StatThermo® - new software for calculation of thermodynamic functions

Dunaev A.M.; Kudin L.S.

DOI: 10.6060/tcct.2017604.5490 УДК: 544.31

STATTHERMO® - НОВАЯ ПРОГРАММА ДЛЯ РАСЧЕТА ТЕРМОДИНАМИЧЕСКИХ ФУНКЦИЙ

А.М. Дунаев, Л.С. Кудин

Анатолий Михайлович Дунаев *, Лев Семенович Кудин

Кафедра физики, Ивановский государственный химико-технологический университет, Шереметевский просп., 7, Иваново, Российская Федерация, 153000. E-mail: amdunaev@ro.ru *

StatThermo - это новое программное обеспечение для расчета термодинамических функций молекул и ионов в состоянии идеального газа по молекулярным постоянным в приближении «жесткий ротатор-гармонический осциллятор». Программа содержит различные встроенные алгоритмы для расчета координат атомов большинства простых молекул (с числом атомов N < 8). Разработанное программное обеспечение может проводить расчеты для двух референтных температур (0 или 298,15 K) и различных давлений. Одной из отличительных черт StatThermo является возможность учета энергии и степени вырождения низколежащих электронных уровней. Программа была протестирована на различных органических и неорганических молекулах, в результате чего были получены следующие средние погрешности расчетов: 0,05 кДжмоль-1 (H°°T)-H°°0)), 0,01 Джмоль-1 K-1 (Ф°(Т)) и 0,002Джмоль-1 •K-1 (S °(Т)). Программа также обладает способностью проводить аппроксимацию готовых наборов термодинамических функций, введенных пользователем. Аппроксимация производится при помощи полиномиальной функции методом LU-раз-ложения. Большой набор функциональных возможностей, гибкие параметры расчета и способность экспорта в виде макросов Visual Basic делают StatThermo мощным инструментом для термодинамических расчетов. StatThermo может взаимодействовать с серверами наиболее широко распространенных табличных процессоров, таких как MS Office и OpenOffice для экспорта полученных данных. Программное обеспечение может обрабатывать выходные файлы наиболее популярных программ для квантово-химических расчетов, среди которых Gaussian, Gamess, FireFly, Jaguar, MolPro, CFour, NWChem, ORCA, Priroda, PSI4, Q-Chem и VASP. Мультиязычная и кросс-платформенная поддержка делают StatThermo доступной для широкого круга пользователей.

Ключевые слова: термодинамические функции, программное обеспечение, жесткий ротатор-гармонический осциллятор, MS Excel, Open Office

UDC: 544.31

STATTHERMO® - NEW SOFTWARE FOR CALCULATION OF THERMODYNAMIC

FUNCTIONS

A.M. Dunaev, L.S. Kudin

Anatoliy M. Dunaev *, Lev S. Kudin

Department of Physics, Ivanovo State University of Chemistry and Technology, Sheremetevskiy ave., 7, Ivanovo, 153000, Russia E-mail: amdunaev@ro.ru *

A new software StatThermo for calculation of thermodynamic functions using the molecular constants in Rigid Rotator - Harmonic Oscillator approximation has been developed. Program includes various prebuilt algorithms to calculate atom coordinates for the majority of simple compounds (with a number of atoms N < 8). The developed software can make the calculation for two reference temperatures (0 or 298.15 K) and different pressures. One of the prominent features of StatThermo is taking into account the low-lying electronic levels. The software was tested on different organic and inorganic molecules and average errors was found as follows: 0.05 kJmol-1 (H°(T)-H°(0)), 0.01 Jmol-1K-1 (Ф°(Т)), and 0.002 Jmol-1K-1 (S°(T)). The program can also approximate by the polynomial the thermodynamic functions defined by user. A wide range of functional possibilities, flexible parameters of calculation, and feature of export results in the Visual Basic macro do the StatThermo powerful software for thermodynamic computations. StatThermo can connect to the MS Office and OpenOffice servers for the export of calculated data. The software can treat the Gaussian, Gamess, FireFly, Jaguar, MolPro, CFour, NWChem, ORCA, Priroda, PSI4, Q-Chem, and VASP output files. A multilingual and cross-platform support makes the StatThermo accessible for a lot of users.

