Thermodynamic properties of active pharmaceutical ingredients that are of interest in COVID-19

Abstract

The pure component properties are estimated for active pharmaceutical ingredients that are related or proposed for the treatment of severe acute respiratory syndrome-CoronaVirus-2. These include Baricitinib, Camostat, Chloroquine, Dexamethasone, Hydroxychloroquine, Fingolimod, Favipiravir, Thalidomide, and Umifenovir. The estimations are based on group contribution⁺ (GC) models that contain combined group contribution and atom connectivity index with uncertainties in the estimated property values. The thermodynamic properties that are reported include boiling point, critical temperature, critical pressure, critical volume, melting point, standard Gibb's energy of formation, standard enthalpy of formation, enthalpy of fusion, enthalpy of vaporization at 298 K, enthalpy of vaporization at boiling point, entropy of vaporization at boiling point, flash point, Hildebrand solubility parameter, octanol/water partition coefficient, acentric factor, and liquid molar volume at 298 K. The reported properties are not available in the literature and thereby is an incremental development for reliable process engineering.

1. Introduction

The Global Pandemic COVID-19 also known as Severe Acute Respiratory Syndrome-CoronaVirus-2 (SARS-CoV-2) has affected the entire world. The pandemic has involved clinicians around the globe to put in an unprecedented effort to develop a better healthcare system. To date, the World health organization (WHO) has issued an emergency use listing for the Pfizer COVID-19 vaccine (BNT162b2), AstraZeneca/Oxford COVID-19 vaccine, and Ad26.COV2. S (Johnson & Johnson). The other includes Sputnik V (Russia), Covaxin (India) Corovac (China), Sinopharm (China), Kexing (China), and Moderna (USA). Ramdesivir has been approved by FDA and has shown clinical evidence for specific treatment against SARS-CoV-2 [1]. Furthermore, the different vaccines are being underdeveloped around and are at various stages of trials. This pandemic as of November 2021, has resulted in 261,926,070 confirmed cases with 5220, 328 deaths, and 236,538,716 recovery cases, while among the active cases, 20,038,269 cases are in mild condition and 83,757 cases in a serious or critical condition [2]. Apart from the vaccine, the treatment of the patient by physicians are mainly dependents on the symptom they possess and for the critically ill patients, mainly oxygen therapy or ventilator support is provided. The drugs/ active pharmaceutical ingredient (API) that are presently used or in combination for the treatment of mild symptoms are hydroxychloroquine [3], chloroquine [4] combination of are hydroxychloroquine and azithromycin [5], remdesivir [6], [7], lopinavir [8], [9] and ritonavir [10]. The candidate drugs in combination are still in clinical trials to combat COVID-19 by various pharmaceutical companies. Likewise, antimalarial drugs such as chloroquine by Sanofi (Aralen) and hydroxychloroquine by CaoSanofi (Plaquenil); Mylan, Teva, Novartis, Bayer, Rising Pharmaceuticals. While the antivirals to combat COVID-19 are Remdesivir by Gilead Sciences; Favipiravir by Fujifilm Toyama Chemical and Umifenovir by Pharm standard. The other drugs such as Baricitinib by Concert Pharmaceuticals, Inc., USA; Dexamethasone by the University of Oxford; Phase-II/III) and fingolimod by Fujian Medical University/Novartis; the clinical stage is presently developed to combat COVID-19.

