Geometry Optimization

A geometry optimization is not much else than repeated single point calculations, where the positions of the atoms are updated according to the forces acting on them. The required changes in the input file are rather small. We change the &CPMD to:

&CPMD
  OPTIMIZE GEOMETRY XYZ
  CONVERGENCE ORBITALS
   1.0d-7
  CONVERGENCE GEOMETRY
   5.0d-4
&END

We have replaced OPTIMIZE WAVEFUNCTION with OPTIMIZE GEOMETRY and added the suboption XYZ to have CPMD write a 'trajectory' of the optimization in a file named GEO_OPT.xyz (so it can be visualized later). Also we specify the convergence parameter for the geometry (see CONVERGENCE) to reflect the relative accuracy of our forces, as here is no gain from trying to converge a geometry more accurately than the accuracy of the forces with respect to the wavefunction cutoff. In fact, this can lead to convergence problems.

This run should take a little longer, than the single point calculation, since we have to do multiple wavefunction optimizations. The change in the input file is reflected in the output.

 OPTIMIZATION OF IONIC POSITIONS

[...]

 CONVERGENCE CRITERIA FOR GEOMETRY OPTIMIZATION:     5.000000E-04
 GEOMETRY OPTIMIZATION BY GDIIS/BFGS
   SIZE OF GDIIS MATRIX:                                        5
GEOMETRY OPTIMIZATION IS SAVED ON FILE GEO_OPT.xyz
 EMPIRICAL INITIAL HESSIAN (DISCO PARAMETRISATION)
 SPLINE INTERPOLATION IN G-SPACE FOR PSEUDOPOTENTIAL FUNCTIONS
    NUMBER OF SPLINE POINTS:                                 5000

CPMD has recognized the job type, our convergence parameter and the request to write a GEO_OPT.xyz file.

 INITIALIZE EMPIRICAL HESSIAN
                           <<<<< ASSUMED BONDS >>>>>
    2 <-->  1
 TOTAL NUMBER OF MOLECULAR STRUCTURES:  1

From this statement in the output you can see that the Hessian has been initialized from a simple guess assuming a molecule with a bond between the two hydrogens. This behavior can be controlled with the keyword HESSIAN. For bulk systems or complicated molecules, it may be better to start from a unit Hessian instead.

[...]

 ================================================================
 =                  GEOMETRY OPTIMIZATION                       =
 ================================================================
 NFI      GEMAX       CNORM           ETOT        DETOT      TCPU
 EWALD| SUM IN REAL SPACE OVER                      1* 1* 1 CELLS
   1  2.616E-02   2.327E-03      -1.106371   -1.106E+00      0.33
   2  6.498E-03   7.998E-04      -1.127410   -2.104E-02      0.33

[...]

  10  2.117E-08   3.412E-09      -1.128431   -6.155E-13      0.34

 RESTART INFORMATION WRITTEN ON FILE                  ./RESTART.1

   ATOM          COORDINATES            GRADIENTS (-FORCES)
   1  H  8.8000  8.0000  8.0000   3.741E-02 -9.246E-18  1.969E-18
   2  H  7.2000  8.0000  8.0000  -3.741E-02 -8.193E-18  1.613E-17
 ****************************************************************
 *** TOTAL STEP NR.    10           GEOMETRY STEP NR.      1  ***
 *** GNMAX=  3.741233E-02                ETOT=     -1.128431  ***
 *** GNORM=  2.160002E-02               DETOT=     0.000E+00  ***
 *** CNSTR=  0.000000E+00                TCPU=          3.30  ***
 ****************************************************************
   1  9.488E-03   2.270E-03      -1.123139    5.292E-03      0.33
   2  1.660E-03   4.156E-04      -1.131147   -8.009E-03      0.33
   3  4.321E-04   6.468E-05      -1.131379   -2.317E-04      0.33

In this part of the output you can see, that an almost identical wavefunction optimization takes place. After printing the positions and forces of the atoms, however, you see a small report block and then another wavefunction optimization starts. The numbers for GNMAX, GNORM, and CNSTR stand for the largest absolute component of the force on any atom, average force on the atoms, and the largest absolute component of a constraint force on the atoms respectively. They allow you to monitor the progress of the convergence of the geometry optimization.

[...]

   ATOM          COORDINATES            GRADIENTS (-FORCES)
   1  H  8.7278  8.0000  8.0000   4.184E-04  6.057E-17  7.198E-17
   2  H  7.2722  8.0000  8.0000  -4.184E-04  1.059E-17 -1.796E-17
 ****************************************************************
 *** TOTAL STEP NR.    26           GEOMETRY STEP NR.      3  ***
 *** GNMAX=  4.184410E-04 [2.93E-03]     ETOT=     -1.131390  ***
 *** GNORM=  2.415870E-04               DETOT=    -3.206E-06  ***
 *** CNSTR=  0.000000E+00                TCPU=          2.32  ***
 ****************************************************************
 ================================================================
 =              END OF GEOMETRY OPTIMIZATION                    =
 ================================================================

Finally, at the end of the geometry optimization, you can see that the forces and the total energy have decreased from their initial values as it is to be expected.