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M. Frenkel
EXPERIMENTAL DATA VALIDATION AND PROPERTY PREDICTION MODELS IN THERMODYNAMICS*
Introduction. Most of the reliable and currently-used prediction methods for thermo-physical and thermochemical properties (with the exception of ab initio) have been developed on the basis of experimental data reported in the open literature. It is, therefore, well understood that discrepancies and errors in the experimental data set used can cause significant problems in the development of robust prediction models for thermodynamic properties ("garbage in — garbage out" computational problem). However, enormous growth in the amount of experimental information reported in the last 20 years in the public domain for thermodynamic properties, while obviously being welcomed as part of the overall scientific discovery process, represents new challenges for property modeling. Indeed, according to statistics accumulated at the Thermodynamics Research Center (TRC) of the U. S. National Institute of Standards and Technology (NIST), the total number of the experimental data points for thermophysical and thermochemical properties published by five major journals in the field (Journal of Chemical and Engineering Data [1], The Journal of Chemical Thermodynamics [2], Fluid Phase Equilibria [3], Thermochimica Acta [4], and the International Journal of Thermophysics [5]) is currently growing by more than a factor of 2 every 10 years (Fig. 1, see also [6]). Such a dramatic increase of productivity in generating experimental information is supported by progress in measurement science, including commercial production of high precision measuring devices for temperature, pressure, and concentration, as well as fully automated control and data acquisition systems. In turn, this trend has led to almost complete elimination of in-house built apparatus from laboratories worldwide involved in measuring thermodynamic and transport properties, resulting in a further increase of productivity of experimental work. Arguably, this increase in productivity in many instances is, unfortunately, accompanied by a decrease of a quality of experimental work because, in part, running highly automated commercial apparatus does not usually require involvement of personnel with high expertise and in-depth knowledge. Shortening of the time for scientific article preparation, as well as the extensive use of multi-step automated technical editing software tools are often additional contributing factors to incomplete or misleading representation of metadata associated with reported thermodynamic quantities. In many instances the traditional peer-review process fails to adequately address these problems, as it is physically impossible to independently assess the high volume of presented experimental information within the limited time available for a review. The results of the analysis of more than 1000 articles published in highly reputable journals presenting experimental data for thermophysical and thermochemical properties showed that at least 10 % of these articles contained some erroneous information either for numerical or metadata [7]. This
Michael Frenkel — PhD, professor, director of the Thermodynamics Research Center at the U.S. National Institute of Standards and Technology, Boulder, Colorado, USA; e-mail: michael.frenkel@nist.gov
* This contribution of the National Institute of Standards and Technology is not subject to copyright in the United States.
Products or companies named here are cited only in the interest of complete technical description, and neither constitute nor imply endorsement by NIST or by the US government. Other products may be found to serve as well.
© M. Frenkel, 2013
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Fig. 1. Total number of experimental data points for thermophysical and thermochemical properties published by five major journals in the field from 1990 to 2011 displayed in order from left to right:
International Journal of Thermophysics, Thermochimica Acta, Fluid Phase Equilibria, The Journal of Chemical Thermodynamics (all white bars), Journal of Chemical and Engineering (black bar); see also [6]
situation is even more serious when taking into account ever increasing efficiency of data dissemination.
There are numerous examples of the truly devastating impact of erroneous experimental data set selection on the development of prediction models. One example was the use of a grossly incorrect value of the enthalpy of sublimation of cubane derived from experimental measurements of the vapor pressure [8] in development of the MM3 force field [9], as well as for validation of results of quantum mechanical calculations [10, 11]. Cubane was also used as a reference compound for calculation of enthalpies of formation of other highly strained hydrocarbons via homodesmic or isodesmic reactions. Interestingly, doubts in the validity of the originally reported experimental data in this case were raised based on a comprehensive analysis of the thermodynamic properties of the mono-, bi-, and multicyclic compounds [12] and subsequently confirmed by new measurements [13].
Another principal problem commonly associated with reported experimental data is either absence or inconsistent representation of uncertainties that are used in development of advanced prediction models. A study [14] conducted at NIST TRC involving review of reporting practices for uncertainty of experimentally measured critical temperature data showed that out of about 600 articles published between 1940 and 2001 there was only one [15] (!) that provided a complete uncertainty analysis with consideration of all possible contributing factors, including sample purity.
In the present paper, we provide an overview of the systems and software tools designed for experimental data validation, and experimental data-driven technologies for thermophys-ical property prediction developed recently at NIST TRC.
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Experimental Data Validation.