Once the aforementioned drugs are clinically approved, there will be a requirement of their bulk scale production which in turn requires their physical and chemical thermodynamic properties data set. This data is useful for chemical/process engineers to perform tasks or understand the process design, simulation, and optimization for product development. For the estimation of properties of compounds, the Quantity Structure-Property Relationship method can be used that contains an empirical relationship [11]. This method uses the chemical structure of the compound in which atoms, bonds, groups of atoms in the molecule, topological indices, and molecular descriptors are used for the estimation of properties. Over the year's different empirical relationships based on group contribution (GC) methods such as Joback and Reid, Lydersen, Klincewicz and Reid, Constantino and Gani, and Marrero and Gani has been reported for the estimation of properties of pure organic, inorganic, organometallic, polysaccharides, polymers, and lipid compounds and their mixtures [12], [13], [14], [15], [16], [17], [18], [19], [20]. This property includes critical properties [21], [22], [23], parameters of state equations [24], [25] acentric factor [26], [27], activity coefficients [28], vapor pressure [29], [30], liquid viscosity [31], gas viscosity [32], heat capacity [33], enthalpy of vaporization [34], entropy of vaporization [34], normal boiling temperature [20], [21], liquid thermal conductivity [35], gas thermal conductivity [36], gas permeability and diffusion coefficients [37], liquid density [38], [39], surface tension [40] and flash temperatures [41]. The application range and reliability of this method are largely dependent on several factors such as the group definitions used to represent the molecular structure of the pure components; the property model and the quantity and quality of the experimental dataset used in the regression to estimate the model parameters. These GC methods generally do not have all the needed parameters, such as groups and/or their contributions for drugs or larger and complex molecular weight compounds for a specific property. For such special cases, where the molecular structure of a given component is not completely described by any of the available groups, the atom connectivity index (CI) method can be employed together with the GC method to create the missing groups and to predict their contributions. This combined approach leads to the development of a group-contribution+ (GC+) method of a wider application range than before since the missing groups and their contributions can now be easily predicted through the regressed contributions of connectivity indices. The statistical indicators that are used are assessing the parameters for the group contribution method includes standard deviation, average absolute or relative error, and regression coefficient. The inclusion of uncertainty into model parameters are added advantages that are not generally reported. This uncertainty in properties plays an important role in the design and simulations of unit operations such as distillation, liquid-liquid extraction, and others [42]. P.M. Mathias [43] and Hajipour and Satyro [44] have shown the necessity and effect of uncertainties on the optimization calculations using computer-aided software (ASPEN, CAMD, MD). So, in consideration of its importance for reliable and accurate property prediction calculations in engineering design, the present work estimates the properties of important compounds based on GC+ property models. This model is developed by A. S. Hukkerikar et al. [45] that considers a systematic property modeling procedure with an extended CAPEC database that includes new experimental data on various polyfunctional, polycyclic, and complex components with their experimental uncertainty. A total of 3510 compounds that include hydrocarbon, oxygenated, nitrogenated, chlorinated, fluorinated, brominated, iodinated, sulfonated, multifunction compounds are used as data set for the regression and parameter estimation. The model helps to estimate the properties of the compound based on their molecular structure and has shown good accuracy for predicting the properties of the chemical, biochemical, and pharmaceutical compounds.

The present study estimates the pure component properties for 9 APIs that include Baricitinib, Camostat, Chloroquine, Dexamethasone, Hydroxychloroquine, Fingolimod, Favipiravir, Thalidomide, and Umifenovir based on the GC method (Table 1 ). A total of 16 pure component properties are estimated that includes the normal boiling point $\left(T_b\right)$, critical temperature $\left(T_c\right)$, critical pressure $\left(P_c\right)$, critical volume $\left(V_c\right)$, normal melting point $\left(T_m\right)$, standard Gibbs energy of formation $\left(\Delta G_f\right)$, standard enthalpy of formation $\left(\Delta H_f\right)$, normal enthalpy of fusion $\left(\Delta H_{fus}\right)$, enthalpy of vaporization at 298 K $\left(H_v\right)$, enthalpy of vaporization at the normal boiling point $\left(H_{vb}\right)$, the entropy of vaporization at the normal boiling point $\left(S_{vb}\right)$, flash point $\left(F_p\right)$, auto-ignition temperature $\left(T_{AiT}\right)$, Hansen solubility parameters $({\delta }_D,{\delta }_P,{\delta }_H)$, Hildebrand solubility parameter $\left(\delta \right)$, octanol/water partition coefficient $\left(Log{K}_{ow}\right)$, acentric factor (ω), and liquid molar volume at 298 K $\left(V_m\right)$. Thereby, the present work is an important source for knowledge about possible drug candidates or active pharma ingredients that are of prime interest shortly

Table 1.

Details on the compounds.

