Step ~1.5 hours on 22 CPUs

CONSTRAINED FRAGMENT OPTIMIZATION IN INTERNAL COORDINATES
Victor P. Vysotskiy, Jonas Boström, Valera Veryazov
Theoretical Chemistry, Chemical Center, P.O.B. 124, Lund 22100, Sweden, E-mail: Victor.Vysotskiy@teokem.lu.se
• Large systems
• Algorithm
The proper description of chemical processes usually requires high levels ab initio methods such as CASPT2/RASPT2, and CCSD(T).
The recent algorithmics developments of the CASPT2 and the CCSD(T) methods together with code improvements in MOLCAS has not been
followed by development of the standard MOLCAS geometry optimization module, SLAPAF. For instance, within the Cholesky Decomposition
and/or Frozen Natural Orbital approaches a CASPT2/RASPT2, or CCSD(T) energy of medium-sized and large systems can now be calculated
pretty fast [1-5]. However, the total number of 3Natoms-6 displacements needed to evaluate numerical gradients (with and without constraints) undermines and signicantly limits the MOLCAS applicability only to small molecular systems. We have adressed this problem by developing a new
module for constrained multi-fragment geometry optimization in internal coordinates [6]. .
The new geometry optimization algorithm relies on the idea of supramolecular approach when a studied system can be naturally decomposed
into smaller rigid groups (or fragments) and their optimal relative positions within the entire structure is a subject of interest.
One area is the calculation of photoactive molecules and metal-organic complexes. Another area is non-covalent intermolecular interactions,
like, e.g., the chemical or physical absorption on a crystalline surface.
The system of interest is manually/heuristically divided into Nfrag fragments;
 The xyz files for each fragment are used as input data; the order of xyz files
determines the connectivity of fragments;
Selection of internal coordinates in the form of combined Z-matrix
(in gray: the rigid part of Z-matrix)
 The global multi-fragment Z-matrix consists of two sets of internal coordinates:
- active (being optimized) inter-fragment coordinates - one small sub-matrix of 6 variables per each pair of connected fragments;
- inactive (frozen by default) intra-fragment coordinates - regular Z-matrix
for each fragment
 By default, only the relative position and orientation between
fragments will be optimized;
 User can provide an own built Z-matrix file with explicitly specified set of
active (i.e., optimized) and frozen coordinates; user-friendly editing/altering
of any frozen/optimized bonds or angles;
The goal: the optimization of the interaction of (frozen) surface with
molecules (catalytic reactions, surface growth, chemical adroption)
 The step is computed in automatically generated internal “Z-matrix” coordinates using numerical 1st and 2nd order energy derivatives, i.e. analytical
gradients are not required;
 The total number of required single points energy evaluations scales with
the number of fragments (~Nfrag2 ) rather than with the total number of atoms
in the system;
 The single point energy calculations can be proceed in parallel on an arbitrary (!) number of processors.
 Reliable and easy-to-use restart mechanism
• Benchmarks
The heme-oxygen complex - C20H13N4Fe…O2.
CASPT2
Step
• Results
~1.5 hours on 22 CPUs
The benzene lithium cation complex - C6H6…Li+
CCSD(T)
Step
● For the case of constrained multi-fragment geometry optimization the developed algorithm is about 10x times faster than the standard SLAPAF
module;
● Now one can perform geometry optimization of large systems using highly accurate methods, including multiconfigurational CASPT2 and
RASPT2 methods as well as the single-reference CCSD(T) method;
● In principle, the multi-fragment optimization can be carried out with respect to any routinely computed target quantity such as excitation energies and/or electronic transition moments, electronic coupling and transfer energy, magnetic properties, and molecular response properties;
● The developed procedure is implemented in a general way and it is not limited to MOLCAS, i.e. it can be interfaced with any ab initio package
• References
[1] F. Aquilante, T. Kumanova Todorova, L. Gagliardi, T. B. Pedersen, B. O. Roos J. Chem. Phys. 034113 (2009).
[2] P.-Å. Malmqvist, K. Pierloot, A. R. Moughal Shahi, C. J. Cramer, L. Gagliardi, J.Chem. Phys. 128, 204109(1-10) (2008).
[3] F. Aquilante, L. D. Vico, N. Ferré, G. Ghigo, P.-Å. Malmqvist, P. Neogrády, T. B. Pedersen, M. Pitoňák, M. Reiher, B. O. Roos, L. Serrano-Andrés, M. Urban, V. Veryazov,
R. Lindh, J. Comput. Chem. 31, 224-247 (2010).
[4] M. Pitonak, F. Aquilante, P. Hobza, P. Neogrady, J. Noga, M. Urban,Collect. Czech. Commun. 76, 713–742 (2011).
[5] S. Vancoillie, M. G. Delcey, R. Lindh, V. Vysotskiy, P.-Å. Malmqvist, V. Veryazov J. Comp. Chem. 34, 1937–1948 (2013)
[6] V. P. Vysotskiy, J. Boström, V. Veryazov “A new module for constrained multi-fragment geometry optimization in internal coordinates implemented in the Molcas package”,
J. Comp. Chem., in press.
http://www.molcas.org