*LINEAR RESPONSE

Linear Response module written by T. Saue and H. J. Aa. Jensen [Saue2003].

General control statements

.PRINT

Print level.

Default:

.PRINT
 0

Definition of the linear response function

.A OPERATOR

Specification of the A operator (see One-electron operators for details).

.B OPERATOR

Specification of the B operator (see One-electron operators for details).

.OPERATORS

Specification of both the A and B operators (see One-electron operators for details).

.EPOLE

Specification of electric Cartesian multipole operators of order L . Specify order.

Example: Electric dipole operators

::
.EPOLE 1

.MPOLE

Specification of magnetic Cartesian multipole operators of order L . Specify order. Example: Magnetic dipole operators

::
.MPOLE 1

.TRIAB

Enforce triangularity of response function.

\begin{equation*} \langle\langle A; B \rangle\rangle_\omega = \langle\langle B; A \rangle\rangle_\omega \end{equation*}

Only one function is calculated.

Default: Deactivated.

.B FREQ

Specify frequencies of operator B.

Example: 3 different frequencies.

.B FREQ
 3
 0.001
 0.002
 0.01

Default: Static case.

.B FREQ
 1
 0.0

.IMAGIN

Employ imaginary frequencies.

.ALLCMB

Form all possible combinations even if imaginary.

Default: Deactivated.

.UNCOUP

Uncoupled calculation.

Control variational parameters

.OCCUP

For each fermion ircop give an Specification of orbital strings of inactive orbitals to include in the linear response calculation.

.VIRTUA

For each fermion ircop give an Specification of orbital strings of virtual orbitals to include in the linear response calculation.

.SKIPEE

Exclude all rotations between occupied positive-energy and virtual positive-energy orbitals.

.SKIPEP

Exclude all rotations between occupied positive-energy and virtual negative-energy orbitals.

Control reduced equations

.MAXITR

Maximum number of iterations.

Default:

.MAXITR
 30

.MAXRED

Maximum dimension of matrix in reduced system.

Default:

.MAXRED
 200

.THRESH

Threshold for convergence of reduced system.

Default:

.THRESH
 1.0D-5

Control integral contributions

The user is encouraged to experiment with these options since they may have an important effect on run time.

.INTFLG

Specify what two-electron integrals to include (default: .INTFLG under **HAMILTONIAN).

.CNVINT

Set threshold for convergence before adding SL and SS integrals to SCF-iterations.

2 (real) Arguments:

.CNVINT
 CNVXQR(1) CNVXQR(2)

Default: Very large numbers.

.ITRINT

Set the number of iterations before adding SL and SS integrals to SCF-iterations.

Default:

.ITRINT
 1 1

Control trial vectors

.REAXVC

Read solution vectors from file XVCFIL

.REAXVC
XVCFIL

Default: No restart on solution vectors. The file has to have six characters. Make sure there is no blank character in front of the file name.

For a restart on solution vectors it is useful to set

.REAXVC
XVCFIL
.ITRINT
 0 0

otherwise LS-integrals (and SS-integrals) are switched on later and one may first iterate away and then back to a possibly converged response vector.

Often you have a converged SCF wave function along with a response vector. In this case make sure that

**DIRAC
#.WAVE FUNCTION

is commented out. Make then also sure that you use the DFCOEF file which has been obtained in the same calculation as the response vector file. Otherwise you may observe more response solver iterations than necessary.

.XLRNRM

Normalize trial vectors. Using normalized trial vectors will reduce efficiency of screening. CLARIFY!

Default: Use un-normalized vectors.

Analysis

.ANALYZ

The linear response function is obtained by contracting the property gradient \(\boldsymbol{E}_{A}^{[1]}\) associated with property \(A\) with the solution vector \(\boldsymbol{X}_{B}\) associated with property \(B\) :

\begin{equation*} \langle\langle\hat{A};\hat{B}\rangle\rangle_{\omega_{b}}=\boldsymbol{E}_{A}^{[1]\dagger}\boldsymbol{X}_{B} \end{equation*}

The indices of the two vectors run over orbital rotation indices, that is, one occupied and one virtual index. This analysis shows the most important contributions from orbital pairs to the dot product as well as the most important occupied and virtual orbitals. More information about these orbitals can then be gleaned from Mulliken population analysis.

.ANATHR

This keyword adjusts the number of terms shown in the above analysis. The threshold is in terms of percentage value to the total value of the linear response function.

Default: \(2.0\) .

Advanced/debug flags

.E2CHEK

Generate a complete set of trial vector which implicitly allows the explicit construction of the electronic Hessian. Only to be used for small systems !

.ONLYSF

Only call FMOLI in sigmavector routine: only generate one-index transformed Fock matrix [Saue2003].

.ONLYSG

Only call FMOLI in sigmavector routine: 2-electron Fock matrices using one-index transformed densities [Saue2003].

.STERNHEIM

Set diagonal elements of orbital part of Hessian equal to

\begin{equation*} -2 m c^2 \end{equation*}

for rotations between occupied positive-energy and virtual negative-energy orbitals.

Default: Deactivated.

.STERNC

(Sternheim complement) allows to separate basis set incompleteness from the replacement of an inner sum over negative-energy orbitals only by the full sum. In order to benefit from this functionality (only for specialists !), you should run with print level 2 under properties.

Then you can do a sequence of calculations: 1) .SKIPEP 2) .STERNH 3) .STERNC The diamagnetic contribution of 1) is the non-relativistic expectation value, whereas 2) is the Sternheim approximation, that is replacing orbital energy differences with

\begin{equation*} -2 m c^2 \end{equation*}

With no basis set incompleteness the sum of the diamagnetic contribution 2) and the paramagnetic contribution 3) should equal the diamagnetic contribution of 1).

Default: Deactivated.

.COMPRESSION

Reduce number of orbital variation parameters by checking corresponding elements of gradient vector against a threshold. This may reduce memory.

Default: No compression.

.COMPRESSION
 0.0

.NOPREC

No preconditioning of initial trial vectors.

Default: Preconditioning of trial vectors.

.RESFAC

New trial vector will be generated only for variational parameter classes whose residual has a norm that is larger than a fraction 1/RESFAC of the maximum norm.

Default:

.RESFAC
 1000.0