eomccgen

eomccgen is an algebra package that relies on second quantization and Wick's theorem to compute automatically normal-ordered strings (with respect to the Fermi vacuum) that corresponds to the following objects:

• Second-quantized strings in normal order
• Coupled-cluster (CC) energy and amplitude equations
• Many-body terms of the similarity-transformed Hamiltonian
• Equation-of-motion coupled-cluster (EOM-CC) equations in terms of many-body terms
• Blocks of the EOM-CC Hamiltonian in terms of the many-body terms

Installation

To use eomccgen, you must have Wolfram Mathematica version 12.3 or higher installed on your computer (the program might work with an earlier version but it is guaranteed). Additionally, you may clone the present repository to access the necessary files via the following command:

git clone   https://github.com/rquintero-88/eomccgen.git

Get Started!

Generalized Wick's Theorem

In this example, we evaluate a string of second-quantized operators in normal order using Wick's theorem.

Input:

SQString = {{SuperDagger[h1], SuperDagger[h2], p2, p1}, {SuperDagger[q1], SuperDagger[q2], q4, q3}, {{SuperDagger[v1], o1}}, {SuperDagger[p3], h3}};
CWick[SQString]

Output:

{KroneckerDelta[h1,h3]KroneckerDelta[o1,q2]KroneckerDelta[p2,q1]KroneckerDelta[p3,q3]KroneckerDelta[q4,v1],-KroneckerDelta[h1,h3]KroneckerDelta[o1,q2]KroneckerDelta[p2,q1]KroneckerDelta[p3,q4]KroneckerDelta[q3,v1],-KroneckerDelta[h1,h3]KroneckerDelta[o1,q1]KroneckerDelta[p2,q2]KroneckerDelta[p3,q3]KroneckerDelta[q4,v1],KroneckerDelta[h1,h3]KroneckerDelta[o1,q1]KroneckerDelta[p2,q2]KroneckerDelta[p3,q4]KroneckerDelta[q3,v1],-KroneckerDelta[h1,q3]KroneckerDelta[h3,q1]KroneckerDelta[o1,q2]KroneckerDelta[p2,p3]KroneckerDelta[q4,v1],
KroneckerDelta[h1,q3]KroneckerDelta[h3,q2]KroneckerDelta[o1,q1]KroneckerDelta[p2,p3]KroneckerDelta[q4,v1],KroneckerDelta[h1,q4]KroneckerDelta[h3,q1]KroneckerDelta[o1,q2]KroneckerDelta[p2,p3]KroneckerDelta[q3,v1],-KroneckerDelta[h1,q4]KroneckerDelta[h3,q2]KroneckerDelta[o1,q1]KroneckerDelta[p2,p3]KroneckerDelta[q3,v1],-KroneckerDelta[h1,o1]KroneckerDelta[h3,q2]KroneckerDelta[p2,q1]KroneckerDelta[p3,q3]KroneckerDelta[q4,v1],KroneckerDelta[h1,o1]KroneckerDelta[h3,q2]KroneckerDelta[p2,q1]KroneckerDelta[p3,q4]KroneckerDelta[q3,v1],
KroneckerDelta[h1,o1]KroneckerDelta[h3,q1]KroneckerDelta[p2,q2]KroneckerDelta[p3,q3]KroneckerDelta[q4,v1],-KroneckerDelta[h1,o1]KroneckerDelta[h3,q1]KroneckerDelta[p2,q2]KroneckerDelta[p3,q4]KroneckerDelta[q3,v1],KroneckerDelta[h1,q3]KroneckerDelta[h3,q1]KroneckerDelta[o1,q2]KroneckerDelta[p2,v1]KroneckerDelta[p3,q4],-KroneckerDelta[h1,q3]KroneckerDelta[h3,q2]KroneckerDelta[o1,q1]KroneckerDelta[p2,v1]KroneckerDelta[p3,q4],-KroneckerDelta[h1,q4]KroneckerDelta[h3,q1]KroneckerDelta[o1,q2]KroneckerDelta[p2,v1]KroneckerDelta[p3,q3],
KroneckerDelta[h1,q4]KroneckerDelta[h3,q2]KroneckerDelta[o1,q1]KroneckerDelta[p2,v1]KroneckerDelta[p3,q3]}