Key words: thermodynamic functions, software, rigid rotator - harmonic oscillator, Gaussian, MS Excel,

Open Office

Для цитирования:

Дунаев А.М., Кудин Л.С. StatThermo® - новая программа для расчета термодинамических функций. Изв. вузов.

Химия и хим. технология. 2017. Т. 60. Вып. 4. С. 40-46.

For citation:

Dunaev A.M., Kudin L.S. StatThermo® - new software for calculation of thermodynamic functions. Izv. Vyssh. Uchebn.

Zaved. Khim. Khim. Tekhnol. 2017. V. 60. N 4. P. 40-46.

INTRODUCTION

Nowadays owing to a great progress in quantum chemistry many structural and energetic data on different organic and inorganic molecules were appeared. Unfortunately, existing databases [1-3] on thermodynamic properties of individual substances include restricted number of objects only and do not cover the requests of specialists. Statistical thermodynamics enables to carry out the calculations of thermodynamic functions on the basis of theoretical data of quantum chemistry. However, to date a cross-platform multilingual software for calculation of thermodynamic functions on molecular constants and energy levels of molecules is absent. In this regard, the development of such program forming thermodynamic databases and convenient for a wide range of users is a topical problem.

This paper presents a description of a new program StatThermo [4] for calculating thermodynamic functions of the molecules in the state of ideal gas on the base of molecular parameters.

METODOLOGICAL ASPECTS

The developed software uses the Rigid Rotator -Harmonic Oscillator (RRHO) approximation. The fundamental constants and atomic masses were taken from [5]. The main formulas were taken from [6, 7]. The software was written on the Object Pascal language us-

ing Lazarus IDE [8]. The program structure was based on the principles of an object-oriented programming. The hierarchy of classes is shown on Fig. 1.

TD3Coord

TFi jnc TLevel

TK 1ol

Fig. 1. The hierarchy of classes used in the StatThermo Рис. 1. Иерархия классов в StatThermo

The TAtom class included the atom designation, the mass, and the Cartesian coordinates gives the description of atom properties. The array of atoms forms the class TMol corresponding to selected molecule. The fields of the TMol class include: type of molecule (nonlinear or linear), point group of symmetry, arrays of internuclear distances, angles and vibrational frequencies, symmetry number, molecular weight, and number of atoms. The low-lying electronic energy levels and their degeneracy factors are also given. Resulting thermodynamic functions of internal energy U(T), enthalpy increment H(T), free energy Ф(Г), Helmholtz energy F(T), isobaric and isochoric specific heat capacity Cp(T) and Cv(T), and entropy S(T)) form the two-dimensional array (temperature - function values).

RESULTS AND DISCUSSION

The user interface is very convenient (Fig. 2). A distinctive feature of the program is availability of various prebuilt algorithms to calculate atom coordinates for the majority of simple compounds (with a number of atoms N < 8) included. User could simply choose a number of atoms, the structure of molecule, and insert the molecular constants. It is very convenient because literature data contain molecular constants in this format. Nevertheless, user can input the geometry of the molecule manually. To do this user must click on "Manual input of geometry" checkbox. The table containing fields with the masses of atoms and their coordinates will appear. Also user must set the type of molecule (nonlinear or linear) as well as the symmetry number.

The StatThermo has its own format of files of input data (*.stf). User can save the initial parameters of calculation by clicking on "Save initial data" button. The software also supports the Gaussian [9], Gamess [10], FireFly [11], Jaguar [12], MolPro [13], CFour [14], NWChem [15], ORCA [16], Priroda [17], PSI4 [18], Q-Chem [19], and VASP [20] output files as input data along with its own format.

The developed software produces calculation for two reference temperatures (0 or 298.15 K) and different pressures (101325 Pa by default). Also user can select the thermodynamic functions for calculation into the corresponding checkboxes, set the temperature interval and increment.

As was recently shown [21] the electronic states are very important for evaluating of thermodynamic functions. The possibility to take into account the low-lying electronic states is one of the remarkable features of the program. It should be noted that software treats all low-lying electronic levels instead of simple splitting of ground state.

After the calculation the window automatically switches on next tab "Results". Here in the table the calculated thermodynamic functions are shown.

However to work with tabulated data is not so convenient as with polynomials. For this purpose the feature of approximation of the thermodynamic functions was added to the program. The software approximates the thermodynamic functions by the polynomial recommended in [7]:

Func(T) = alnx + bx~2 + cx+ dx + ex2 + fx3,

(x = T/1000), (1)

here Func(T) is a thermodynamic function.

