10  US 9,052,590 B2  9  As preferred substituents that can be introduced in these  groups, there can be mentioned a hydroxyl group; a halogen  atom (fluorine, chlorine, bromine or iodine); a nitro group; a  cyano group; an amido group; a sulfonamido group; any of  the alkyl groups mentioned above with respect to R$_{11 }$to R$_{13}$;  an alkoxy group, such as a methoxy group, an ethoxy group,  a hydroxyethoxy group, a propoxy group, a hydroxypropoxy  group or a butoxy group; an alkoxycarbonyl group, such as a  methoxycarbonyl group or an ethoxycarbonyl group; an acyl  group, such as a formyl group, an acetyl group or a benzoyl  group; an acyloxy group, such as an acetoxy group or a  butyryloxy group; and a carboxyl group. A hydroxyl group  and a halogen atom are especially preferred.  In general formula (I), each of Ru, R$_{12 }$and R$_{13 }$is prefer› ably a hydrogen atom, an alkyl group or a halogen atom. A  hydrogen atom, a methyl group, an ethyl group, a trifluorom› ethyl group (-CF  3 ), a hydroxymethyl group (----CH $_{2}$---0H),  a chloromethyl group (----CH$_{2}$----Cl) and a fluorine atom are  especially preferred.  X$_{11 }$ represents ---0-, -S-, -CO-, -S0$_{2}$-,  -NR- (R represents a hydrogen atom or an alkyl group), a  bivalent nitrogenous nonaromatic heterocyclic group or a  group composed of a combination of these.  With respect to -NR-, the alkyl group represented by R  is an optionally substituted linear or branched alkyl group.  Particular examples thereof are the same as those of the alkyl  groups represented by R$_{1 }$ i,  R$_{12 }$and R$_{13}$. R is most preferably  a hydrogen atom, a methyl group or an ethyl group.  The bivalent nitrogenous nonaromatic heterocyclic group  refers to a preferably 3- to 8-membered nonaromatic hetero› cyclic group having at least one nitrogen atom. In particular,  there can be mentioned, for example, bivalent connecting  groups with the following structures.  First, general formula (I) will be described.  In general formula  (I), each of Ru, R$_{12 }$and R$_{13 }$indepen› dently represents a hydrogen atom, an alkyl group, a monova› lent aliphatic hydrocarbon ring group, a halogen atom, a  cyano group or an alkoxycarbonyl group.  X$_{11 }$ is preferably -0-, -CO-, -S0$_{2}$ -,  -NR- (R  represents a hydrogen atom or an alkyl group) or a group  composed of a combination of these. X$_{11 }$ is most preferably  -COO- or -CONR- (R represents a hydrogen atom or  an alkyl group).  L$_{11 }$ represents an alkylene group, an alkenylene group, a  bivalent aliphatic hydrocarbon ring group or a group com› posed of a combination of two or more of these, provided that  in the group composed of a combination, two or more groups  combined together may be identical to or different from each  other and may be linked to each other through, as a connecting  group, ---0-,  -S-, -CO-, -S0$_{2}$ -,  -NR- (R rep› resents a hydrogen atom or an alkyl group), a bivalent nitrog› enous nonaromatic heterocyclic group, a bivalent aromatic  ring group or a group composed of a combination of these.  As the monovalent aliphatic hydrocarbon ring group, there  can be mentioned an optionally substituted monocyclic or  polycyclic aliphatic hydrocarbon ring group.  An  substituted monocyclic monovalent aliphatic hydrocarbon  ring group having 3 to 8 carbon atoms, such as a cyclopropyl  group, a cyclopentyl group or a cyclohexyl group, is pre› ferred.  The alkyl group is an optionally substituted linear or  branched alkyl group, preferably an optionally substituted  alkyl group having 20 or less carbon atoms, such as a methyl  group, an ethyl group, a propyl group, an isopropyl group, an  n-butyl group, a sec-butyl group, a hexyl group, a 2-ethyl› hexyl group, an octyl group or a dodecyl group.  An  alkyl  group having 8 or less carbon atoms is more preferred.  An  alkyl group having 3 or less carbon atoms is most preferred.  *  (~) CJ ( 1 )  I  I  N  *  *  I  *  *  i  i  0()()  I  N  N  •  I  I  (III)  (II)  R11  R13  I  I  -+C-C+- (I)  1  I  R12 X11  I  L11  I  X12  I  Ar1  I  X13  I  L12  I  Z1 