Non-Relativistic Framework

Method	IP	EA	EE
EOM-CCSD	YES	YES	YES
EOM-CCSD*	YES	—	—
ADC(2)	YES	YES	YES
ADC(2)-X	YES	YES	YES
ADC(3)	YES	YES	YES
UCC3	YES	—	YES
qUCCSD	—	—	YES

For non-relativistic ground state correlation energy calculation one can use the spin-adapted formulation for closed shell systems. Available ground state methods in spin-adapted and spin-orbital implementations are summerized below,

Method	Spin-orbital	Spin-adapted
CCSD	YES	YES
CCSD(T)	YES	YES
CC3	YES	—
UCC3	YES	—
qUCCSD	YES	—
qUCCSD[T]	YES	—

For excited states

Method	Spin-orbital	Spin-adapted
EE-EOM-CCSD	YES	YES
IP-EOM-CCSD	YES	YES
EA-EOM-CCSD	YES	YES
IP-EOM-CCSD*	YES	YES
EE-ADC(2)	YES	YES
IP-ADC(2)	YES	YES
EA-ADC(2)	YES	YES
EE-ADC(2)-X	YES	YES
IP-ADC(2)-X	YES	YES
EA-ADC(2)-X	YES	YES
EE-ADC(3)	YES	—
IP-ADC(3)	YES	YES
EA-ADC(3)	YES	YES
EE-UCC3	YES	—
IP-UCC3	YES	—
EE-qUCCSD	YES	—

While writing input file

Ground State Energy

Coupled Cluster (CC)

\[{E_{corr}} = 2\sum\limits_{ia} {f_i^at_i^a} + 2\sum\limits_{ijab} {\tau _{ij}^{ab}\left\langle {ia\left\| {\left. {jb} \right\rangle } \right.} \right.} - \sum\limits_{ijab} {\tau _{ij}^{ab}\left\langle {ib\left\| {\left. {ja} \right\rangle } \right.} \right.}\]

where

\[\tau _{ij}^{ab} = \sum {(t_i^at_j^b} + t_{ij}^{ab})\]

Coupled Cluster Singles Doubles (CCSD)

! CCSD unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Coupled Cluster Singles Doubles with perturbative Triples (CCSD(T))

! CCSD(T)  unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Coupled Cluster approximate Triples (CC3)

! CC3 spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Unitary Coupled Cluster (UCC)

Third-order Unitary Coupled Cluster (UCC3)

! UCC3 spinorbital  unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Quadratic Unitary Coupled Cluster (qUCCSD)

! QUCCSD spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Quadratic Unitary Coupled Cluster Triples (qUCCSD[T])

! QUCCSD[T] spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

The “Density Fitting” (DF) approximation can be applied within this UCC framework by including the keyword “DF True” within the %cc block. The following input file can be used for this purpose.

Third-order Unitary Coupled Cluster (UCC3)

! UCC3 spinorbital  unc-ccpvdz

%cc
incore 5
df True
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Quadratic Unitary Coupled Cluster (qUCCSD)

! QUCCSD spinorbital unc-ccpvdz

%cc
incore 5
df True
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Quadratic Unitary Coupled Cluster Triples (qUCCSD[T])

! QUCCSD[T] spinorbital unc-ccpvdz

%cc
incore 5
df True
cc_convergence 1e-7
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

! QUCCSD[T] spinorbital ccpvdz ccpvdz-ri

%cc incore 5 df True cc_convergence 1e-7 end

*xyz 0 1 H 0.0 0.0 0.0 F 0.0 0.0 0.9168

Rank Reduced Coupled Cluster (RRCCSD)

!  RRCCSD sto3g

%cc
NumProc 4
projector_type MP2
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Excited State Energy

Equation of Motion Coupled Cluster (EOM-CC)

EOM-Coupled Cluster Singles Doubles (EOM-CCSD)

To calculate excitation energy in EOM-CCSD framework, the following input format can be used

! EE-EOM-CCSD spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
eom_convergence 1e-6
nroots 10
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Similarly, for ionization potential (IP), one needs to change the name of the method to IP-EOM-CCSD, for example

! IP-EOM-CCSD spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
eom_convergence 1e-6
nroots 10
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

For electron affinity (EA), the name of the method should be replaced with EA-EOM-CCSD

! EA-EOM-CCSD spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
eom_convergence 1e-6
nroots 10
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

EOM-Coupled Cluster approximate Triples (EOM-CC3)

! EE-EOM-CC3 spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
eom_convergence 1e-6
nroots 10
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Excited state using Unitary Coupled Cluster

Third-order Unitary Coupled Cluster (UCC3)

! EE-UCC3 spinorbital unc-ccpvdz

%cc
incore 5
cc_convergence 1e-7
ucc_convergence 1e-6
nroots 10
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

To calculate the ionisation potential in the UCC framework, one can write IP-UCC3 in place of method in the input file.

Quadratic Unitary Coupled Cluster (qUCCSD)

 ! EE-QUCCSD spinorbital unc-ccpvdz

 %cc
 incore 5
 cc_convergence 1e-7
 ucc_convergence 1e-6
 nroots 10
 end



*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

The “DF” approximation can also be applied to excited-state calculations. The following input file can be used for this purpose.

Third-order Unitary Coupled Cluster (UCC3)

! EE-UCC3 spinorbital unc-ccpvdz

%cc
incore 5
df True
cc_convergence 1e-7
ucc_convergence 1e-6
nroots 10
end

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Quadratic Unitary Coupled Cluster (qUCCSD)

 ! EE-QUCCSD spinorbital unc-ccpvdz

 %cc
 incore 5
 df True
 cc_convergence 1e-7
 ucc_convergence 1e-6
 nroots 10
 end



*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

The convergence criteria for the ground and excited states can be controlled using the keywords cc_convergence and ucc_convergence, respectively.

Algebraic Diagrammatic Construction Theory (ADC)

Second order ADC (ADC(2))

! EE-ADC(2) spinorbital unc-ccpvdz

%cc
incore 5
nroots 10
End

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Second order-extended ADC (ADC(2)-X)

! EE-ADC(2)-X spinorbital unc-ccpvdz

%cc
incore 5
nroots 10
End

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

Third order ADC (ADC(3))

! EE-ADC(3) spinorbital unc-ccpvdz

%cc
incore 5
nroots 10
End

*xyz 0 1
H 0.0 0.0 0.0
F 0.0 0.0 0.9168

To calculate the ionisation potential and electron affinity in the ADC framework, one can write IP-ADC(2), IP-ADC(2)-X, IP-ADC(3), EA-ADC(2), EA-ADC(2)-X, and EA-ADC(3) in place of method in the input file.

Properties

First order property

Second order property