2+T3+T4)) *(FN+VN)*exp(T1+T2+T3+T4) $ \langle$$ \Phi_{{IJKL}}^{{ABCD}}$| e-$\scriptstyle \hat{T}$($ \hat{F}_{N}^{}$ + $ \hat{V}_{N}^{}$)e$\scriptstyle \hat{T}$|$ \Phi$$ \rangle$, $ \hat{T}$ = $ \hat{T}_{1}^{}$ + $ \hat{T}_{2}^{}$ + $ \hat{T}_{3}^{}$ + $ \hat{T}_{4}^{}$ linked CCSDTQ quadruples projection
A1* FN+A4* VN*T2 $ \langle$$ \Phi_{I}^{A}$|$ \hat{F}_{N}^{}$|$ \Phi$$ \rangle$ + $ \langle$$ \Phi_{{IJKL}}^{{ABCD}}$|$ \hat{V}_{N}^{}$$ \hat{T}_{2}^{}$|$ \Phi$$ \rangle$ this is also valid



Operators


T1 = $\displaystyle \hat{T}_{1}^{}$ = $\displaystyle \sum_{{ia}}^{}$tia$\displaystyle \hat{a}_{a}^{\dagger}$$\displaystyle \hat{a}_{i}^{}$  
T2 = $\displaystyle \hat{T}_{2}^{}$ = $\displaystyle \sum_{{ijab}}^{}$tijab$\displaystyle \hat{a}_{a}^{\dagger}$$\displaystyle \hat{a}_{b}^{\dagger}$$\displaystyle \hat{a}_{i}^{}$$\displaystyle \hat{a}_{j}^{}$  
  $\displaystyle \vdots$    
FN = $\displaystyle \hat{F}_{N}^{}$ = $\displaystyle \sum_{{pq}}^{}$$\displaystyle \langle$p|| q$\displaystyle \rangle${$\displaystyle \hat{a}_{p}^{\dagger}$$\displaystyle \hat{a}_{q}^{}$}  
HN = $\displaystyle \hat{V}_{N}^{}$ = $\displaystyle \sum_{{pqrs}}^{}$$\displaystyle \langle$pq|| rs$\displaystyle \rangle${$\displaystyle \hat{a}_{p}^{\dagger}$$\displaystyle \hat{a}_{q}^{\dagger}$$\displaystyle \hat{a}_{s}^{}$$\displaystyle \hat{a}_{r}^{}$}  
       
A1 = $\displaystyle \hat{A}_{1}^{}$ = $\displaystyle \hat{a}_{I}^{\dagger}$$\displaystyle \hat{a}_{A}^{}$  
A2 = $\displaystyle \hat{A}_{2}^{}$ = $\displaystyle \hat{a}_{J}^{\dagger}$$\displaystyle \hat{a}_{I}^{\dagger}$$\displaystyle \hat{a}_{B}^{}$$\displaystyle \hat{a}_{A}^{}$  
  $\displaystyle \vdots$    



The input grammar: 

input: expr ';' ; 

expr: sq
        | expr '*' expr
        | expr '+' expr
        | expr '-' expr
        | '-' expr %prec NEG
        | '(' expr ')'  
        | exp_Token '(' expr ')'
        ;       

sq: one | a | t | fn | vn | error;
a:	A_Token NUM ;
t:	T_Token NUM ;
fn:	FN_Token ;
vn:	VN_Token ;

Footnotes

... values1
For this demo excitation operators are limited to 4th order. The input line is truncated to 100 characters. Output is limited to one page.
... operators:2
Please be patient. PNG-image cropping and conversion takes some time...

Michael Hanrath 2008-08-13