Molecule Name	Structure	Formula	Molar Mass (g/mol)	CAS No.
Baricitinib		C16H17N7O2S	371.42	1,187,594–09–7
Camostat		C20H22N4O5	398.412	59,721–29–8
Chloroquine		C18H26ClN3	319.872	54–05–7
Dexamethasone		C22H29FO5	392.464	50–02–2
Favipiravir		C5H4FN3O2	157.104	259,793–96–9
Fingolimod		C19H33NO2	307.471	162,359–55–9
Hydroxychloroquine		C18H26ClN3O	335.872	118–42–3
Thalidomide		C13H10N2O4	258.23	50–35–1
Umifenovir		C22H25BrN2O3S	477.414	131,707–23–8

2. Model and methodology

The details about the model development and methodology are reported by A.S. Hukkerikar et al. [45] and Marrero and Gani (MG) [46]. In brief, the estimation of properties is based on a collection of 3 different types of groups viz. 1st order, 2nd order, and 3rd order are present in the compound. In the 1st order, simple molecules are considered that allow estimating the contributions to the property of different classes of organic compounds. The larger group or polycyclic, polyfunctional, and heterocyclic are not be considered here and each group is be kept as small as possible. The entire molecule needs to be covered and no fragments of the given should be left out in 1st order estimations. The overlapping is not allowed and the contributions are independent of the molecule in which the group has occurred. While in the case of 2nd and 3rd order groups, the information/contribution of the molecular fragments or the structural information is considered that otherwise is not provided by the 1st order group. The contributions of the polyfunctional and isomeric compounds are better described by the 2nd order group and the entire molecule need not be covered/described as that in the case of 1st order. Partial overlapping is allowed but one group should not completely overlap the others and in such case the molecule with the complete overlapping need to be considered. 2nd order group fails to provide the information of multi-ring compounds. The information about a multi-ring compound or fused aromatic rings, non-aromatic rings, and non-fused rings joined by chains with the different functional groups are covered in the 3rd order groups. The property prediction model with multilevel successive contribution can be described by the following general Eq. (1) given by MG:

$$f\left(x\right)=\sum _i{N}_i{C}_i+w\sum _j{M}_j{D}_j+z\sum _k{O}_k{E}_k$$ (1)

In this equation, the function $f\left(x\right)$ is dependent on the property $X$. The $C_i$ is the contribution of the 1st order group of type $i$ that has an occurrence of $N_i$ times, $D_j$is the contribution of the 2nd order group of type $j$ that has an occurrence of$M_j$ times and $E_k$ is the contribution of the 3rd order group of type$k$ that has an occurrence of $O_k$ times in the molecule. In the first step, the value of $w$ and $z$ are set zero for the 1st level of estimation of a given property with $C_i$ contribution. In the second step case of the 2nd level of estimation, the constants $w$ and $z$ are assigned unity and zero values, respectively because only 1st and 2nd order groups are involved while in the 3rd level, both $w$ and $z$ are set to unity values. The property function $f\left(x\right)$ is used to define the different properties and is detailed in Table 2 . The universal constant/adjustable parameters required for the estimation of 16 thermodynamic properties are reported in Table 3 . The MG method reported herein is analyzed through step-wise regression method (STRM) and simultaneous regression method (SIRM) and the results are detailed in the next section.

Table 2.

Property, function and group contributions for the estimation of properties of the compound.

