A Time Line

With the development of digital computers in the late 1950's came the opportunity to mechanise the tedious calculations of stability constants from data such as potentiometric titration data which, up to that time, were done using hand-calculations and graphical methods. The principle was well-known, having been developed by Gauss in the 19th. century - to minimise an objective function, a sum of (weighted) squared residuals, with respect to some parameters. A residual would be the difference between observed and calculated pH (or electrode potential) and the parameters would be the stability constants. According to Gauss, it is necessary to obtain the partial derivatives of each calculated quantity (such as calculated pH) with respect to each parameter in order to do the calculation. Here it is that there appears to be a serious obstacle: calculated pH is an implicit function of the stability constants and so the derivative cannot be obtained directly. Much of the early effort was directed at overcoming this apparent difficulty.

For detailed bibligraphy see: P. Gans, A. Sabatini and A. Vacca, Talanta, (1996) 43, 1739-1753. view paper (requires Acrobat reader)

1961 Pit-mapping (Ingri and SillÚn) was described as a means of minimising the objective function. The pit was assumed to be a quadratic function of the parameters so that its minimum could be located by fitting the function
1963 GaussG (Tobias and Yasuda). Used Gauss's least squares method with partial derivatives calculated numerically by means of a difference formula. Never widely used, but part of this program formed the basis of SCOGS (see below)
1964 Letagrop (Ingri and Sillén). The first general purpose computer program for stability constant calculation. Used pit-mapping. Separate modules for different kinds of data.
1967 SCOGS (Perrin and Sayce). Generalised the approach used in GaussG. The most widely used program after Letagrop.
1974 Miniquad (Sabatini, Vacca and Gans) The objective function was derived from the total concentrations of the reagents. Partial derivatives could be obtained from analytical formulae. Outperformed SCOGS in speed and reliability and was faster than Letagrop. (in those days execution speed was important as many people had to "pay" for central processor time)
1975 SQUAD (Leggett and McBryde) Applied the same process used in SCOGS to spectrophotometric data
1976 Miniquad75 improvements in speed and reliability
1978 Psequad (Zekany and Nagypal) Used implicit differentiation to minimize the objective function in pH or absorbance. With hindsight it is a mystery why this was not done earlier as the process is described in text-books on advanced calculus!
1982 Titfit (Zuberbühlr and Kaden) The first published program in the field to use a "game" computer.
1985 Specfit (Kaden, Maeder and Zuberbühler). A general program for spectrophotometric data with for an early "desk-top" computer (HP 9835). Further developed and gained wide acceptance.
1985 Superquad (Gans, Sabatini and Vacca). Used implicit differentiation as in Psequad, though originally developed independently. Mainframe computer program. Over 1000 citations.
1988 Superquad (2) (Pettit) A version for the IBM PC (as it was known then) with a simple data editor integrated into the program.
1992 Hyperquad (1) (Gans, Sabatini and Vacca) An extension of Superquad to allow both potentiometric and spectrophotometric data to be treated. (Mainframe program)
1993 EQNMR (Hynes) The first general-purpose program for NMR data.
1995 HypNMR (Gans, Sabatini and Vacca) Our program for NMR data.
1996 Hperquad (2) A suite of 12 linked MS-DOS programs including data preparation and analysis modules.
1997 Equispec (Maeder) A development from Specfit.
1999 pHab (Gans, Sabatini and Vacca) Designed for spectroscopic data at measured pH. Windows application.
2000 Hyperquad2000 All modules now integrated into a single Windows application.
2004 HypNMR2004 An all-singing all dancing Windows application.
2005 HyperQuad Data file A single data file to hold the data for all stability constant programs. Is used in Hyperquad2006
2006 HypDH Determination of stability constants and reaction enthalpies from calorimetric data (under development).
2008 Hyperquad2008 Program written entirely in Visual basic. New structure with "live" data.

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