Guided Data Capture. One of the major sources of error in propagating experimental data from original sources to end-users is attributed to data capture and storage. Guided Data Capture software (GDC) [16] has been designed to serve as a data-capture expert by guiding the extraction of information from the literature, ensuring completeness of the information extracted, validating the information through data definition, range checks, etc., and guiding uncertainty assessment to ensure consistency between compilers with diverse levels of experience. GDC consists of three major components providing functionalities for: 1) metadata processing (phases, constraints, variables, units, uncertainties); 2) tabulated numerical data processing; and 3) graphical representation of the numerical data. GDC is capable of generating two types of the outputs: text-based and ThermoML-based. Ther-moML [17, 18] was developed at TRC in cooperation with experts around the world and later was accepted by the International Union of Pure and Applied Chemistry (IUPAC) [19] as its standard [20] for thermophysical and thermochemical property data communications. Text-based GDC output files are directly loaded into the SOURCE Data Archival System [21, 22], a comprehensive data storage facility for thermophysical properties of pure compounds, binary mixtures and ternary mixtures, as well as thermochemical properties of chemical reactions. ThermoML-based output files can be used for the purposes of data exchange, support of collaborative data-intensive scientific and engineering projects, and establishment of well structured data collection systems.
A key feature of GDC is the capture of information in close accord with customary original-document formats and leaving conversion to formalized data records and ThermoML formats within the scope of the software procedures. GDC is primarily driven by pull-down menus and supported by predefined enumeration lists to avoid typing, which is commonly a significant source of erroneous data processing. The GDC software completely relieves the compiler of the need for knowledge related to the structure of the SOURCE Data System or ThermoML formats, thereby eliminating common errors related to data types, length, letter case, and allowable codes.
GDC supports the unique capability of independent assessment of the combined expanded uncertainties [23-25] for experimental thermophysical and thermochemical property data as it was interpreted for the field of thermodynamics by Chirico et al [26] based on the information provided in the original source and taking into account the purity of the sample studied, the quality of the experimental apparatus used, and propagation of the uncertainties from variables and constraints to the target property. GDC is also designed to detect inconsistencies of various components of the data information reported within a single original source document [7].
NIST ThermoData Engine. The NIST ThermoData Engine (TDE) software [27] represents the first full-scale implementation of the concept of dynamic data evaluation for thermophysical properties [28, 29]. This concept requires large electronic databases capable of storing essentially all relevant experimental data known to date with metadata and uncertainties. The combination of these databases with expert-system software, designed to automatically generate recommended property values based on available experimental and predicted data, leads to the ability to produce critically evaluated data dynamically or on demand.
TDE has evolved from its first release, limited to thermophysical properties of pure compounds [30] to on-demand generation of equations of state (EOS) [31], dynamic web-based updates of local data resources [31] through the TRC-SOURCE data storage system [21, 22], support for binary mixtures, including phase equilibria [32], properties of chemical
reactions [33], experiment planning and product design tools [34], dynamic web-based dissemination of properties of pure components through the NIST Web Thermo Tables [35], evaluation of properties of ternary mixtures, including vapor-liquid equilibrium (VLE) and liquid-liquid equilibrium (LLE) generated through on-demand evaluation of the binary subsystems [36], and most recently properties of multi-component material streams and functionalities for solvent design [37]. TDE is used in a multitude of applications including chemical process and product design [38, 39]. It is also a core component in implementation of the concept of Global Information Systems in Science with application to the field of thermodynamics [6].
TDE enforces consistency between all thermodynamically related properties within their respective ranges of the combined expanded uncertainties, as well as consistency between related properties of pure compounds, multi-component mixtures, and chemical reactions. In combination with the fact that TDE operates over the "entire body of knowledge" accumulated in the last 200 years in the public domain and collected in the SOURCE Data Archival System, it provides a unique opportunity to determine on an algorithmic level whether data reported in a given original source are consistent with the current state of knowledge in the field.
Global Data Validation Process. Scientific journals represent the dominant venue for reporting new contributions to the knowledge in the field, in part, due to a well-established peer-review process. However, in light of the dramatically increasing volume of information coming to the public domain in science, in general, and in thermodynamics, in particular, the traditional peer-review process fails in many instances, as was previously discussed [7], leading to publication of data that are grossly erroneous and, at times, inconsistent with the fundamental laws of nature. To address these deficiencies, a new global data validation process in thermodynamics [7] was developed as a result of cooperation between NIST TRC and five major journals in the field [1-5]. This process is based on a variety of software tools developed at NIST TRC, taking advantage of the Guided Data Capture software [16] enforcing consistency of information reported within a single new article, and ThermoData Engine [27, 30-37] testing consistencies within the ranges of assigned uncertainties between the information reported in a single new article and all other relevant information contained in the SOURCE Data Archival System [21, 22], as well as results of on-demand critical data evaluation performed by the TDE.
