The ALMO-CIS^{Closser:2015} and ALMO-CIS+CT^{Ge:2017} methods are local
variants of configuration interaction singles (CIS), and are formulated through
the use of absolutely localized molecular orbitals (ALMOs). They share the same
spirit with the TDDFT(MI) method (Section 12.18), but were
originally designed to target large numbers of excited states in
atomic/molecular clusters, such as the entire $n=2$ band in helium clusters
that contain hundreds of atoms.

In ALMO-CIS and ALMO-CIS+CT, we solve a truncated non-orthogonal CIS eigen-equation:

$${A}_{ia,jb}{t}^{jb}=\omega {S}_{ia,jb}{t}^{jb}$$ | (12.70) |

The use of ALMOs allows associating each MO index ($i$, $a$, $j$ or $b$) to a fragment. In ALMO-CIS, approximation is made such that only the amplitudes corresponding to intrafragment transitions are non-zero, i.e., ${t}^{jb}=0$ if the occupied orbital $j$ and the virtual orbital $b$ reside on two different fragments. The Hamiltonian and overlap matrix are also truncated, with $i$ ($j$) and $a$ ($b$) belonging to the same fragment. This approximation excludes interfragment charge transfer (CT) excitations entirely and sometimes may lead to insufficient accuracy. In ALMO-CIS+CT, the CT effect is reintroduced by setting a distance cutoff ${r}_{\mathrm{cut}}$, so that transitions between neighboring fragments within a distance smaller than ${r}_{\mathrm{cut}}$ are allowed ($i$ ($j$) and $a$ ($b$) belonging to such a pair of fragments are also included in the eigen-equation). In both ALMO-CIS and ALMO-CIS+CT, dimension of the eigenvalue problem scales linearly with respect to system size, instead of having a quadratic scaling as in standard CIS. Because of the reduction of matrix size, it is computationally feasible to explicitly build the Hamiltonian and diagonalize it to get a full band of eigenstates for relatively large systems, and the overall scaling of ALMO-CIS/ALMO-CIS+CT is cubic, in contrast with the sixth order scaling of standard CIS for a full-spectrum calculation.

Besides the full-spectrum calculations described above, use of the Davidson algorithm is also available for ALMO-CIS and ALMO-CIS+CT, which targets a few lowest excited states. This implementation, unlike the original full-spectrum version, also supports the local variants of TDDFT/TDA calculations that share the same working equation (eq. 12.70).

In addition to the standard CIS job controls variables described in
Section 7.2.7, there are several additional *$rem* variables
to specify for an ALMO-CIS/ALMO-CIS+CT calculation.

LOCAL_CIS

Invoke ALMO-CIS/ALMO-CIS+CT.

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

0
Regular CIS
1
ALMO-CIS/ALMO-CIS+CT without RI(slow)
2
ALMO-CIS/ALMO-CIS+CT with RI

RECOMMENDATION:

2 if ALMO-CIS is desired.

NN_THRESH

The distance cutoff for neighboring fragments (between which CT is enabled).

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

0
Do not include interfragment transitions (ALMO-CIS).
$n$
Include interfragment excitations between pairs of fragments the distances between whom
are smaller than $n$ Bohr (ALMO-CIS+CT).

RECOMMENDATION:

None

EIGSLV_METH

Control the method for solving the ALMO-CIS eigen-equation

TYPE:

INTEGER

DEFAULT:

0

OPTIONS:

0
Explicitly build the Hamiltonian then diagonalize (full-spectrum).
1
Use the Davidson method (currently only available for restricted cases).

RECOMMENDATION:

None

$molecule 0 1 -- 0 1 He 2.8 0. 0. -- 0 1 He 0. 0. 0. $end $rem BASIS gen AUX_BASIS rimp2-cc-pvdz PURECART 1111 METHOD hf SYM_IGNORE true SYMMETRY false FRGM_METHOD stoll CIS_N_ROOTS 8 CIS_TRIPLETS false LOCAL_CIS 2 ! use RI for ALMO-CIS NN_THRESH 10 $end $rem_frgm cis_n_roots 0 $end $basis **** HE 0 S 3 1.000000 3.84216340D+01 2.37660000D-02 5.77803000D+00 1.54679000D-01 1.24177400D+00 4.69630000D-01 S 1 1.000000 2.97964000D-01 1.00000000D+00 SP 1 1.000000 4.80000000D-02 1.00000000D+00 1.00000000D+00 **** $end