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properties_and_expectation_values [2025/08/25 14:35] – [Derivatives with respect to fields (dipole, quadrupole, second and third moments)] dollproperties_and_expectation_values [2025/09/10 06:37] (current) – add example for pop , spin doll
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 ci;dm,9000.2; ci;dm,9000.2;
 pop;density,9000.2 pop;density,9000.2
 +</code>
 +
 +In the following example, the population for charge and spin is computed:
 +
 +<code - examples/li_pop.inp>
 +geometry={li}
 +basis=vdz
 +hf
 +pop;
 +pop;density,type=spin
 </code> </code>
  
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 ''FPOL,OPER=DM,PROC=myproc'' ''FPOL,OPER=DM,PROC=myproc''
  
-where ''myproc'' has to be defined. Instead of ''FGRAD,OPER=DM'' simply ''FGRAD,DM'' may be used, if the operator is the first argument which follows ''FGRAD'' or ''FPOL''.+where ''myproc'' has to be defined.
  
 By default a two-point formula is used for first derivatives (keyword ''CENTRAL''). Alternatively, a forward-difference formula ''FORWARD'' (fast, but inaccurate) or a fourpoint formula may be used ''FOURPOINT'' . By default a two-point formula is used for first derivatives (keyword ''CENTRAL''). Alternatively, a forward-difference formula ''FORWARD'' (fast, but inaccurate) or a fourpoint formula may be used ''FOURPOINT'' .
  
-For second derivatives, central (3 points for the diagonal part, 2*2 points for the off-diagonal part) and four-point formulas (central point + 4 more points for the diagonal part, 4*4 points for the off-diagonal part) are implemented. If available, analytical first gradients may be used with the keyword ''use_grad'' so that only the second derivative is done numerically. This may require the ''expec'' keyword to compute the analytical first derivative.+For second derivatives, central (1 central point + 2 more points for the diagonal part, 2*2 points for the off-diagonal part) and four-point formulas (central point + 4 more points for the diagonal part, 4*4 points for the off-diagonal part) are implemented. If available, analytical first gradients may be used with the keyword ''use_grad'' so that only the second derivative is done numerically. This may require the ''expec'' keyword to compute the analytical first derivative.
  
 The default step size is 0.001 a.u. and may be changed with the option ''STRENGTH''.  The default step size is 0.001 a.u. and may be changed with the option ''STRENGTH''.