Initial implementation of this process is illustrated in the Fig. 2 [7]. After completion of the peer-review process, this flow structure allows for checking of experimental data to be published for (a) integrity (GDC communication line) and (b) consistency with the recommended data evaluated on the basis of the entire body of knowledge available to date (TDE communication line). Consistency is checked for the particular property, as well as for those linked through thermodynamic identities and correlations. At the end of the process, the validated data are converted to the ThermoML format and posted on the Internet as open domain, free access ThermoML Web Archive [40] available for download and further exploration by end-users. This process was made a mandatory part of the overall article submission procedure in a joint statement of the 18 editors stating, in part: "We, the Editors, are convinced that this additional data review will substantially benefit the scientific and engineering communities because of the increase in quality and usefulness of the reported experimental data... " [41].
In the last several years this process has been modified a number of times, becoming more streamlined and efficient, but keeping the principal elements without change. Significant further improvement was related to the implementation of the requirement of reporting
Fig. 2. Global thermophysical and thermochemical data validation and delivery process (see also [7])
sample characterization and uncertainty information in tabular form [42] following the IUPAC Recommendations of 2012 formulated by Chirico et al. [43]. NIST TRC support is now envisioned to be split into reports: Literature Report in the beginning of the review process and Data Report at the end of the review process [42]. NIST TRC will enable the authors to generate the Literature Report automatically using the new Web tool called Ther-moLit [44]. The Literature Report can then be submitted by the authors simultaneously with the submission of the article to assure that all necessary and relevant comparisons of the reported new experimental data with those available from the literature are made.
In order to respond to the increasing need of the scientific and engineering communities for experiment planning in the field of thermophysical property measurement science envisioned to undergo transformation "from accuracy to fitness for purpose" [45] and to minimize redundant and unnecessary measurements, the free access-open domain Web tool ThermoPlan [46] was designed and developed at NIST TRC. ThermoPlan provides recommendations for the relative merit of a given measurement via assessment of the existing body of knowledge, including availability of experimental thermophysical property data, variable ranges studied, associated uncertainties, state of prediction methods, and availability of parameters for deployment of prediction methods. This Web application supports utilities for the assessment of specific property measurements for pure and binary chemical systems,
2D Chemical Structure Definition
the broader data needs of pure systems, and recommendations for binary mixture measurements that could extend the current UNIFAC prediction model. The algorithmic approach to experiment planning implemented in ThermoPlan is based on the TDE technology [34].
Experimental Data Quality and Property Prediction in Thermodynamics. While in the discussion above we focused on issues related to the quality of experimental ther-mophysical and thermochemical property data and the means of its validation and improvement, this part of the article will provide two examples of prediction methods for thermody-namic properties recently developed at NIST TRC [QSPR (Quantitative Structure-Property Relationship)-based and UNIFAC (UNIversal Functional Activity Coefficient)-based] that take advantage of well-defined data uncertainties and data quality tests, as well as an example of simultaneous use of experimental data for multiple properties to develop transferrable force fields for Monte Carlo calculations.
QSPR-SVM (Support Vector Machines) Methodology for Critical Properties. The effort of developing reliable QSPR technology at NIST TRC for prediction of critical constants based on large datasets was recently described in detail by Kazakov et al. [47]. QSPR is one of the most widely used methodologies for data mining and correlation development in pharmaceutical and agricultural applications [48]; it is also gaining use in empirical modeling of a wide variety of physical properties [49-51]. The basic idea of QSPR is to relate a property of interest to molecular numerical features derived theoretically from chemical structures. These numerical features are referred to as descriptors. The relationship is established through regression analysis using large collections of data, which makes this approach particularly attractive for data mining. In the study cited, only original experimental data and their combined expanded uncertainties from SOURCE Data Archival System [21, 22] for critical temperature of 865 compounds were used to develop correlations.
