Numerical Sequence of Borane Series ENOS

A table of hydroborane families has been created. The table links boranes of different families(homologous series) and members of the same family based on k number. The table is useful deducing straight away whether a borane( molecular formula) is closo, nido or arachno or something else. The table also indicates that boranes are formed according to natural periodic function (arithmetical progression). The empirical formula utilized is extremely versatile, simple and based on the principle of Nobel gas configuration. It could be used in both simple and complex boranes and carboranes. The closo members which portray characteristic shapes also have characteristic k1 numbers.


INTRODUCTION
As a result of the carbon (C) atom to catenate and also form strong bonds with a hydrogen atom, it is able to generate a vast range of families of hydrocarbons.Some of the common families may be given by the formulas F 1 = C n H 2n+2 (alkanes), F 2 = C n H 2n (alkenes), and F 3 = C n H 2n-2 (alkynes).
For each of these families, the carbon atom obeys the octet (8) rule which has its base in a noble gas configuration of neon (Ne).On the other hand the boron atom (B) which is next to the carbon atom one valence electron less, mimics the hydrides have been grouped into families.These families are known as CLOSO, NIDO, ARACHNO and HYPO and the rare one KLADO.These families may be represented by the formulas given below.
. These series (families) are given in Table 1.Each member of the family has been given a number (k 1 value).The k 1 values are calculated from the empirical formula k 1 = ½ (E-V), where E = sum of octet electrons and V = sum of valence electrons in the cluster.This empirical formula has been discussed in our previous publications [1][2] .What is interesting about the empirical formula is that it predicts a quadruple bond for C 2 diatomic molecule as found from high level theoretical calculation methods [3][4] .

Analysis of k 1 values
The k 1 numbers do vary from family to family and also within the members of the same boron family.A movement from one family member to the next family member (horizontally, similar to a period in the periodic table), the k 1 number varies by 1.On the other hand a movement from one member to the next member of the same family( similar to a group in the periodic

CONCLUSION
Borane series tend to occur in families just like hydrocarbons.The driving force for cluster formation is probably due to boranes attempting to obey the octet rule.A given borane that obeys the octet rule may be classified to belong to a particle family using the table.Both the known boranes and the theoretically established as being stable appear to fit into one of the families.Just as the elements of the periodic table follow a simple arithmetical progression, the boranes across the row horizontally (families-similar to the period in the periodic table)) and vertically( within the family members-similar to a group within the periodic table) as well as diagonally (similar to the diagonal relationship of elements in the periodic table) follow simple arithmetical progression.The k 1 values are useful in organizing the boron families and their members.

Table 5 .
Table 1 has been extended on the left to cover the boron families headed by symbols C 0 , D, E, and G.The whole Table 1 covers the series B n H n-10 to B n H n+14.