CC with doubles (CCD)

To generate the CCD energy and amplitude equations, one must define the following input

Input:

ClusterOperator = {{"2h2p"}};
EOMOperator = {{"0h0p"}};
CCgen[ClusterOperator,EOMOperator]

Output:

'CC Energy'
{1/4 ERI[[o1,o2,v1,v2]] t2[[o1,o2,v1,v2]]}
'CC Amplitude equations'
{-ERI[[p2,p1,h1,h2]]-F[[p2,v1]] t2[[h1,h2,v1,p1]]+F[[p1,v1]] t2[[h1,h2,v1,p2]]-1/2 ERI[[p2,p1,v1,v2]] t2[[h1,h2,v1,v2]]-F[[o1,h2]] t2[[o1,h1,p2,p1]]+ERI[[o1,p2,v1,h2]] t2[[o1,h1,v1,p1]]-ERI[[o1,p1,v1,h2]] t2[[o1,h1,v1,p2]]+F[[o1,h1]] t2[[o1,h2,p2,p1]]-ERI[[o1,p2,v1,h1]] t2[[o1,h2,v1,p1]]+ERI[[o1,p1,v1,h1]] 
t2[[o1,h2,v1,p2]]-1/2 ERI[[o1,o2,h1,h2]] t2[[o1,o2,p2,p1]]-1/4 ERI[[o1,o2,v1,v2]] t2[[h1,h2,v1,v2]] t2[[o1,o2,p2,p1]]-1/2 ERI[[o1,o2,v1,v2]] t2[[h1,h2,v2,p2]] t2[[o1,o2,v1,p1]]+1/2 ERI[[o1,o2,v1,v2]] t2[[h1,h2,v2,p1]] t2[[o1,o2,v1,p2]]-1/2 ERI[[o1,o2,v1,v2]] t2[[o1,h2,v1,v2]] t2[[o2,h1,p2,p1]]+ERI[[o1,o2,v1,v2]] t2[[o1,h2,v1,p2]] 
t2[[o2,h1,v2,p1]]+1/2 ERI[[o1,o2,v1,v2]] t2[[o1,h1,v1,v2]] t2[[o2,h2,p2,p1]]-ERI[[o1,o2,v1,v2]] t2[[o1,h1,v1,p2]] t2[[o2,h2,v2,p1]]}

IP-EOM-CC with singles and doubles (IP-EOM-CCSD)

In this example, the IP-EOM-CCSD equations are generated thanks to the following input

Input:

ClusterOperator = {{"1h1p"}, {"2h2p"}};
EOMOperator = {{"1h0p"}, {"2h1p"}};
EOMCCgen[ClusterOperator, EOMOperator]

Output:

'Many-body terms'