The StatThermo can also approximate the functions in any specified temperature range. The reference pressure can also be adjusted. To find the coefficients of polynomial (1) the LU-decomposition is used.

The obtained polynomial together with tabulated data can be exported into the MS Excel or OpenOffice (LibreOffice) Calc. To export these results as macro of Visual Basic user must enter the macro name and push the "Export" button. After the export the chosen application will be open and new macro file will be linked to it. All exported files are saved in the "Export" folder inside the main directory of StatThermo.

User can also approximate by the polynomial its own functions. To do this the user must clear the results table and paste into it the prepared functions. First column always must contain the temperature values, other columns should correspond to the order of functions in results table (H°(T) - first, O0(T) - second, etc.).

Fig. 2. User interface of StatThermo Рис. 2. Интерфейс StatThermo

The software StatThermo has been tested by comparison the calculation results of the thermodynamic functions for reference molecules with those from the databases [1, 2]. They were chosen to cover more wide set of input parameters (linear or nonlinear structure, different point group of symmetry, number of atoms, and electronic levels). Table 1 contains the molecular constants for selected molecules from [7].

The relative differences of tabulated [2] and calculated thermodynamic functions are collected in Table 2. Analysis of Table 2 shows a good agreement between the tabulated values and calculated by Stat-Thermo. None of the errors exceeds the 1%. The aver-

age errors of StatThermo are as follows: 0.05 kJ-mol 1 (H°(T)-H°(0)), 0.01 J-moH•K-1 (0°(T)), and 0.002 J-mol-1-K-1 (S°(T)). Mainly they explained by the divergence of the fundamental constants.

Table 1

Molecular constants of reference molecules

Molecule Point group of symmetry Internuclear distances, Á Angles Vibrational frequencies, cm 1 Electronic levels, cm-1

GeO2 DMh 1.65 180.0 860; 280(2) 1); 1062 0(1) 1)

GeCl2 C2v 2.186 100.4 395; 160; 370 0(1)

Be2O DMh 1.4 180.0 620; 320(2); 1200 0(3)

Na2F2 D2h 2.08 95.0 406; 229; 271; 176; 350; 371 0(1)

АЫб D2h 2.449 (rt)2); 2.634 (rr) 115.0 (at); 99.6 (ar) 340; 145; 93; 42; 20; 310; 82; 82; 415; 90; 13; 405; 54; 291 0(1)

Cel3 Dsh 2.92 120.0 142; 27; 191(2); 35(2) 0(2); 40(2); 110(2); 2200(8)

COOH Ci r(O-H) = 0.97; r(C-O) = 1.32; r(C=0) = 1.23 107 (C-O-H); 123 (O-C-O) 3316; 1797; 1261; 1088; 620; 615 0(2)

CBr4 Td 1.942 109.28 268; 122(2); 680(3); 182(3) 0(1)

Notes: 1) - the degeneracy of level or vibrational frequency is given in parentheses, 2) - the values corresponding to the torsion and ring attributes are designated by "t" and "r", respectively

Примечания: 1) - в скобках дана степень вырождения частот колебаний, 2) - величины, соответствующие торсионному и кольцевому участку, обозначены как "t" и "r" соответственно

Table 2

Comparison of tabulated and calculated by StatThermo (ST) thermodynamic functions of some molecules Таблица 2. Сравнение табличных и рассчитанных StatThermo (ST) термодинамических функций неко-

