PMID- 24353469
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20211021
IS  - 1364-5021 (Print)
IS  - 1471-2946 (Electronic)
IS  - 1364-5021 (Linking)
VI  - 469
IP  - 2160
DP  - 2013 Dec 8
TI  - Two-dimensional molecular magnets with weak topological invariant magnetic 
      moments: mathematical prediction of targets for chemical synthesis.
PG  - 20130373
LID - 20130373
AB  - An open problem in applied mathematics is to predict interesting molecules that 
      are realistic targets for chemical synthesis. In this paper, we use a spin 
      Hamiltonian-type model to predict molecular magnets (MMs) with magnetic moments 
      that are intrinsically robust under random shape deformations to the molecule. 
      Using the concept of convergence in probability, we show that for MMs in which 
      all spin centres lie in-plane and all spin centre interactions are ferromagnetic, 
      the total spin of the molecule is a 'weak topological invariant' when the number 
      of spin centres is sufficiently large. By weak topological invariant, we mean 
      that the total spin of the molecule depends only upon the arrangement of spin 
      centres in the molecule, and is unlikely to change under shape deformations to 
      the molecule. Our calculations show that only between 20 and 50 spin centres are 
      necessary for the total spin of these MMs to be a weak topological invariant. The 
      robustness effect is particularly enhanced for two-dimensional ferromagnetic MMs 
      that possess a small number of spin rings in the structure.
FAU - Packwood, D M
AU  - Packwood DM
AD  - WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, 
      Katahira, Aoba-ku, Sendai 980-8577, Japan.
FAU - Reaves, K T
AU  - Reaves KT
AD  - WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, 
      Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , 
      Texas A&M University , College Station, TX 77843-3003, USA.
FAU - Federici, F L
AU  - Federici FL
AD  - WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, 
      Katahira, Aoba-ku, Sendai 980-8577, Japan ; Department of Physics and Astronomy , 
      University College London , Gower Street, London WC1E 6BT, UK.
FAU - Katzgraber, H G
AU  - Katzgraber HG
AD  - Materials Science and Engineering , Texas A&M University , College Station, TX 
      77843-3003, USA ; Department of Physics and Astronomy , Texas A&M University , 
      College Station, TX 77843-4242, USA.
FAU - Teizer, W
AU  - Teizer W
AD  - WPI-Advanced Institute for Materials Research , Tohoku University , 2-1-1, 
      Katahira, Aoba-ku, Sendai 980-8577, Japan ; Materials Science and Engineering , 
      Texas A&M University , College Station, TX 77843-3003, USA ; Department of 
      Physics and Astronomy , Texas A&M University , College Station, TX 77843-4242, 
      USA.
LA  - eng
PT  - Journal Article
PL  - England
TA  - Proc Math Phys Eng Sci
JT  - Proceedings. Mathematical, physical, and engineering sciences
JID - 9891746
PMC - PMC3857868
OTO - NOTNLM
OT  - Ising model
OT  - mathematical chemistry
OT  - molecular magnets
OT  - single-molecule magnets
OT  - spin Hamiltonian
OT  - topological invariance
EDAT- 2013/12/20 06:00
MHDA- 2013/12/20 06:01
PMCR- 2014/12/08
CRDT- 2013/12/20 06:00
PHST- 2013/06/05 00:00 [received]
PHST- 2013/08/27 00:00 [accepted]
PHST- 2013/12/20 06:00 [entrez]
PHST- 2013/12/20 06:00 [pubmed]
PHST- 2013/12/20 06:01 [medline]
PHST- 2014/12/08 00:00 [pmc-release]
AID - rspa20130373 [pii]
AID - 10.1098/rspa.2013.0373 [doi]
PST - ppublish
SO  - Proc Math Phys Eng Sci. 2013 Dec 8;469(2160):20130373. doi: 
      10.1098/rspa.2013.0373.