\[Chi]1[[h3,h1]]==-F[[h3,h1]]-F[[h3,v1]] t1[[h1,v1]]+t1[[o1,v1]] ERI[[h3,o1,v1,h1]]+t1[[h1,v2]] t1[[o1,v1]] ERI[[h3,o1,v1,v2]]+1/2 ERI[[h3,o1,v1,v2]] t2[[o1,h1,v1,v2]]
\[Chi]1[[h4,p3]]==F[[h4,p3]]-t1[[o1,v1]] ERI[[h4,o1,v1,p3]]
\[Chi]2[[h4,h3,h1,p3]]==ERI[[h4,h3,h1,p3]]+t1[[h1,v1]] ERI[[h4,h3,v1,p3]]
\[Chi]2[[h3,p1,h1,h2]]==t1[[o1,p1]] ERI[[h3,o1,h1,h2]]-t1[[h2,v1]] t1[[o1,p1]] ERI[[h3,o1,v1,h1]]+t1[[h1,v1]] t1[[o1,p1]] ERI[[h3,o1,v1,h2]]+t1[[h1,v1]] t1[[h2,v2]] t1[[o1,p1]] ERI[[h3,o1,v1,v2]]-ERI[[h3,p1,h1,h2]]+t1[[h2,v1]] ERI[[h3,p1,v1,h1]]-t1[[h1,v1]] ERI[[h3,p1,v1,h2]]-t1[[h1,v1]] t1[[h2,v2]] ERI[[h3,p1,v1,v2]]-F[[h3,v1]] t2[[h1,h2,v1,p1]]+1/2 t1[[o1,p1]] ERI[[h3,o1,v1,v2]] t2[[h1,h2,v1,v2]]-1/2 ERI[[h3,p1,v1,v2]] t2[[h1,h2,v1,v2]]+t1[[o1,v1]] ERI[[h3,o1,v1,v2]] t2[[h1,h2,v2,p1]]-ERI[[h3,o1,v1,h2]] t2[[o1,h1,v1,p1]]+t1[[h2,v1]] ERI[[h3,o1,v1,v2]] t2[[o1,h1,v2,p1]]+ERI[[h3,o1,v1,h1]] t2[[o1,h2,v1,p1]]-t1[[h1,v1]] ERI[[h3,o1,v1,v2]] t2[[o1,h2,v2,p1]]
\[Chi]1[[p1,p3]]==F[[p1,p3]]-F[[o1,p3]] t1[[o1,p1]]-t1[[o1,v1]] t1[[o2,p1]] ERI[[o1,o2,v1,p3]]+t1[[o1,v1]] ERI[[o1,p1,v1,p3]]-1/2 ERI[[o1,o2,v1,p3]] t2[[o1,o2,v1,p1]]
\[Chi]2[[h4,h3,h1,h2]]==-ERI[[h4,h3,h1,h2]]+t1[[h2,v1]] ERI[[h4,h3,v1,h1]]-t1[[h1,v1]] ERI[[h4,h3,v1,h2]]-t1[[h1,v1]] t1[[h2,v2]] ERI[[h4,h3,v1,v2]]-1/2 ERI[[h4,h3,v1,v2]] t2[[h1,h2,v1,v2]]
\[Chi]2[[h4,p1,h2,p3]]==t1[[o1,p1]] ERI[[h4,o1,h2,p3]]+t1[[h2,v1]] t1[[o1,p1]] ERI[[h4,o1,v1,p3]]-ERI[[h4,p1,h2,p3]]-t1[[h2,v1]] ERI[[h4,p1,v1,p3]]-ERI[[h4,o1,v1,p3]] t2[[o1,h2,v1,p1]]
\[Chi]3[[h4,h3,p1,h1,h2,p3]]==ERI[[h4,h3,v1,p3]] t2[[h1,h2,v1,p1]]

'EOM-CC matrix in terms of many-body terms'

{{-\[Chi]1[[h3, h1]], -KroneckerDelta[h1, h4] \[Chi]1[[h3, p3]] + 
  KroneckerDelta[h1, h3] \[Chi][[h4, p3]] + \[Chi][[h4, h3, h1, p3]]},
 {-\[Chi]2[[h3, p1, h2, h1]], -KroneckerDelta[h2, h4] KroneckerDelta[p1, p3] \[Chi]1[[h3, h1]] + KroneckerDelta[h1, h4] KroneckerDelta[p1, p3] \[Chi]1[[h3, h2]] + KroneckerDelta[h2, h3] KroneckerDelta[p1, p3] \[Chi]2[[h4, h1]] - KroneckerDelta[h1, h3] KroneckerDelta[p1, p3] \[Chi]1[[h4, h2]] - KroneckerDelta[h1, h4] KroneckerDelta[h2, h3] \[Chi]1[[p1,  p3]] + KroneckerDelta[h1, h3] KroneckerDelta[h2, h4] \[Chi]1[[p1, p3]]
    - KroneckerDelta[h2, h4] \[Chi]2[[h3, p1, h1, p3]] + KroneckerDelta[h1, h4] \[Chi]2[[h3, p1, h2, p3]] + KroneckerDelta[p1, p3] \[Chi]2[[h4, h3, h2, h1]] +  KroneckerDelta[h2, h3] \[Chi]2[[h4, p1, h1, p3]] - KroneckerDelta[h1, h3] \[Chi]2[[h4, p1, h2, p3]] + \[Chi]3[[h4, h3,  p1, h2, h1, p3]]} }

Single block of DEA-EOM-CCSD in terms of many-body terms.

