Ž . Chemical Physics 226 1998 231–251 Exchange transfer in high-nuclearity mixed valence magnetic clusters: Theoretical approach and expected manifestations J.J. Borras-Almenar a, ) , E. Coronado a , A.V. Palii a,1 , B.S. Tsukerblat a,1 , ´ R. Georges b a Dept. Quımica Inorganica, UniÕersidad de Valencia, Dr. Moliner 50, Burjassot 46100, Spain ´ ´ b ICMB, AÕ. du Dr. Schweitzer, Pessac 33600, France Received 2 June 1997 Abstract We report here a general solution of the exchange transfer problem in the high-nuclearity mixed valence clusters containing arbitrary number of itinerant electrons. The concept of two kinds of exchange transfer, namely kinetic and potential, is introduced by analogy with basic Anderson’s mechanisms of the magnetic exchange. The kinetic exchange transfer is treated as a second order transfer process between two centres through the excited state of a third centre. The potential exchange transfer is also considered as a three-centre interaction but in this case only the ground states of the constituent ions are involved. The actual parameters of the exchange transfer are expected to be of the same order of magnitude as those for the magnetic exchange. An efficient computational approach is proposed making it possible to build up the matrices of all kinds of exchange transfer interactions in a closed analytical form, expressing the matrix elements in terms of the relevant spin quantum numbers. As distinguished from the magnetic exchange the kinetic and potential contributions to the exchange transfer act independently and their parameters cannot be, in general, combined to give a joint parameter of the exchange transfer. The magnetic manifestations of the exchange transfer are considered for selected trimeric Ž . systems with different topologies linear and trigonal and different electronic shells involving either migrating electrons or holes. The magnetic nature of the ground state is found to depend on the topology of the system and on the sign of the double exchange parameter. q 1998 Elsevier Science B.V. 1. Introduction wx wx wx The double exchange concept was pioneered by Zener 1 , Anderson and Hasegawa 2 and de Gennes 3 Ž . and applied firstly to the binuclear mixed valence MV systems consisting of localized magnetic moments and itinerant ‘extra’ electrons hopping over the two exchange-coupled magnetic sites. In this case, delocalization of ) Corresponding author. Tel.rfax: q34-6-3864859; e-mail: coronado@vm.ci.uv.es. 1 On leave from the Quantum Chemistry Dept., Institute of Chemistry, Academy of Sciences of Moldova, MD-2028 Kishinev, Moldova. 0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. Ž . PII S0301-0104 97 00292-9