Understanding the CASSCF Output (Part 1)¶
Unlike RHF or CIS, a CASSCF output contains considerably more information because the program must optimize both the molecular orbitals and the multiconfigurational wavefunction.
This section explains the first part of the output, which contains
- the job setup,
- MCSCF input parameters,
- construction of the active space,
- and the GUGA configuration table.
Understanding these sections is essential before interpreting the electronic states.
1. Echo of the Input¶
Search for
Near the beginning of the output you will find
EXECUTION OF GAMESS BEGUN 20:38:16 15-JUL-2026
ECHO OF THE FIRST FEW INPUT CARDS
$CONTRL RUNTYP=ENERGY SCFTYP=MCSCF MULT=1 ISPHER=1
$MCSCF CISTEP=GUGA FULLNR=.T. MAXIT=120 FORS=.T.
$DRT GROUP=C1 FORS=.T. NMCC=99 NDOC=2 NVAL=2
...
Why is this important?¶
Before analyzing any calculation, always verify that GAMESS has read the intended input correctly.
This section confirms
- the calculation type,
- active-space definition,
- basis set,
- number of states,
- and molecular geometry.
If an input keyword has been mistyped, it is usually visible here.
2. MCSCF Input Parameters¶
Search for
You will find
----------------------
MCSCF INPUT PARAMETERS
----------------------
CONVERGER SELECTION:
FOCAS = F
SOSCF = F
FULLNR = T
QUD = F
JACOBI= F
SECULAR EQUATION METHOD
CISTEP = GUGA
MAXIT = 120
ACURCY = 1.000E-05
ENGTOL = 1.000E-10
METHOD = DM2
FORS = T
NORB = 465
What does this mean?¶
This section tells us how the CASSCF optimization will be performed.
Orbital Optimization Method¶
The Full Newton–Raphson algorithm is selected.
Rather than making small corrections to the molecular orbitals, this algorithm computes the optimal orbital rotation using second derivatives of the energy.
Although computationally more demanding than first-order methods, it generally provides faster and more reliable convergence for multiconfigurational calculations.
Configuration Interaction Solver¶
The Configuration Interaction problem is solved using the Graphical Unitary Group Approach (GUGA).
Instead of constructing every Slater determinant explicitly, GUGA generates Configuration State Functions (CSFs) that are already spin-adapted.
This has two major advantages:
- fewer configurations are required,
- spin symmetry is preserved automatically.
Later in the output, the electronic states will be expressed as linear combinations of these CSFs.
Maximum Number of Iterations¶
GAMESS is allowed to perform 120 orbital optimization cycles. These iteration cycles can be increased if the convergence is not achieved.
Fortunately, as we shall see later, this calculation converged after only 13 iterations.
Convergence Threshold¶
The orbital gradient must become smaller than
before the optimization is considered converged.
Smaller values correspond to stricter convergence criteria.
Energy Convergence¶
Successive iterations must change the total electronic energy by less than
This ensures that the final wavefunction is numerically stable.
Number of Orbitals¶
During the optimization, GAMESS internally considers 465 molecular orbitals.
However, after removing redundant Cartesian functions, the actual variational space contains
which agrees with the value specified in
from the input file.
3. Basis Set Summary¶
Immediately after the MCSCF parameters, GAMESS prints
THE POINT GROUP IS C1
AFTER EXCLUDING CONTAMINANT COMBINATIONS
THE NUMBER OF SPHERICAL HARMONICS KEPT
IN THE VARIATION SPACE IS 438
This confirms
- the molecular symmetry (C₁),
- and that 438 basis functions are used in the calculation.
Because C₁ possesses no symmetry operations other than the identity, every molecular orbital belongs to the same irreducible representation.
4. GUGA Distinct Row Table¶
Search for
This is one of the most important sections of the entire CASSCF output.
The beginning of the table is
What is the Distinct Row Table?¶
The Distinct Row Table (DRT) is the data structure used by the GUGA algorithm to generate every possible spin-adapted electronic configuration within the chosen active space.
Instead of listing millions of determinants, the DRT efficiently constructs only the configurations allowed by
- the number of electrons,
- the active orbitals,
- spin,
- and molecular symmetry.
Understanding the Active Space¶
The most important quantities are
These divide the molecular orbitals into three groups.
| Quantity | Meaning |
|---|---|
| NMCC = 99 | 99 inactive (core) orbitals that remain doubly occupied. |
| NDOC = 2 | Two active orbitals initially occupied by electron pairs. |
| NVAL = 2 | Two active virtual orbitals available for electron excitation. |
Therefore, the active space contains
This is exactly the active space selected during the previous Active Space Selection tutorial.
Maximum Electron Excitation¶
Further down, GAMESS prints
Since four active orbitals are available, the program allows every possible redistribution of the active electrons among these orbitals.
This is what makes the method a Complete Active Space calculation.
Every allowed electronic configuration inside the active space is included automatically.
Orbital Symmetry¶
Next, GAMESS prints
followed by
This tells us that the active space consists of
- two initially doubly occupied orbitals,
- followed by two initially empty virtual orbitals.
These are precisely the orbitals that were selected from the previous CIS calculation.
Number of Electrons¶
The output continues with
Therefore,
- total electrons = 202
- spin multiplicity = 1
- electronic state = ¹A
This agrees with the singlet specified in the input.
Number of Configurations¶
Near the end of the DRT section we find
This is an extremely important result.
Although the molecule contains 202 electrons and 438 molecular orbitals, only
are required to describe the complete active-space wavefunction.
These CSFs will later be combined with different coefficients to form each electronic state.
Summary¶
At this point, the CASSCF calculation has not yet optimized the wavefunction.
GAMESS has simply
- read the molecular geometry,
- read the RHF molecular orbitals,
- constructed the Complete Active Space,
- generated the GUGA Distinct Row Table,
- and prepared the Configuration State Functions required for the multiconfigurational calculation.
The next stage is the MCSCF optimization, where both the molecular orbitals and the CI coefficients are optimized simultaneously.