It is possible to generate a single block as follows:

Input:

ClusterOperator = {{"1h1p"}, {"2h2p"}};
EOMOperator = {{"2h0p"}, {"3h1p"}};
EOMBlock = {2, 1};
EOMCCpBLOCKgen[ClusterOperator, EOMOperator, EOMBlock]

Output:

'Many-body terms'

\[Chi]2[[h5,p1,h2,h3]]==t1[[o1,p1]] ERI[[h5,o1,h2,h3]]-t1[[h3,v1]] t1[[o1,p1]] ERI[[h5,o1,v1,h2]]+t1[[h2,v1]] t1[[o1,p1]] ERI[[h5,o1,v1,h3]]+t1[[h2,v1]] t1[[h3,v2]] t1[[o1,p1]] ERI[[h5,o1,v1,v2]]-ERI[[h5,p1,h2,h3]]+t1[[h3,v1]] ERI[[h5,p1,v1,h2]]-t1[[h2,v1]] ERI[[h5,p1,v1,h3]]-t1[[h2,v1]] t1[[h3,v2]] ERI[[h5,p1,v1,v2]]-F[[h5,v1]] t2[[h2,h3,v1,p1]]+1/2 t1[[o1,p1]] ERI[[h5,o1,v1,v2]] t2[[h2,h3,v1,v2]]-1/2 ERI[[h5,p1,v1,v2]] t2[[h2,h3,v1,v2]]+t1[[o1,v1]] ERI[[h5,o1,v1,v2]] t2[[h2,h3,v2,p1]]-ERI[[h5,o1,v1,h3]] t2[[o1,h2,v1,p1]]+t1[[h3,v1]] ERI[[h5,o1,v1,v2]] t2[[o1,h2,v2,p1]]+ERI[[h5,o1,v1,h2]] t2[[o1,h3,v1,p1]]-t1[[h2,v1]] ERI[[h5,o1,v1,v2]] t2[[o1,h3,v2,p1]]
\[Chi]3[[h5,h4,h3,p1,h1,h2]]==ERI[[h5,h4,v1,h3]] t2[[h1,h2,v1,p1]]-t1[[h3,v1]] ERI[[h5,h4,v1,v2]] t2[[h1,h2,v2,p1]]-ERI[[h5,h4,v1,h2]] t2[[h1,h3,v1,p1]]+t1[[h2,v1]] ERI[[h5,h4,v1,v2]] t2[[h1,h3,v2,p1]]+ERI[[h5,h4,v1,h1]] t2[[h2,h3,v1,p1]]-t1[[h1,v1]] ERI[[h5,h4,v1,v2]] t2[[h2,h3,v2,p1]]

'Block (2,1)'

KroneckerDelta[h3,h5]\[Chi]2[[h4,p1,h2,h1]]+KroneckerDelta[h2,h5]\[Chi]2[[h4,p1,h3,h1]]+KroneckerDelta[h1,h5]\[Chi]2[[h4,p1,h3,h2]]-KroneckerDelta[h3,h4]\[Chi]2[[h5,p1,h2,h1]]-
KroneckerDelta[h2,h4]\[Chi]2[[h5,p1,h3,h1]]-KroneckerDelta[h1,h4]\[Chi]2[[h5,p1,h3,h2]]-\[Chi]3[[h5,h4,p1,h3,h2,h1]]

Single many-body term using a Hamiltonian.