Generation of molecular descriptors requires knowledge of 3-dimensional structures and associated molecular properties obtained from quantum-chemical calculations. Those are obtained as follows (Fig. 3). One starts with two-dimensional structure representations that include stereo assignments where applicable. Then, an initial pool of three-dimentional structures is generated using a variety of distance geometry treatments and molecular mechanics optimization tools. Further refinement of the conformer population is performed with systematic rotor searches for small molecules and simulated annealing procedures for the systems involving many ro-tatable bonds or large flexible rings. Finally, the produced three-dimensional structures are optimized with the use of quantum-chemical methods and a single representative conformer
Initial 3D Structure(s) (distance geometry and molecular mechanics)
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Conformer Generation (systematic or via simulated annealing)
►^^InCHVerification"^^
Optimized 3D Structures (quantum chemistry)
-►Ci^InChVerification
Single Representative Conformer (lowest energy or lowest free energy)
c
Descriptors
Fig. 3. QSPR descriptors generation process based on 3D molecular structures
is chosen for descriptor generation. Throughout this process, the InChI (International Chemical Identifier) [22, 52] keys were produced for validation purposes.
The Support Vector Machines (SVM) machine learning approach [53] was used for regression analysis. Uncertainty analysis of the predicted data was conducted using Monte Carlo sampling procedures [54] commonly used to evaluate the propagation of uncertainty through systems of such complexity, with account for the uncertainties of the experimental data used in the regression. It is important to note that experimental data uncertainties are commonly ignored in the development of QSPR-based correlations.
The results obtained with the technology described above [47] are shown to be far superior to those calculated with commonly used group contribution (GC) prediction methods [55-58] (Fig. 4).
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QSPR-SVM vs Joback
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Fig. 4- Comparison of results obtained with the QSPR-SVM developed at NIST TRC and group contribution (GC) methods for prediction of critical temperature (Tc): each group of bars defined by the deviation range, the order of bars is QSPR-SVM (training/validation set; small crosshatch), QSPR-SVM (testing set; solid black), GC method (training/validation set; solid white), and GC method (testing set; large crosshatch); the GC method considered is shown in each figure — Joback—Joback method
[55]; CG — Constantinou—Gani method
[56]; WJ — Wilson—Jasperson method [57]; MP — Marrero—Pardillo method [58] (see also [47])
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UNIFAC Prediction Models and Vapor—Liquid Equilibria Experimental Data Quality. Vapor—liquid equilibrium (VLE) data are critical for design and operation of separation processes for fluid mixtures. These data require careful reporting and interpretation, due to the complexities of the systems studied (i.e., multiphase, multicomponent systems). In turn, this creates a significant probability for VLE data being reported either erroneously or incompletely, leading to development of low fidelity models used for chemical process design [59]. In addition to the combined expanded uncertainties characterizing generally quality of the VLE data, as well as other thermophysical properties [26], VLE data quality analysis should include analysis of their compliance with two principal thermodynamic constraints. One is related to the restrictions following from the Gibbs—Duhem equation, and the other is concerned with enforcement of the consistencies between the binary mixture
VLE data and pure compound vapor pressures. A number of consistency tests based on the Gibbs—Duhem equation have been developed, providing opportunities for screening VLE data sets on a pass/fail basis. They include the Herington test [60], Van Ness test [61], Point test (Differential test) [62, 63], and Infinite Dilution test [62, 63]. Unfortunately, as we have shown previously, a particular VLE data set might pass some consistency tests and fail some others (see Table, [59, 64-68]), which leads to very subjective judgments regarding its quality. In order to address this problem, quantitative assessment of VLE data quality encompassing four tests designed for compliance with the Gibbs—Duhem equation, as well as for consistency of the VLE data with the vapor pressure of relevant pure compounds, was developed at NIST TRC:
QvLE = ipure(itesti + Ftest2 + Ftest3 + Ftest4), 0 < QvLE ^ 1, (1)
where QVLE is an overall numerical quality factor for a VLE data set; Fpure is a quality factor characterizing consistency between the VLE data and vapor pressures for the pure compounds, and Ftest1, Ftest2, Ftest3, Ftest4 are quality factors characterizing results of the consistency tests for Herington test, Van Ness test, Point Test, and Infinite Dilution test, correspondingly.
The usefulness of the numerical VLE data quality factor is demonstrated (Fig. 5, [59]) with the analysis of the isobaric data set methanol-ethanol reported in the literature [69] with erroneously reversed identification of the mixture compounds.
The concept of numerical data quality for VLE data has been successfully used in developing new methods for evaluating UNIFAC parameters [70]. For the regression of UNIFAC parameters, the following adequacy (objective) function is used:
Atotal = WVLE^VLE + »HE^HE + »AC A AC, (2)
where AVLE, AHE and Aac are the adequacy functions for VLE, excess enthalpy, and activity coefficients, respectively, and w represents a weighting factor associated with each quantity. Definitions of AHE and Aac include combined expanded uncertainty in the measured variable for each experimental data point, while the definition of AVLE includes both combined expanded uncertainty of the measured variable for each experimental data point, as well as data quality factor for the whole data set.