Property $\left(\mathrm{x}\right)$	Function $\left(\mathrm{f}\left(\mathrm{x}\right)\right)$	Group Contribution terms
Normal boiling point $\left(T_b\right)$	$exp\left(T_b/T_{b0}\right)$	$\sum _i{N}_i{T}_{b1i}+\sum _j{M}_j{T}_{b2j}+\sum _k{O}_k{T}_{b3k}$
Critical temperature $\left(T_c\right)$	$exp\left(T_c/T_{c0}\right)$	$\sum _i{N}_i{T}_{c1i}+\sum _j{M}_j{T}_{c2j}+\sum _k{O}_k{T}_{c3k}$
Critical pressure $\left(P_c\right)$	$\left(P_c--P_{c1}\right)-0.5--P_{c2}$	$\sum _i{N}_i{P}_{c1i}+\sum _j{M}_j{P}_{c2j}+\sum _k{O}_k{P}_{c3k}$
Critical volume $\left(V_c\right)$	$V_c--V_{c0}$	$\sum _i{N}_i{V}_{c1i}+\sum _j{M}_j{V}_{c2j}+\sum _k{O}_k{V}_{c3k}$
Normal melting point$\left(T_m\right)$	$exp\left(T_m/T_{m0}\right)$	$\sum _i{N}_i{T}_{m1i}+\sum _j{M}_j{T}_{m2j}+\sum _k{O}_k{T}_{m3k}$
Standard Gibbs energy of formation $\left(G_f\right)$	$G_f--G_{f0}$	$\sum _i{N}_i{G}_{f1i}+\sum _j{M}_j{G}_{f2j}+\sum _k{O}_k{G}_{f3k}$
Standard enthalpy of formation $\left(H_f\right)$	$H_f--H_{f0}$	$\sum _i{N}_i{H}_{f1i}+\sum _j{M}_j{H}_{f2j}+\sum _k{O}_k{H}_{f3k}$
Standard enthalpy of vaporization at 298 K$\left(H_v\right)$	$H_v--H_{v0}$	$\sum _i{N}_i{H}_{v1i}+\sum _j{M}_j{H}_{v2j}$
Normal enthalpy of fusion $\left(H_{fus}\right)$	$H_{fus}--H_{fus0}$	$\sum _i{N}_i{H}_{fus1i}+\sum _j{M}_j{H}_{fus2j}+\sum _k{O}_k{H}_{fus3k}$
Octanol/Water partition coefficient $\left(Log{K}_{ow}\right)$	$Log{K}_{ow}-K_{ow0}$	$\sum _i{N}_{i}Log{K}_{ow1i}+\sum _j{M}_{j}Log{K}_{ow2j}+\sum _k{O}_{k}Log{K}_{ow3k}$
Flash point $\left(F_p\right)$	$F_p-F_{p0}$	$\sum _i{N}_i{F}_{p1i}+\sum _j{M}_j{F}_{p2j}+\sum _k{O}_k{F}_{p3k}$
Enthalpy of vaporization at normal boiling point $\left(H_{vb}\right)$	$H_{vb}-H_{vb0}$	$\sum _i{N}_i{H}_{vb1i}+\sum _j{M}_j{H}_{vb2j}+\sum _k{O}_k{H}_{vb3k}$
Entropy of vaporization at normal boiling point $\left(S_{vb}\right)$	$S_{vb}-S_{vb0}$	$\sum _i{N}_i{S}_{vb1i}+\sum _j{M}_j{S}_{vb2j}+\sum _k{O}_k{S}_{vb3k}$
Hildebrand solubility parameter $\left(\delta \right)$	$\delta -{\delta }_0$	$\sum _i{N}_i{\delta }_{D1i}+\sum _j{M}_j{\delta }_{D2j}+\sum _k{O}_k{\delta }_{D3k}$
Acentric factor ($\omega )$	$exp{\left(\frac{\omega }{{\omega }_a}\right)}^{{\omega }_b}-{\omega }_c$	$\sum _i{N}_i{\omega }_{1i}+\sum _j{M}_j{\omega }_{2j}+\sum _k{O}_k{\omega }_{3k}$
Liquid molar volume $\left(V_m\right)$	$V_m-V_{m0}$	$\sum _i{N}_i{V}_{m1i}+\sum _j{M}_j{V}_{m2j}+\sum _k{O}_k{V}_{m3k}$

Table 3.

Value of universal constants for different methods.