Input:

ClusterOperator = {{"1h1p"}, {"2h2p"}};
EOMOperator = {{"0h0"}};
ManyBodyOp = {{{p1}, {SuperDagger[p3], SuperDagger[p4], 
     h3}}, {{SuperDagger[h1], p2, p1}, {SuperDagger[p3]}}};
ManyBodyTermsEOM[ClusterOperator, EOMOperator, ManyBodyOp]

Output:

'Many Body Terms'
\[Chi]2[[h3,p1,p4,p3]]==-t1[[o1,p1]] ERI[[h3,o1,p4,p3]]+ERI[[h3,p1,p4,p3]]
\[Chi]2[[p2,p1,h1,p3]]==t1[[o1,p2]] t1[[o2,p1]] ERI[[o1,o2,h1,p3]]+t1[[h1,v1]] t1[[o1,p2]] t1[[o2,p1]] ERI[[o1,o2,v1,p3]]-t1[[o1,p2]] ERI[[o1,p1,h1,p3]]-t1[[h1,v1]] t1[[o1,p2]] ERI[[o1,p1,v1,p3]]+t1[[o1,p1]] ERI[[o1,p2,h1,p3]]+t1[[h1,v1]] t1[[o1,p1]] ERI[[o1,p2,v1,p3]]+ERI[[p2,p1,h1,p3]]+t1[[h1,v1]] ERI[[p2,p1,v1,p3]]+F[[o1,p3]] t2[[o1,h1,p2,p1]]-ERI[[o1,p2,v1,p3]] t2[[o1,h1,v1,p1]]+ERI[[o1,p1,v1,p3]] t2[[o1,h1,v1,p2]]+1/2 ERI[[o1,o2,h1,p3]] t2[[o1,o2,p2,p1]]+1/2 t1[[h1,v1]] ERI[[o1,o2,v1,p3]] t2[[o1,o2,p2,p1]]+t1[[o1,v1]] ERI[[o1,o2,v1,p3]] t2[[o2,h1,p2,p1]]-t1[[o1,p2]] ERI[[o1,o2,v1,p3]] t2[[o2,h1,v1,p1]]+t1[[o1,p1]] ERI[[o1,o2,v1,p3]] t2[[o2,h1,v1,p2]]

Left-hand side equations of EA-EOM-CC with singles and doubles (IP-EOM-CCSD) with the product l*Hbar

In this example, the left-hand side IP-EOM-CCSD equations are generated including the product of l vectro with the EOMCC matrix. To achieve that the following inputs are needed Input:

ClusterOperator = {{"1h1p"}, {"2h2p"}};
EOMOperator = {{"1h0p"}, {"2h1p"}};
LeftRigthEOM = {"L"};
EOMCCgen[ClusterOperator, EOMOperator]

Output:

'Many-body terms'

