# The seniority quantum number in Tensor Network States

### Submission summary

 Authors (as Contributors): Klaas Gunst
Submission information
Code repository: https://github.com/klgunst/T3NS
Date accepted: 2021-01-05
Date submitted: 2020-12-15 17:25
Submitted by: Gunst, Klaas
Submitted to: SciPost Chemistry
Ontological classification
Specialties:
• Quantum Physics
• Theoretical and Computational Chemistry
Approaches: Theoretical, Computational

### Abstract

We employ tensor network methods for the study of the seniority quantum number -- defined as the number of unpaired electrons in a many-body wave function -- in molecular systems. Seniority-zero methods recently emerged as promising candidates to treat strong static correlations in molecular systems, but are prone to deficiencies related to dynamical correlation and dispersion. We systematically resolve these deficiencies by increasing the allowed seniority number using tensor network methods. In particular, we investigate the number of unpaired electrons needed to correctly describe the binding of the neon and nitrogen dimer and the $D_{6h}$ symmetry of benzene.

Published as SciPost Chem. 1, 001 (2021)

We would like to thank the referees for their helpful comments and the thorough reading. We have revised the manuscript taking into account their request for changes.

### List of changes

In response to the first referee:

1. We agree with the remark of the referee. We have modified the statement to reflect active space calculations.

2. We agree with the remark of the referee, we have changed the statement to only reflect on the accurate energies obtained by AP1roG.

3. We have further expanded on the explanation of Eq. 4 in the resubmission.

4. We have defined the acronym FCI in the resubmission.

5. The calculation indeed does not involve an orbital optimization. We have included a mention to this in the body of the text. We have also added a reference to an example-calculation in our github repository as to not clutter the body of the paper with it.

6. We have added to the description of Table 1 that the given complexities concern calculations without orbital optimization.

7. The reviewer is correct to note that only a convergence with respect to an increasing seniority number is shown. We have adapted the manuscript appropriately.

8. We have used the experimental value as given in the NIST database for the distances between the center of mass and the different atoms. We keep these fixed and indeed only variate the angle. We have added this to the manuscript.

9. As requested, we have changed "bonding" to "bound".

10. We indeed mean to say the tensor network calculations with full seniority. We have adapted the manuscript accordingly.

11. The DOCI-optimized orbital for the Neon dimer are delocalized on one of the two atoms for larger separations. We have clarified this in the manuscript.

12. We have elaborated further upon the computational complexity and the general usefulness of seniority-restricted tensor network calculations at the end of section 2.

In response to the second referee:

1. We have commented upon the usage of DOCI-TNS in combination with orbital optimization in the conclusions.

2. We have further commented on the entanglement present in the seniority-restricted wave functions at the end of section 2.

3. We have elaborated on this in section 2.2.

4. We have left out the mention of size-consistency of orbital optimized DOCI in the manuscript. This does not impinge the general message of the paragraph.

### Submission & Refereeing History

Resubmission scipost_202008_00004v2 on 15 December 2020
Submission scipost_202008_00004v1 on 4 August 2020

## Reports on this Submission

### Report

The authors have addressed the comments from the reviewers. I therefore recommend publication.

• validity: top
• significance: high
• originality: top
• clarity: top
• formatting: excellent
• grammar: excellent