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Input

XMCQDPT Input File

The XMCQDPT input is almost identical to the CASSCF input discussed in the previous section. Since XMCQDPT uses the converged CASSCF wavefunction as its reference, most of the input groups remain unchanged.

The important additions are the keywords that activate the perturbation calculation and control how the second-order energy correction is performed.

The complete input file used in this tutorial is shown below.

 $CONTRL SCFTYP=MCSCF RUNTYP=ENERGY UNITS=ANGS ISPHER=1 MPLEVL=2 $END

 $SYSTEM MWORDS=1000 MEMDDI=8000 $END

 $BASIS GBASIS=CCD $END

 $GUESS GUESS=MOREAD NORB=438 $END

 $MCSCF CISTEP=GUGA FULLNR=.T. MAXIT=120 FORS=.T. FINCI=MOS $END

 $DRT GROUP=C1 FORS=.T. NMCC=99 NDOC=2 NVAL=2 STSYM=A $END

 $GUGDIA NSTATE=3 ITERMX=120 $END

 $GUGDM2 WSTATE(1)=1,1,1 $END

 $MRMP MRPT=MCQDPT $END

 $MCQDPT KSTATE(1)=1,1,1 XZERO=.T. EDSHFT=0.04 $END

 $DATA
 ...
 $END

Since all CASSCF-related input groups have already been discussed, we focus here only on the keywords introduced for XMCQDPT.

1. MPLEVL=2

$CONTRL
 MPLEVL=2
$END

The keyword MPLEVL specifies the level of perturbation theory to be applied.

For an XMCQDPT calculation,

MPLEVL = 2

requests a second-order perturbative correction to the converged CASSCF wavefunction.

This correction accounts for the dynamic electron correlation that is missing from the CASSCF calculation.

Unlike conventional MP2, where the reference is a single Hartree–Fock determinant, the perturbation is applied to a multiconfigurational CASSCF reference.

2. FINCI=MOS

$MCSCF
 FINCI=MOS
$END

This keyword instructs GAMESS to save the optimized molecular orbitals after the CASSCF calculation.

These orbitals become the reference orbitals used by the subsequent XMCQDPT calculation.

Without these optimized orbitals, the perturbation calculation cannot proceed correctly.

3. $MRMP

$MRMP
 MRPT=MCQDPT
$END

The $MRMP group activates the multireference perturbation module.

The keyword

MRPT=MCQDPT

tells GAMESS to perform an Extended Multiconfiguration Quasi-Degenerate Perturbation Theory (XMCQDPT) calculation using the converged CASSCF wavefunction.

This is the input group that distinguishes an ordinary CASSCF calculation from an XMCQDPT calculation.

4. $MCQDPT

The $MCQDPT group contains the parameters that control the perturbation calculation.

$MCQDPT
 KSTATE(1)=1,1,1
 XZERO=.T.
 EDSHFT=0.04
$END

Each keyword has a specific purpose.

KSTATE

KSTATE(1)=1,1,1

This keyword specifies which electronic states will receive the perturbative correction.

Since the preceding CASSCF calculation optimized three electronic states,

S0

S1

S2

the keyword

KSTATE(1)=1,1,1

requests XMCQDPT corrections for all three states.

The number of entries should match the number of states included in the state-averaged CASSCF calculation.

XZERO

XZERO=.T.

XZERO activates the extended multistate formulation of MCQDPT.

Rather than treating each electronic state independently, the method allows interactions between nearby electronic states during the perturbation calculation.

This is particularly important when

  • several states are close in energy,
  • avoided crossings occur,
  • conical intersections are present,
  • or excited-state mixing is significant.

For most excited-state calculations, XZERO=.T. is the recommended choice.

EDSHFT

EDSHFT=0.04

One of the most common numerical problems in multireference perturbation theory is the appearance of intruder states.

An intruder state is an external electronic configuration whose energy becomes very close to the reference state, causing the perturbation denominator to approach zero.

To stabilize the calculation, XMCQDPT introduces a small energy shift,

EDSHFT=0.04

which slightly increases the perturbation denominator.

This greatly improves numerical stability while introducing only a small effect on the final energies.

Typical values range from

0.02 – 0.05 Hartree

depending on the system being studied.

Relationship Between the Input Groups

The complete workflow can be summarized as

CASSCF

↓

Optimized Orbitals

↓

State-Averaged Wavefunctions

↓

$MRMP

↓

Activate XMCQDPT

↓

$MCQDPT

↓

Choose States

↓

Apply Second-Order Perturbation

↓

Corrected Electronic Energies

The CASSCF calculation generates the multiconfigurational reference wavefunction, while the XMCQDPT input groups determine how dynamic electron correlation is added to that reference.

Summary of New Keywords

Input Keyword Purpose
MPLEVL=2 Enables second-order perturbation theory
FINCI=MOS Saves optimized CASSCF molecular orbitals for the perturbation calculation
$MRMP MRPT=MCQDPT Activates the XMCQDPT module
KSTATE Specifies which electronic states receive perturbative corrections
XZERO=.T. Enables the extended multistate treatment
EDSHFT Applies a level shift to reduce intruder-state problems

Before Running XMCQDPT

Ensure that the preceding CASSCF calculation has converged successfully and that the chosen active space has been carefully validated. XMCQDPT does not optimize the orbitals or the active space—it simply improves the electronic energies by adding dynamic correlation to the existing CASSCF reference wavefunction.