Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
properties_and_expectation_values [2025/07/31 12:25] – [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
Line 1: Line 1:
- 
- 
 ====== Properties and expectation values ====== ====== Properties and expectation values ======
  
Line 271: Line 269:
 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>
  
Line 419: Line 427:
 ''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, two-point and four-point formulas 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''. 
  
-The quadrupole tensor is traceless which is exploited by default. It may be switched off with ''ZERO_TRACE_UNUSED''+The quadrupole tensor is traceless which is exploited by default in the case of first derivatives. It may be switched off with ''ZERO_TRACE_UNUSED''
  
 The energy calculation has to be done with a ''PROCEDURE'' (alternatively, ''STARTCMD'' may also be used).  The energy calculation has to be done with a ''PROCEDURE'' (alternatively, ''STARTCMD'' may also be used). 
  
  
-==== Example ====+==== Examples ====
  
-The example shows how dipole, quadrupole and third moments can be obtained by computing derivatives with respect to the corresponding fields, and the dipole polarizability.+This example shows how dipole, quadrupole and third moments can be obtained by computing derivatives with respect to the corresponding fields, and the dipole polarizability.
  
 <code - examples/h2o2_fgrad_fpol.inp> <code - examples/h2o2_fgrad_fpol.inp>
 geometry={4 geometry={4
 H2O2 H2O2
-O1      0.0000  0.7375  -0.0528 +O1      0.0000   0.7375  -0.0528 
-O2      0.0000  -0.7375         -0.0528 +O2      0.0000  -0.7375  -0.0528 
-H3      0.8190  0.8170  0.4220 +H3      0.8190   0.8170   0.4220 
-H4      -0.8190         -0.8170         0.4220+H4     -0.8190  -0.8170   0.4220
 } }
  
Line 462: Line 470:
  
 </code> </code>
 +
 +This example shows how ''use_grad'' may be used:
 +
 +
 +<code - examples/h2o_fpol_dm_use_grad_ccsd.inp>
 +geometry={   3
 +H2O
 +O          0.0000000000        0.0000000000       -0.0573384885
 +H          0.7581330543        0.0000000000        0.5338192442
 +H         -0.7581330543        0.0000000000        0.5338192442
 +}
 +
 +basis=def2-svp
 +{hf}
 +
 +!use first analytial derivative
 +fpol,dm,proc=myproc,use_grad
 +
 +proc myproc
 +{hf}
 +{ccsd
 +expec,dm}
 +endproc
 +
 +
 +!compare with twofold numerical derivative
 +fpol,dm,proc=myproc
 +</code>
 +
  
 ===== Relativistic corrections ===== ===== Relativistic corrections =====