TOEP2 with quantum nucleus

Here, we compute the second order propagator theory (Propagathor Theory, PT) corrections to a partially ionized water molecule electronic orbital (HOMO). The TOEP2 method requires a UHF reference.

First, run a regular UHF calculation to generate the molecular orbitals, let’s name it “H2O.UHF.lowdin”. These molecular orbitals will be used as the guess for the partially ionized SCF.

GEOMETRY
	e-(O)	6-31G	    0.0000  0.0000  0.1173 multiplicity=1 	
	e-(H)	6-31G	    0.0000  0.7572 -0.4692
	e-(H)	6-31G       0.0000 -0.7572 -0.4692
	O	dirac	    0.0000  0.0000  0.1173 
	H-a_1	Nakai-7-SPD 0.0000  0.7572 -0.4692
	H-b_1	Nakai-7-SPD 0.0000 -0.7572 -0.4692
END GEOMETRY

TASKS
	method = "UHF"
END TASKS

Now, we generate the TOEP2 input, let’s name it “H2O.TOEP2.lowdin”. In addition to the PT2 flag, “propagatorTheoryCorrection=2”, we add to the input the flag “ptTransitionOperator=T” along with “IonizeMO” and “ionizeSpecies” to select the orbital and the species, and “MOfractionOccupation” to select the occupation.

GEOMETRY
	e-(O)	6-31G	    0.0000  0.0000  0.1173 multiplicity=1 	
	e-(H)	6-31G	    0.0000  0.7572 -0.4692
	e-(H)	6-31G       0.0000 -0.7572 -0.4692
	O	dirac	    0.0000  0.0000  0.1173 
	H-a_1	Nakai-7-SPD 0.0000  0.7572 -0.4692
	H-b_1	Nakai-7-SPD 0.0000 -0.7572 -0.4692
END GEOMETRY

TASKS
	method = "UHF"
	propagatorTheoryCorrection=2
END TASKS

CONTROL
	readCoefficients=T         !read molecular orbitals generated with H2O.UHF.lowdin
	ionizeSpecies="E-ALPHA"
	ionizeMO=5
	MOfractionOccupation=0.5
	ptTransitionOperator=T
END CONTROL

Before running this calculation, rename the molecular orbitals file “H2O.UHF.vec” to “H2O.TOEP2.vec”

The output will include the summary of the P2 corrections to the partially ionized orbital

         PROPAGATOR FORMALISM FOR SEVERAL FERMIONS SPECIES 
          ORDER OF CORRECTION =     2  + TRANSITION OPERATOR
            The following articles must be cited:
            -------------------------------------
               J. Chem. Phys. 127, 134106 (2007) 
               J. Chem. Phys. 137, 074105 (2012) 
               J. Chem. Phys. 138, 194108 (2013) 
                                 CPL coming soon 
            -------------------------------------
         SPECIES:   E-ALPHA
         ------------------------------------------------------------------------------------------
             Orbital     KT (eV)    EP2 (eV)        P.S   SCS-EP2(eV)       P.S   SOS-EP2(eV)       P.S  
         ------------------------------------------------------------------------------------------
                5      -10.364472  -10.768693    0.327967  -10.740363    0.357031  -10.725240    0.369623
         ------------------------------------------------------------------------------------------

This summary includes the Koopmans’ (KT) and self-energy corrected (EP2) binding energy for the selected orbital. In addition, PT2 calculations with UHF reference include opposite-spin-scaled (SOS) and spin-component-scaled (SCS) results.

For the transition-operator results, the Pole Strength (P.S) value does not indicates the quality of the approximation.