Deployment of the procedure described here led to establishment of the two new modifications of the UNIFAC approach: NIST-UNIFAC and NIST-KT-UNIFAC [70]. The important distinctive feature of the new method is the use of experimental data with assessed quality, which allows regression without the need for labor-intensive manual pre-screening. This approach provides for simple, rapid, and continuous improvement of the interaction parameters and for extension of the parameter matrix based on the ever increasing experimental literature in the field.
Force Fields for Predictive Monte Carlo Calculations. Molecular simulation methods, including Monte Carlo and molecular dynamics, are gradually emerging as powerful
Comparison of quality assessment results for five data sets selected from the literature for ethanol + water [59]
Data Set Data Test*
[Reference] Type 1 2 3 4
[64] Isothermal - - - -
[65] Isobaric + - - -
[66] Isothermal - + - -
[67] Isothermal - - - +
[68] Isothermal + + + +
* Test 1 is the Herington test; test 2 is the Van Ness test; test 3 is the Point test; test 4 is the Infinite Dilution test; "+" indicates test passage; "—" indicates test failure.
Fig. 5. Comparison of UNIFAC predictions and experimental data for isobaric methanol + ethanol system at p = 101.32 kPa, data from Arce et al. [69]:
UNIFAC predictions (line); experimental values; 1 — liquid composition; 2 — vapor before the correction (a), ethanol (1) + methanol (2), Qvle = 0.02; after the correction (b), methanol (1) + ethanol (2), Qvle = 0.62 (see also [59])
tools for quantitative description of thermodynamic properties [71]. The issue of critical importance for quantitative predictions is the availability of a well-calibrated force field.
Determination of force field parameters requires significant computational resources and substantial human expertise. To accommodate the anticipated need in large-scale modeling, the formal procedures for force field development promoting automation of the process and decrease of the degree of expert involvement using TOWHEE code [72] were developed at NIST TRC [73]. The focus of this work was calculation of the VLE properties of fluorinated hydrocarbons. Optimization of the Lennard-Jones parameters was carried out using available experimentally derived critically evaluated data [37, 74] for saturated vapor pressure, enthalpy of vaporization, and liquid density. Parameter optimization was performed through use of a solution mapping methodology [75-77].
In order to decrease the computational time, the following bootstrap procedure was adopted (Fig. 6). First, simulations are performed at four temperatures for a compound
Force Field Parameters
Fig. 6. A bootstrap procedure used at NIST TRC [73] for optimization of force field parameters for Monte Carlo simulation of thermophysical properties of fluorohydrocarbons
that has four adjustable parameters. Using the results obtained, preliminary optimization of these parameters is carried out. The preliminary values of the parameters are used to tune the solution mapping boundaries for the second compound with the same parameters. Then, based on the results for both compounds, optimized parameters are obtained. These optimized parameters are then utilized for the simulation of molecules that contain as-yet un-optimized parameter sets.
The results of the Monte Carlo molecular simulations utilizing the generated parameters agree well with associated reference equations of state [37, 74]. The formal nature of the proposed approach opens possibilities of automated generation of force field parameters in the future.
Conclusions.
1. Components, structure, and software tools for a global validation process for experimental data in the field of thermodynamics are reviewed.
2. QSPR-based and UNIFAC-based prediction methods developed at NIST TRC are discussed with the emphasis on the importance of the use of the combined expanded uncertainties of the experimental data selected and performance of the phenomenological data quality tests to obtain high fidelity predictive models.
3. A formal procedure for generation of transferrable force fields for Monte Carlo molecular simulations with simultaneous use of well-defined experimental data for a number of properties (liquid density, vapor pressure, enthalpy of vaporization) is described for the chemical class of fluorohydrocarbons.
It is my distinct pleasure to contribute this paper to the issue of the Vestnik dedicated to honor Professor Natalia Smirnova and Professor Alexey Morachevsky whose outstanding contributions to the field of thermodynamics are very well known.
I also want to acknowledge my colleagues Drs. Robert Chirico, Vladimir Diky, Chris Muzny, Andrei Kazakov, Kenneth Kroenlein, and Joseph Magee of the NIST TRC, as well as Professors Jeong Won Kang of Korea university and Eugene Paulechka of Belarussian state university (both guest researchers at NIST TRC) who led the research efforts described in this paper.
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Статья поступила в редакцию 4 октября 2012 г.