Universal Constants	Units	Values
		Step-wise Method	Simultaneous Method
$T_{b0}$	$\left[K\right]$	244.5165	244.7889
$T_{c0}$	$\left[K\right]$	181.6716	181.6738
$P_{c1}$	$\left[bar\right]$	0.0519	0.0519
$P_{c2}$	$\left[bar-0.5\right]$	0.1347	0.1155
$V_{c0}$	$\left[cc/mol\right]$	28.0018	14.6182
$T_{m0}$	$\left[K\right]$	143.5706	144.0977
$G_{f0}$	$\left[kJ/mol\right]$	−1.3385	8.5016
$H_{f0}$	$\left[kJ/mol\right]$	35.1778	83.9657
$H_{fus0}$	$\left[kJ/mol\right]$	−1.7795	−1.2993
$K_{ow0}$	$[--]$	0.4876	0.752
$F_{p0}$	$\left[K\right]$	170.7058	150.0218
$H_{v0}$	$\left[kJ/mol\right]$	9.6127	10.4327
$H_{vb0}$	$\left[kJ/mol\right]$	15.4199	15.0884
$ı0$	$\left[MPa1/2\right]$	21.6654	20.7339
${\omega }_{\alpha }$	$[--]$	0.908	0.9132
${\omega }_b$	$[--]$	0.1055	0.0447
${\omega }_c$	$[--]$	1.0012	1.0039
$V_{mo}$	$\left[cc/kmol\right]$	0.016	0.0123
$Ai{t}_1$		0	71.2584
$Ai{t}_2$	$\left[K\right]$	0	525.93

The deviation in the estimated thermodynamic properties was used using absolute relative deviation (ARD) that is defined as

$$ARD=\frac{x_i-x_j}{x_j}\times 100$$ (2)

Here, $x_j$ is the experimental thermodynamic property and $x_i$ is predicated on the thermodynamic property based on STRM and SIRM.

3. Result and discussion

The thermodynamic properties of the API were estimated based on the group contribution⁺ (GC) model that contains combined group contribution and the atom connectivity index. The model parameters considered have standard uncertainties in the prediction of the thermodynamic property. Each drug/molecule is split into different subgroups at each level for the estimation of the property. Table 4 reports the subgroups, group number, and their occurrence that are considered for predicting the thermodynamic properties of Baricitinib, Camostat, Chloroquine, Dexamethasone, Hydroxychloroquine, Fingolimod, Favipiravir, Thalidomide, and Umifenovir. Based on their contribution at each level i.e., contributions to 1st order group, 2nd order group, and 3rd order groups, the overall contribution to thermodynamic functions $f\left(x\right)$ is calculated using Eq. (1). Table S1 reports the detailed contribution that is considered for the estimation of thermodynamic properties ($T_b$, $T_c$, $P_c$, $V_c$, $T_m$, $\Delta G_f$, $\Delta H_f$, $\Delta H_{fus}$, $H_v$, $H_{vb}$, $S_{vb}$, $F_p$,$\delta$, $Log{K}_{ow}$, ω, and $V_m$) based stepwise (STRM) and simultaneous (SIRM) regression methods. While the estimated thermodynamic properties are reported in Table 5 . Among the 16 thermodynamic properties estimated for the 9 APIs, only the experimental normal melting point $\left(T_m\right)$ and for a few octanol/water partition coefficients $\left(Log{K}_{ow}\right)$ is reported in the open literature and is mentioned also mentioned in Table 5. The other thermodynamic properties are not found in the literature to the best of our knowledge. The estimated normal melting point $\left(T_m\right)$ and octanol/water partition coefficient $\left(Log{K}_{ow}\right)$ was therefore compared with that of literature for the performance evaluation of the mentioned GC method. The statistical performance indicator used in the present study is an absolute relative deviation (ARD).

Table 4.

Group orders, group number and their occurrence in each compound for the estimation of thermodynamic properties.

