Differences

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--- properties_and_expectation_values [2025/07/31 13:39] – add example doll
+++ properties_and_expectation_values [2025/09/10 06:37] (current) – add example for pop , spin doll
@@ Line 269: / Line 269: @@
 ci;dm,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>
@@ Line 417: / Line 427: @@
 ''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'' .
-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 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).
@@ Line 461: / Line 471: @@
 </code>
-This example shows ''how use_grad'' may be used:
+This example shows how ''use_grad'' may be used:
@@ Line 486: / Line 496: @@
 !compare with twofold numerical derivative
-fpol,dm,proc=myproc,strength=0.001
+fpol,dm,proc=myproc
 </code>