Excited state calculations

Excited state calculations in ORCA can be carried out in multiple ways in ORCA.

ΔSCF calculations and orbital rotations

It is sometimes possible to guide SCF calculations (HF or DFT) to an excited state solution of the same multiplicity (to find the first excited state of a different multiplicity is trivial). To converge to an excited state solution, one would typically first converge to the ground-state solution and next rotate the orbitals that correspond to a 1-electron (or more) orbital excitation (e.g. the HOMO and the LUMO). There is no guarantee that this would work as often the SCF simply converges to the ground-state solution again or possibly a different excited state.

However, when this works (should be checked by orbital and population analysis), one has a genuine excited state SCF solution, taking into account orbital relaxation effects that are not covered by TDDFT for example.

This is also useful if an SCF calculation accidentally ended up in an excited state solution and you want to reconverge to the ground state.

! BP86 def2-SVP def2/J MOREAD
%moinp "ground-state-orbitals.gbw" # Reads in the gbw file from a converged ground-state calculation.
%scf
rotate {50,51,90,0,0} end
end

# Orbital 50 might here be the HOMO and orbital 51 the LUMO. "90" means a 90° rotation of the two orbitals which interchanges them. "0,0" stands for the alpha orbital set (choose 1 for beta orbitals).

Time-dependent density functional theory

See TDDFT chapter

Configuration-Interaction Singles

See also the ROCIS module below.

The CIS module is essentially the same as the TDDFT module. Main difference being that a CIS calculation will use a restricted/unrestricted Hartree-Fock reference instead of a DFT reference. Note that TD-HF (also called RPA) is not available.

! RHF def2-SVP TightSCF

%cis
Nroots 2
MaxDim 5
end

CIS with doubles correction, CIS(D) can also be performed that can improve the results of a CIS calculation with added computational cost (comparable to RI-MP2). Requires an auxiliary basis set ("/C" basis).

! RHF def2-SVP def2-SVP/C TightSCF

%cis
dcorr 2 # There are 4 different algorithms to choose from here (1,2,3 and 4).
Nroots 2
MaxDim 5
end

An excited state geometry optimization can also be performed as analytical gradients are available. Using the IRoot keyword you select which excited state you want to optimize the geometry for.

! RHF def2-SVP TightSCF Opt

%cis
Nroots 2 # The number of excited states to calculate.
MaxDim 5
IRoot 2 # Selecting the excited state to perform a geometry optimization on.
end

Open-shell Configuration-Interaction Singles calculations: ROCIS module

Using the ROCIS module one can perform configuration interaction single excitation calculations using either a restricted open-shell reference (ROHF) or a RHF (for closed-shell, equivalent to using the CIS module) or UHF reference (will use QRO orbitals).

! def2-SVP TightSCF
%rocis
NRoots 2
MaxDim 5
end

* xyz -2 2
Cu 0 0 0
Cl 2.25 0 0
Cl -2.25 0 0
Cl 0 2.25 0
Cl 0 -2.25 0
*

CASSCF calculations

See CASSCF chapter

EOM-CC calculations (to be updated)

Equations of motion coupled cluster theory is now available in ORCA, supporting both singles and double excitations. The current version will only work with a closed-shell reference. Excitation energies and transition moments are now available. After the convergence of the ground-state coupled cluster calculation (i.e. standard CCSD), the EOM-CCSD routine is activated and the EOM equations are solved.

An EOM-CCSD calculation can be as easy as the input below:

! RHF EOM-CCSD cc-pVDZ TightSCF
%mdci
nroots 2
end

The back-transformed PNO-based EOM method is an economical version of EOM-CCSD that uses DLPNO-CCSD to speed up the CCSD ground-state step.

bt-PNO-EOM-CCSD

! RHF bt-PNO-EOM-CCSD cc-pVDZ def2/J cc-pVDZ/C TightSCF
%mdci
nroots 2
end

EOM theory also allows access to ionized or electron-attached states from a closed-shell reference state. Here shown using the PNO approximation:

bt-PNO-IP-EOM-CCSD
(this would calculated 1-electron oxidized states of the closed-shell reference):

! RHF bt-PNO-IP-EOM-CCSD cc-pVDZ def2/J cc-pVDZ/C TightSCF

%mdci
nroots 2
end

bt-PNO-EA-EOM-CCSD
(this would calculated 1-electron attached anion states of the closed-shell reference):

! RHF bt-PNO-EA-EOM-CCSD cc-pVDZ def2/J cc-pVDZ/C TightSCF
%mdci
nroots 2
end

STEOM-CCSD

The similarity transformed EOM-CCSD method by Nooijen and coworkers is now available in ORCA 4.0. It is a more efficient version of EOM-CCSD theory. A backtransformed PNO-based variant is also available. See chapters 8.8 and 9.21 for more information

STEOM-CCSD:

! RHF STEOM-CCSD cc-pVDZ TightSCF

%mdci
nroots 2
end

bt-PNO-STEOM-CCSD:

! RHF STEOM-CCSD cc-pVDZ TightSCF
%mdci
nroots 2
end