Baricitinib				Camostat						Chloroquine					Dexamethasone
Groups	Gr. No.	FN		Groups	Gr. No.			FN		Groups			Gr. No.	FN	Groups	Gr. No	FN
First-order				First-order						First-order					First-order
CH3	1	1		CH3	1			1		CH3			1	1	CH3	1	3
CH2	2	1		CH2	2			9		CH2			2	9	OH	29	3
aCH	15	5		aCH	15			4		CH			3	1	CH2CO	34	1
aC fused with aromatic ring	16	2		aC except as above	18			1		aCH			15	4	CF	116	1
aC except as above	18	2		CH2CO	34			1		aC fused with aromatic ring			16	1	CH2 (cyclic)	168	4
aN in-aromatic ring	19	5		aC—CO	37			1		aN in-aromatic ring			19	2	CH(cyclic)	169	4
CH2CN	68	1		CH2—COO	41			1		CH2N			61	2	C (cyclic)	170	3
SO2	149	1		aC—O	53			1		aC—NH			63	1	CH CH (cyclic)	171	1
CH2 (cyclic)	168	2		CH3N	60			1		aC—Cl			123	1	CH C (cyclic)	172	1
C (cyclic)	170	1		aC—NH	63			1							CO (cyclic)	180	1
N (cyclic)	176	1		NH2 expect as above	65			1
				C = N	67			1
Second-order				Second-order						Second-order					Second-order
Ccyc-CH2	100	1		aC—CH2—COO	64			1		No Occurrences					CHcyc-OH	84	1
AROMRING s1s4	106	1		AROMRING s1s4	106			2							Ccyc-CH3	99	2
															Ccyc-OH	101	1
															CHcyc-CH3	76	1
Third orders				Third-order						Third-order					Third-order
aC- aC (different ring)	15	1		aC—O-C-aC (different rings)	47			1		ARMOFUSED [2]S1S4		55		1	CH multiring	22	2
AROMFUSED S1	52	1
Favipiravir				Fingolimod	Hydroxychloroquine						Thalidomide				Umifenovir
Groups	Gr. No.		FN	Groups	Gr. No.	FN	Groups		Gr. No.	FN	Groups	Gr. No		FN	Groups	Gr. No.	FN
First-order				First-order			First-order				First-order				First-order
aCH	15		1	CH3	1	1	CH3		1	2	aCH	15		4	CH3	1	1
aN in- AR	19		2	CH2	2	9	CH2		2	5	aC fused with non-AR	17		2	CH2	2	9
aC—OH	30		1	aCH	15	4	CH		3	1	CH(cyclic)	169		1	aCH	15	4
aC—CONH2	94		1	C	4	1	aCH		15	1	CH2 (cyclic)	168		2	aC fused with AR	16	1
NH2 expect as above	65		1	NH2 expect as above	65	1	aC fused with AR		16	2	NHCO except as above	107		1	aN in- AR	19	2
aC—CO	37		1	OH	29	2	aN in- AR		19	2	N(cyclic)	176		1	aCH2	21	2
aC-F	124		1	aC—CH2	21	2	OH		29	1	CO(cyclic)	180		3	aC—OH	30	1
							CH2N		61	1					aC—COO	45	1
							aC—Cl		123	1					CH3N	60	1
															aC-Br	126	1
															aC-S-	147	1
Second-order				Second-order			Second-order				Second Order				Second Order
AROMRING s1 s2s4	108		1				No Occurrences				No Occurrences				AROMFUSED [2]	51	1
															aC—CH2-S-	59	1
Third-order							Third-order				Third-order				Third-order
No Occurrences							ARMOFUSED [2]S1S4		55	1	aC- CO cyc (Fused rings)	32		2	PYRIDINE FUSED [2]	64	1
											AROMFUSED [2]	51		1

FN: Occurrences.

Gr.No: Group Number.

AR: Aromatic Ring.

Table 5.

Estimated properties of compounds based on stepwise regression method (STRM) and simultaneous regression method (SIRM).