\[Chi]1[[h1,h3]]==-F[[h1,h3]]-F[[h1,v1]] t1[[h3,v1]]+t1[[o1,v1]] ERI[[h1,o1,v1,h3]]+t1[[h3,v2]] t1[[o1,v1]] ERI[[h1,o1,v1,v2]]+1/2 ERI[[h1,o1,v1,v2]] t2[[o1,h3,v1,v2]]
\[Chi]1[[h2,p1]]==F[[h2,p1]]-t1[[o1,v1]] ERI[[h2,o1,v1,p1]]
\[Chi]2[[h2,h1,h3,p1]]==ERI[[h2,h1,h3,p1]]+t1[[h3,v1]] ERI[[h2,h1,v1,p1]]
\[Chi]2[[h1,p3,h4,h3]]==t1[[o1,p3]] ERI[[h1,o1,h3,h4]]-t1[[h4,v1]] t1[[o1,p3]] ERI[[h1,o1,v1,h3]]+t1[[h3,v1]] t1[[o1,p3]] ERI[[h1,o1,v1,h4]]+t1[[h3,v1]] t1[[h4,v2]] t1[[o1,p3]] ERI[[h1,o1,v1,v2]]-ERI[[h1,p3,h3,h4]]+t1[[h4,v1]] ERI[[h1,p3,v1,h3]]-t1[[h3,v1]] ERI[[h1,p3,v1,h4]]-t1[[h3,v1]] t1[[h4,v2]] ERI[[h1,p3,v1,v2]]-F[[h1,v1]] t2[[h3,h4,v1,p3]]+1/2 t1[[o1,p3]] ERI[[h1,o1,v1,v2]] t2[[h3,h4,v1,v2]]-1/2 ERI[[h1,p3,v1,v2]] t2[[h3,h4,v1,v2]]+t1[[o1,v1]] ERI[[h1,o1,v1,v2]] t2[[h3,h4,v2,p3]]-ERI[[h1,o1,v1,h4]] t2[[o1,h3,v1,p3]]+t1[[h4,v1]] ERI[[h1,o1,v1,v2]] t2[[o1,h3,v2,p3]]+ERI[[h1,o1,v1,h3]] t2[[o1,h4,v1,p3]]-t1[[h3,v1]] ERI[[h1,o1,v1,v2]] t2[[o1,h4,v2,p3]]
\[Chi]1[[p3,p1]]==F[[p3,p1]]-F[[o1,p1]] t1[[o1,p3]]-t1[[o1,v1]] t1[[o2,p3]] ERI[[o1,o2,v1,p1]]+t1[[o1,v1]] ERI[[o1,p3,v1,p1]]-1/2 ERI[[o1,o2,v1,p1]] t2[[o1,o2,v1,p3]]
\[Chi]2[[h2,h1,h4,h3]]==-ERI[[h2,h1,h3,h4]]+t1[[h4,v1]] ERI[[h2,h1,v1,h3]]-t1[[h3,v1]] ERI[[h2,h1,v1,h4]]-t1[[h3,v1]] t1[[h4,v2]] ERI[[h2,h1,v1,v2]]-1/2 ERI[[h2,h1,v1,v2]] t2[[h3,h4,v1,v2]]
\[Chi]2[[h2,p3,h4,p1]]==t1[[o1,p3]] ERI[[h2,o1,h4,p1]]+t1[[h4,v1]] t1[[o1,p3]] ERI[[h2,o1,v1,p1]]-ERI[[h2,p3,h4,p1]]-t1[[h4,v1]] ERI[[h2,p3,v1,p1]]-ERI[[h2,o1,v1,p1]] t2[[o1,h4,v1,p3]]
\[Chi]3[[h2,h1,p3,h4,h3,p1]]==ERI[[h2,h1,v1,p1]] t2[[h3,h4,v1,p3]]



'EOM-CC matrix in terms of many-body terms'

{{l[[h3]] \[Chi]1[[h1,h3]],-l[[h2]] \[Chi]1[[h1,p1]]+l[[h1]] \[Chi]1[[h2,p1]]+l[[h3]] \[Chi]2[[h2,h1,h3,p1]]},{l[[h3,h4,p3]] \[Chi]2[[h1,p3,h4,h3]],\[Chi]1[[p3,p1]] l[[h1,h2,p3]]+\[Chi]1[[h2,h4]] l[[h1,h4,p1]]-\[Chi]1[[p3,p1]] l[[h2,h1,p3]]-\[Chi]1[[h1,h4]] l[[h2,h4,p1]]-\[Chi]1[[h2,h3]] l[[h3,h1,p1]]+\[Chi]1[[h1,h3]] l[[h3,h2,p1]]+l[[h3,h2,p3]] \[Chi]2[[h1,p3,h3,p1]]-l[[h2,h4,p3]] \[Chi]2[[h1,p3,h4,p1]]+l[[h3,h4,p1]] \[Chi]2[[h2,h1,h4,h3]]-l[[h3,h1,p3]] \[Chi]2[[h2,p3,h3,p1]]+l[[h1,h4,p3]] \[Chi]2[[h2,p3,h4,p1]]+l[[h3,h4,p3]] \[Chi]3[[h2,h1,p3,h4,h3,p1]]}}

Conventions

Index Convention

For the operators belonging to the bra and the ket, we use p1, p2, $\cdots$, h1, h2, $\cdots$. For the particles/holes that play the role of dummy indices in the cluster operator $\hat{T}$ we use o1, o2, $\cdots$, v1, v2, $\cdots$, where the notations o and v refer to occupied and virtual, respectively. Finally, for the arbitrary indexes that can be either particle or hole, we use q1, q2, q3, $\cdots$.