торых молекул

Molecule T, K Thermodynamic function Error, %

[2] ST

H(T)-H(0), kJ-mol-1

GeO2 298.15 11.268 11.258 0.091

1000 50.344 50.330 0.028

GeCl2 298.15 13.277 13.277 0.002

1000 53.125 53.123 0.003

Be2O 298.15 11.190 11.190 -0.003

1000 50.460 50.451 0.018

Na2F2 298.15 16.682 16.682 0.001

1000 73.194 73.191 -0.004

Al2l6 298.15 40.920 40.598 -0.786

1000 166.836 166.38 -0.272

CeIs 298.15 22.018 22.018 0.001

1000 81.581 81.596 0.019

COOH 298.15 10.813 10.813 -0.003

1000 52.059 52.046 0.024

CBr4 298.15 20.365 20.365 0.001

1000 91.818 91.804 0.015

Ф(Г), J-moH-K-1

GeO2 298.15 203.374 203.365 0.004

1000 256.677 256.655 0.009

GeCl2 298.15 251.185 251.191 -0.002

1000 310.872 310.877 -0.002

Be2O 298.15 190.312 190.265 0.025

1000 243.681 243.628 0.022

Na2F2 298.15 241.840 241.838 -0.001

1000 321.247 321.242 -0.002

Al2l6 298.15 452.271 453.215 0.209

1000 638.732 638.767 0.005

Cel3 298.15 357.992 357.990 -0.001

1000 452.275 452.280 0.002

COOH 298.15 215.355 215.398 -0.020

1000 267.640 267.675 -0.013

CBr4 298.15 289.643 289.641 0.001

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

1000 387.647 387.631 0.004

S(T), J-mol-1-K-1

GeO2 298.15 241.134 241.124 0.004

1000 307.020 306.985 0.011

GeCl2 298.15 295.716 295.722 -0.002

1000 363.998 364.000 -0.001

Be2O 298.15 227.843 227.798 0.020

1000 294.141 294.078 0.021

Na2F2 298.15 297.792 297.790 -0.001

1000 394.441 394.434 -0.002

Al2l6 298.15 589.517 589.382 -0.023

1000 805.567 805.149 -0.052

Cel3 298.15 431.841 431.840 0.000

1000 533.856 533.883 0.005

COOH 298.15 251.622 251.666 -0.017

1000 319.700 319.721 -0.005

CBr4 298.15 357.948 357.945 0.001

1000 479.465 479.435 0.006

The software can work under the MS Windows operating system (XP, Vista, 7, 8, 10) as well as Linux (Debian based distributives). Both x86 and x64 architecture is supported. The minimal system requirements depend on chosen exporting server (MS Excel XP, MS Excel 2007, OpenOffice Calc etc.). If user won't use the export function it is enough 512 Mb RAM, 1 GHz processor frequency, and 3 Mb free disk space.

The StatThermo has multilingual support: English and Russian language available. Nevertheless, user interface is easily translatable. In "languages" folder user can duplicate the STATThermo.en.po file, change the language code suffix, and edit the file in any appropriate editor (PoEdit [22], for example).

CONCLUSION

The new software StatThermo for calculation of the thermodynamic functions of molecules in the state of ideal gas using the molecular constants has

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9. Frisch M.J., Trucks G.W., Schlegel H.B., Scuseria G.E., Robb M.A., Cheeseman J.R., Scalmani G., Barone V., Mennucci B., Petersson G.A., Nakatsuji H., Caricato M., Li X., Hratchian H.P., Izmaylov A.F., Bloino J., Zheng G., Sonnenberg J.L., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Vreven T., Montgomery J.A., Jr., Peralta J.E., Ogliaro F., Bearpark M., Heyd J.J., Brothers E., Kudin K.N., Staroverov V.N., Kobayashi R., Normand J., Raghavachari K., Rendell A., Burant J.C., Iyengar S.S., Tomasi J., Cossi M., Rega N., Millam J.M., Klene M., Knox J.E., Cross J.B., Bakken V., Adamo C., Jaramillo J., Gom-perts R., Stratmann R.E., Yazyev O., Austin A.J., Cammi R., Pomelli C., Ochterski J.W., Martin R.L., Morokuma K., Zakrzewski V.G., Voth G.A., Salvador P., Dannenberg J.J., Dapprich S., Daniels A.D., Farkas Ö., Foresman J.B., Ortiz J.V., Cioslowski J., Fox D.J. Gaussian 09, Revision

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been developed. Program has a lot of prebuilt algorithms for calculation of the geometry of small molecules, takes into account low-lying electronic states, and can perform calculation for different reference temperatures and pressures. A wide range of functionality, flexible parameters of calculation and possibility to approximate and export results as a macro do the StatThermo powerful software for thermodynamic chemical calculations. Low hardware requirements, multilingual and cross-platform support makes the StatThermo accessible for a lot of users. To download the StatThermo please visit official website www.isuct.ru/htms/en/statthermo.

Acknowledgments. This work was supported by the Ministry of Education and Science of the Russian Federation № 4.32.32.2017/pp (in the framework of Government order). Authors also acknowledge Dr. Vladimir Motalov and Dr. Dmitry Sergeev for testing of the developed software.

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