Property	Units	Baricitinib				Camostat			Chloroquine			Dexamethasone			Favipiravir
		STRM		SIRM	[47]	STRM	SIRM	[49]	STRM	SIRM	[50]	STRM	SIRM	[51]	STRM	SIRM	[52]
$T_b$	[K]	794.469		760.077		757.482	771.300		688.550	682.652		722.347	717.264		618.948	688.871
$T_c$	[K]	997.035		973.995		934.420	949.155		907.967	907.964		905.005	905.004		815.160	815.158
$P_c$	[bar]	0.076		0.091		0.140	0.145		0.152	0.147		0.100	0.109		0.063	0.064
$V_c$	[cc/mol]	58.885		903.061		1381.063	1410.628		1196.016	1175.118		−1061.953	1080.050		299.645	326.270
$T_m$	[K]	492.478		458.127	487.15	453.792	468.250	467.15	393.375	385.545	363.15	467.128	462.022	524.15	465.514	497.056	450.15
$G_f$	[kJ/mol]	632.951		395.881		−122.228	−121.518		737.893	757.660		−536.591	−574.299		−187.165	−173.038
$H_f$	[kJ/mol]	223.416		107.378		−706.079	−634.774		145.400	259.584		−1054.777	−994.887		−385.972	−417.504
$H_{fus}$	[kJ/mol]	100.855		49.657		66.271	66.260		70.036	51.288		32.559	33.055		53.974	46.568
$\log K{w}_0$		0.5811		2.32		5.4578	3.6913		5.463	6.0219		1.743	1.844		−0.867	−2.097
$F_P$	[K]	–		607.007		–	150.022		570.936	552.786		723.751	736.511		–	–
$H_V$	[kJ/mol]	–		118.800		–	10.433		149.382	154.790		184.173	182.672		118.959	124.073
$H_{Vb}$	[kJ/mol]	–		–		–	–		–	–		143.507	144.740		–	–
$S_{Vb}$	[kJ/mol]	–		–		–	–		–	–		204.871	207.947		–	–
$\delta$	[MPa1/2]	27.197		27.445		23.924	26.165		14.350	16.843		27.291	26.661		27.886	27.635
$\omega$		0.013		−0.002		0.023	–		0.013	−0.001		0.024	0.018		0.015	−0.001
$V_m$	[cc/kmol]	0.251		0.301		0.507	–		0.333	0.333		0.278	0.462		0.134	0.129
Property	Units		Fingolimod			Hydroxychloroquine			Thalidomide				Umifenovir
			STRM	SIRM	[53]	STRM	SIRM	[55]	STRM	SIRM	[57]		STRM		SIRM		[58]
$T_b$	[K]		687.396	689.003		681.390	714.345		648.734	650.895			776.060		772.496
$T_c$	[K]		848.840	848.839		909.231	920.028		936.906	931.518			973.718		973.718
$P_c$	[bar]		0.106	0.115		1.335	0.142		2.419	0.069			0.142		0.146
$V_c$	[cc/mol]		1058.116	1069.218		865.489	1199.529		566.423	575.560			1292.282		–
$T_m$	[K]		398.693	396.310	400.15	417.170	414.588	367.1	441.490	440.390	543.15		447.213		448.603		415
$G_f$	[kJ/mol]		−21.235	−2.948		346.872	595.810		−229.399	−255.484			171.261		–
$H_f$	[kJ/mol]		−478.253	−448.244		−63.171	45.765		−456.385	−446.716			−397.082		–
$H_{fus}$	[kJ/mol]		48.469	46.357		58.150	55.237		23.906	32.053			70.472		–
$\log K{w}_0$			4.532	4.064		3.2266	4.6854		0.0915	0.3946			6.251		6.1162
$F_P$	[K]		615.936	616.728		594.016	640.443		567.197	570.199			–		–
$H_V$	[kJ/mol]		162.707	162.094		144.748	178.760		147.419	152.094			–		–
$H_{Vb}$	[kJ/mol]		98.831	–		–	–		99.785	159.024			–		–
$S_{Vb}$	[kJ/mol]		134.617	–		–	–		168.272	181.299			–		–
$\delta$	[MPa1/2]		28.506	29.829		18.645	19.895		23.247	27.758			21.665		–
$\omega$			0.022	–		0.013	–		0.011	−0.002			0.019		−0.013
$V_m$	[cc/kmol]		0.360	0.294		14.941	0.337		0.168	0.160			0.419		−1.453