List of variables using in eomccgen

Description	Mathematical symbol	Mathematica notation
Fock elements	$f_{q}^{p}$	F[[p,q]]
Two-electon integrals	$v_{rs}^{pq}$	ERI[[p,q,r,s]]
Single amplitudes	$t_{i}^{a}$	t1[[i,a]]
Double amplitudes	$t_{ij}^{ab}$	t2[[i,j,a,b]]
Triple amplitudes	$t_{ijk}^{abc}$	t3[[i,j,k,a,b,c]]
Quadruple amplitudes	$t_{ijkl}^{abcd}$	t4[[i,j,k,l,a,b,c,d]]
One-body terms	$\chi_{q}^{p}$	$\chi$1[[p,q]]
Two-body terms	$\chi_{qs}^{pq}$	$\chi$2[[p,q,r,s]]
Three-body terms	$\chi_{stu}^{pqr}$	$\chi$2[[p,q,r,s,t,u]]
Four-body terms	$\chi_{tuvw}^{pqrs}$	$\chi$3[[p,q,r,s,t,u,v,w]]
EOMCC right-hand single-excitation	$r_{i}^{a}$	r[[i,a]]
EOMCC right-hand double-excitation	$r_{ij}^{ab}$	r[[i,j,a,b]]
EOMCC right-hand triple-excitation	$r_{ijk}^{abc}$	r[[i,j,k,a,b,c]]
EOMCC left-hand single-excitation	$l_{i}^{a}$	l[[i,a]]
EOMCC left-hand double-excitation	$l_{ij}^{ab}$	l[[i,j,a,b]]
EOMCC left-hand triple-excitation	$l_{ijk}^{abc}$	l[[i,j,k,a,b,c]]

Citation

@software{rauleomccgen2023,
  title = {eomccgen},
  author = {Quintero-Monsebaiz,Raul  and Loos,Pierre-François},
  year = {2023},
  publisher = {GitHub},
  url={https://github.com/rquintero-88/eomccgen.git}
  }

eomccnum

eomccnum is a notebook designed to perform quantum chemistry calculations for both ground state using CC methods and charge and neutral excited states using EOM-CC methods. The notebook is written in Wolfram Mathematica version 12.3. It is intended to be used alongside eomccgen, where you can generate equations with eomccgen and then implement them in eomccnum. The features of this notebook are the following:

• Implements Coupled Cluster calculations for ground state and excited states.
• Provides three implemented examples: EE-EOM-CCSD, IP-EOM-CCSD, and DEA-EOM-CCSD.
• Requires electronic integrals to be included in the int directory. Some integral files for small atoms and molecules are provided.

Example: EE-EOM-CCSD for H2O in the STO-3G basis

To calculate the excitation energies of water using the EE-EOM-CCSD method with the basis STO-3G, use the following input:

eomccnum[10,7,{{0.,0.,-0.06990256},{0.,0.75753241,0.51843495},{0.,-0.75753241,0.51843495}},{8.,1.,1.}, "h2o.sto-3g","EE"]

This input specifies:

• Number of electrons: 10
• Number of basis functions: 7
• Molecular coordinates: {{0., 0., -0.06990256}, {0., 0.75753241, 0.51843495}, {0., -0.75753241, 0.51843495}}
• Nuclear charges: {8., 1., 1.}
• File name: "h2o.sto-3g"
• EOM-CC method: "EE"

Please, ensure that you provide the correct values for each parameter.

For more information and additional examples, refer to the eomccnum user manual.