REFERENCES

[1] L. W. Chung, S. Hayashi, M. Lundberg, T. Nakatsu, H. Kato, and K. Morokuma, J. Am. Chem. Soc. 2008,

130, 12880-12881.

[2] I. Navizet, Y.-J. Liu, N. Ferré, D. Roca-Sanjuán, and R. Lindh, ChemPhysChem, 2011, 12, 3064-3076.

[3] Y. Ma, S. Knecht, S. Keller, R. Lindh, and M. Reiher, in preparation.

[4] T. Dresselhaus, J. Neugebauer, S. Knecht, S. Keller, Y. Ma, and M. Reiher, J. Chem. Phys., 2015, 142, 044111.

[5] G. Barcza, Ö. Legeza, K. H. Marti, and M. Reiher, Phys. Rev. A, 2011, 83, 012508.

[6] K. Boguslawski, K. H. Marti, and M. Reiher, J. Chem. Phys., 2011, 134, 224101.

EXAMPLE: GEOMETRY OPTIMIZATIONS

Since the gradients can be obtained readily, the geom-

etry optimization using DMRG-SCF could be carried

out.

The same optimized minimum geometries of n → σ∗state and σ → σ∗ state can be obtained when compar-

ing to those of CASSCF results:

σ → σ∗

n→ σ∗

Additionally, the transition state (TS) and conical in-

tersection point could also be determined, e.g.

Figure : Optimized TS(O-O) (left) and CI(C-C) (right) structures

* Larger active space results are currently under con-

sideration.

EXAMPLE: DMRG-IN-DFT EMBEDDING

The DMRG-in-DFT embedding may facilitate accu-

rate calculations on systems with strong static corre-

lation embedded in environments whose effects are

important beyond a classical description.

Table: Dipole moment µ in Debye from DMRG-in-

DFT calculations

ENTANGLEMENT AND EXCITATION ANALYSIS

The single-orbital entropy s(1)i [5], which can be un-

derstood as a measure of the interaction of one orbital

with all other orbitals,

s(1)i = −∑α

wα,i ln wα,i

two-orbital entropy s(2)i,j [5],

s(2)i,j = −∑α

wα,i,j ln wα,i,j

and mutual information Ii,j [5], which measure the en-

tanglement between different orbitals,

Ii,j = 12(s(2)i,j − s(1)i − s(2)j)(1− δi,j)

are all supported.

The sampling-reconstruction complete active space

(SR-CAS) algorithm [6] is also supported. It allows

the character of an electronic state can be analyzed

using the Slater-determinant (SD) language.

CONCLUSION

DMRG-SCF calculations are now possible in the

MAQUIS-MOLCAS environment developed by us.

The FDE scheme is used with a freeze-and-thaw strat-

egy to consider the environment effects. Entangle-

ment and excitation analyses are also supported in or-

der to investigate the nature of electronic correlations

in the studied systems.

DMRG EMBEDDED IN QUANTUM ENVIRONMENT

The DMRG calculations can be embedded in an en-

vironment described by density functional theory [4].

The frozen density embedding (FDE) scheme is used

with a freeze-and-thaw strategy for a self-consistent

polarization of the orbital-optimized wavefunction

and the environmental densities.

THE GRADIENT OF A DMRG-SCF STATE

The orbital Lagrangian in this case is symmetric and

thus the calculation of the energy gradient can be di-

rectly deduced based on the Hellmann-Feynman theo-

rem,

g = ∂E

∂r= ∂〈Ψ|H|Ψ〉

∂r= 〈Ψ|H

∂r|Ψ〉

Thus, it is straightforward in the state-specific case.

For the state-averaged case, however, further treat-

ment needs to be considered and currently an approx-

imate but efficient way has been implemented in our

MAQUIS-MOLCAS interface [3].

BRIEF OVERVIEW OF MCSCF/CASSCF/DMRGSCF

The DMRG-SCF wave function contains the matrix-

product states (MPS) as well as the orbital rotation

parameter eR,

The orbital-optimization process is based on a series

of unitary transformations, in which the exponential

expansion of orbital rotation matrix R is involved,

BACKGROUND

Theoretical treatment of chemical reactions involving

excited electronic states has been a challenging prob-

lem for a long time. Photochemical systems such as

the bioluminescent have received significant compu-

tational attention [1, 2].

In order to give a reliable description of the above-

mentioned bioluminescence process, many degener-

ated electronic states should be calculated simultane-

ously with in a multi-configurational (MC) ansatz.

Considering that the DMRG algorithm can handle

much larger active orbital spaces than that of tradi-

tional MC methods, DMRG is a suitable alternative.

DMRG-SCF MODULE (MAQUIS-MOLCAS INTERFACE) IN MOLCASWITH APPLICATION TO SIMPLIFIED BIOLUMINESCENCE MODEL

Yingjin Ma1, Stefan Knecht1, Sebastian Keller1, Roland Lindh2,and Markus Reiher1

1Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich,Switzerland

Email: {yingjin.ma, stefan.knecht, sebastian.keller, markus.reiher}@phys.chem.ethz.ch2 Department of Chemistry - Ångström, POB 518, SE-751 20 Uppsala, Sweden

Email: roland.lindh@kemi.uu.se