TY - JOUR

T1 - Estimation of molecular properties by high-dimensional model representation

AU - Hayes, Michael Y.

AU - Li, Baiqing

AU - Rabitz, Herschel

PY - 2006/1/12

Y1 - 2006/1/12

N2 - Additivity models have been widely employed to approximate unknown molecular properties based on previously measured or calculated data for similar molecules. This paper proposes an improved formulation of additivity, which is based on high-dimensional model representation (HDMR). HDMR is a general functionmapping technique that expresses the output of a multivariate system in terms of a hierarchy of cooperative effects among its input variables. HDMR rests on the general observation that, for many physical systems, only relatively low-order input variable cooperativity is significant. A molecule is expressed as a multivariate system by defining binary-valued input variables corresponding to the presence or absence of a chemical bond, with the molecular property as the output. Conventional additivity decomposes a molecular property into contributions from nonoverlapping subcomponents of fixed size. On the other hand, HDMR decomposes a molecular property into the exact contributions from the full hierarchy of its variable-sized subcomponents and contains additivity as a special case. The complete hierarchical structure of HDMR can in many cases lead to a much more accurate estimate than conventional additivity. Also, when full group additivity is not possible, HDMR gives an expression for a lower-order approximation for the missing group additivity value, greatly expanding the scope of HDMR compared to additivity. The component terms in an HDMR approximation have well-defined physical significance. Moreover, HDMR gives an exact expression for the truncation error in any given HDMR approximation, also with a well-defined physical significance. The HDMR model is tested for the enthalpy of formation of a broad range of organic molecules, and its advantages over additivity are illustrated.

AB - Additivity models have been widely employed to approximate unknown molecular properties based on previously measured or calculated data for similar molecules. This paper proposes an improved formulation of additivity, which is based on high-dimensional model representation (HDMR). HDMR is a general functionmapping technique that expresses the output of a multivariate system in terms of a hierarchy of cooperative effects among its input variables. HDMR rests on the general observation that, for many physical systems, only relatively low-order input variable cooperativity is significant. A molecule is expressed as a multivariate system by defining binary-valued input variables corresponding to the presence or absence of a chemical bond, with the molecular property as the output. Conventional additivity decomposes a molecular property into contributions from nonoverlapping subcomponents of fixed size. On the other hand, HDMR decomposes a molecular property into the exact contributions from the full hierarchy of its variable-sized subcomponents and contains additivity as a special case. The complete hierarchical structure of HDMR can in many cases lead to a much more accurate estimate than conventional additivity. Also, when full group additivity is not possible, HDMR gives an expression for a lower-order approximation for the missing group additivity value, greatly expanding the scope of HDMR compared to additivity. The component terms in an HDMR approximation have well-defined physical significance. Moreover, HDMR gives an exact expression for the truncation error in any given HDMR approximation, also with a well-defined physical significance. The HDMR model is tested for the enthalpy of formation of a broad range of organic molecules, and its advantages over additivity are illustrated.

UR - http://www.scopus.com/inward/record.url?scp=31144449373&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31144449373&partnerID=8YFLogxK

U2 - 10.1021/jp053197w

DO - 10.1021/jp053197w

M3 - Article

C2 - 16392864

AN - SCOPUS:31144449373

VL - 110

SP - 264

EP - 272

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 1

ER -