The estimated $T_m$ for the Baricitinib was found to be 492.478 K that showed an ARD of 1.093 (STRM) with that of reported A. S. Alshetaili et al. [47]. While the enthalpy of fusion $\Delta H_{fus}$ showed a high ARD of 18.7 with that reported in the literature [47]. The Hansen solubility $\left(\delta \right)$ for the Baricitinib was found to be 27.197 MPa^1/2 and was closer with reported literature [47] with a value of 28.90 MPa^1/2. While the octanol/water partition coefficient $\left(Log{K}_{ow}\right)$ is estimated to be 0.252 and consistent with Pengfei Xu et al. (0.24) [48]. The Camostat estimated $T_m$ was found to be 497.05 K (SIRM) with an ARD of 2.85 with that of experimental data reported by J. Yin et al. [49]. While the Chloroquine estimated $T_m$ was found to be 385.54 K against the reported value of 363.15 K by M. Staderini et al. [50]. The estimated$T_m$ for Dexamethasone showed an ARD of 10.87 with that of reported $T_m$ of 524.60 K [51] and was mainly with complex structure and fluorinated compounds present in it. Also, the normal enthalpy of fusion $\left(\Delta H_{fus}\right)$ was found to be 32.55 kJ/mol and that showed very high ARD (29.27) with reported by X. Cai et al. [50]. The estimated $T_m$for Favipiravir was found to be 465.51 K with a relatively low deviation of 3.41 K with that reported by Q. Guo et al. [52]. Fingolimod showed the lowest ARD with an estimated $T_m$of 398.69 K and 396.30 K based on STRM and SIRM method. An ARD of 0.36 and 0.95 was found with that reported by S. R. Shaikh et al. [53]. H. Gunaydin reported the octanol/water partition coefficient $\left(Log{K}_{ow}\right)$ of 2.8 that has a percentage ARD of 0.29 with STRM (4.5) [54] The estimated $T_m$for Hydroxychloroquine is 417.16 K (STRM) with an ARD 12.05 [55]. Also, the estimated octanol/water partition coefficient based on STRM $\left(Log{K}_{ow}\right)$ (3.22) was found coherent with that reported by M. Nimgampalle et al. with a value of 3.58 [56]. Similar to dexamethasone, Thalidomide estimated$T_m\left(441.49K\right)$ should a high ARD of 18.71 with that of reported $T_m$ of 543.15 K by et al. B.D. Vu et al. [57]. The presence of carboxyl carbonyl groups and fused aromatic rings are the possible reason for larger deviations. The Umifenovir estimated $T_m$ was found to be 447.21 K (STRM) with an ARD of 7.72 58. A. Kons et al. [58].

Based on the above statistical analysis of $T_m$ the overall average relative deviation for all the APIs was found to be 7.27 and 8.39 for STRM and SIRM methods, respectively. This relative deviation in the predicted properties is related to the experimental data set that was used for regression and the estimation of universal constants for empirical correlations. The group-contribution+ (GC+) method used in the present work is developed from the DIPPR 801® databank that has used experimental data with reported uncertainties. The experimental data itself has standard uncertainties in the measurements. For example, the normal boiling point [K] with data points of 1306 has an experimental average measurement error of 6.32% while that of predication based on the GC + method has 6.17%. Similarly, the deviations are seen for Normal melting point [K] with data points of 1385 has an experimental average measurement error of 5.10 while that of predication has 15.99. It has been found that for the 16 estimated properties the prediction error is lower than (or at least comparable to) the average measurement error, except for the case of normal melting point $\left(T_m\right)$ and standard enthalpy of fusion $\left(\Delta H_{fus}\right)$. For these two properties, group contribution methods, in general, have difficulties in providing a reliable estimation. This is mainly due to the strong dependency of the melting point on intermolecular interaction and molecular symmetry. With low deviation in STRM and SIRM method, the present GC+ method showed its capability to accurately predict the thermodynamic properties. The predicted thermodynamic properties not perfect/exact (lack of experimental value) still provide the basis for engineering design.

4. Conclusion

The group contribution (GC) method was used to estimate thermodynamic properties for the drugs/compounds/API that are related or proposed for the treatment of severe acute respiratory syndrome-CoronaVirus-2. The GC method based on stepwise regression parameters showed a low average deviation for the melting point. A total of 16 thermodynamic properties are reported for 9 API which is helpful in the product-process design, simulation, and optimization calculations. The properties contribute to reliable and robust engineering solutions for pharmaceutical product development.

Disclosure statement

No potential conflict of interest was reported by the authors.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.