# *LINEAR RESPONSE¶

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

## 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.

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.

### .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¶

## 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 \(B\) :

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

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

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
```

### .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
```