# 4.2.2. AVERD¶

## 4.2.2.1. Description¶

AVERD computes average densities and corresponding natural molecular orbitals. Given a set of density matrices in the same basis set, an average density matrix is constructed and diagonalized to give average natural orbitals. These orbitals have non-integer occupation numbers, although they usually are fairly well clustered in one strongly occupied part and one weakly occupied part. From basic mathematical properties of natural orbitals, a truncated set of the orbitals constructed this way constitutes the most compact basis of one-electron functions of that given size. In other words, the smallest set of functions to span the average space within a certain accuracy has been obtained. AVERD is in essence very similar to GENANO.

## 4.2.2.2. Dependencies¶

AVERD needs a set of input densities. Any of the programs, which generate a density must precede.

## 4.2.2.3. Files¶

Below is a list of the files that are used/created by AVERD.

### 4.2.2.3.1. Input files¶

- RUNFILE
File for communication of auxiliary information generated by the program SEWARD.

- ONEINT
File with one-electron integrals generated by SEWARD.

- RUN***
A set of RunFiles on which a density matrix is stored. This density matrix is read and added to the average. If ORBItals is given, these files are not needed.

- NAT***
A set of orbitals in the format generated by SCF or RASSCF. The orbitals are used to generate a density matrix, which is added to the average. Only required if ORBItals is given.

### 4.2.2.3.2. Output files¶

- AVEORB
The average orbitals generated by AVERD. They are stored in the same way as SCF-orbitals and can be used as INPORB.

## 4.2.2.4. Input¶

- TITLe
Title of the calculation.

- WSET
Followed by two rows. On the first the number of input orbitals are given, \(N\). Second row contains \(N\) numbers each giving a weight for the \(k\)th input density matrix to the average density. The weights are normalized by AVERD, hence only the ratio of the numbers have any significance.

**This keyword is mandatory.**Print level. 1 is default. Higher than 3 is not recommended for the average user.

- ORBItals
This keyword signifies that the densities should be created from average orbitals in the files NAT***, not directly from the density matrices on the files RUN***. The default is to use the density matrices on RUN***.

- OCCUpation
Followed by one number. The number of average orbitals with an occupation higher than this number is reported for each symmetry. Since the occupation is the guide for how to truncate the orbitals in subsequent applications, this is an easy way to get hold of that number. The default is \(10^{-5}\).

### 4.2.2.4.1. Input example¶

In this example, two density matrices are averaged and their average orbitals are computed.

```
&Seward
Basis set
O.ano-s.Pierloot.10s6p3d.7s4p2d.
O 0.0000 0.0000 0.3000
End of Basis set
Basis set
H.ano-s.Pierloot.7s3p.4s1p.
H1 0.0000 -1.4300 -0.8070
H2 0.0000 1.4300 -0.8070
End of Basis Set
&FfPt
Dipo
z 0.005
End of Input
&Scf
Occupation
5
>>COPY $Project.RunFile RUN001
&FfPt
Dipo
z -0.005
&Scf
Occupation
5
End of Input
>>COPY $Project.RunFile RUN002
&Averd &End
Wset
2
1.0 1.0
Occupation
1d-6
```