synthesis and qsrr study for a series of phosphoramidic acid derivatives

Heteroatom ChemistryVolume 24, Number 2, 2013

Synthesis and QSRR Study for a Series ofPhosphoramidic Acid DerivativesMihaela Petric,1 Luminita Crisan,1 Manuela Crisan,1

Andreea Micle,2 Bianca Maranescu,1 and Gheorghe Ilia1,3

1Institute of Chemistry, Timisoara of Romanian Academy, 300223, Timisoara, Romania

2Laboratory of Drug Analysis and Profiling, General Inspectorate of Romanian Police, 300042,Timisoara, Romania

3Faculty of Chemistry–Biology–Geography, West University of Timisoara, 300115, Timisoara,Romania

Received 17 July 2012; revised 17 December 2012

ABSTRACT: New phosphoramidic acid derivativeswere synthesized by three different methods in theliquid–liquid and liquid–solid systems. The highestyields were obtained when the liquid–solid system wasused. Moreover, for these compounds, the retentionfactor was predicted, using a robust model obtained fora set of phosphoramidic acid derivatives, which werepreviously synthesized in our laboratory. For thesecompounds, the retention factor (k′′) was determinedby means of the high performance liquid chromatog-raphy technique, using a Nucleosil C18 column as astationary phase and methanol as a mobile phase. Thestepwise multiple linear regression (MLR) and partialleast square (PLS) methodology were used to investi-gate the correlation between the retention factor anda number of molecular descriptors for the mentionedcompounds. In both procedures, a considerably largenumber of molecular descriptors have been used. Thestatistical qualities of MLR and PLS equations havebeen assessed on the basis of several parameters suchas squares of the correlation coefficient (R2 = 0.985),standard error of estimate (SEE = 0.149), Fischer test(F = 257.528), and the cumulative sum of squares ofthe correlation coefficient R2

Y(CUM) = 0.984, the cu-

Correspondence to: Luminita Crisan; e-mail: [email protected].

Contract grant sponsor: Institute of Chemistry Timisoara of theRomanian Academy (Projects 1.2 and 2.2).C© 2013 Wiley Periodicals, Inc.

mulative fraction of the total variation of the Y valuesthat can be predicted for all the extracted principalcomponents by cross-validation Q2

(CUM) = 0.971, re-spectively, and by the Y-randomization test. The MLRand PLS equations can be useful for the estimationand comparison of the retention factor, for new syn-thesized phosphoramidic acid derivatives, using theselected molecular descriptors. C© 2013 Wiley Peri-odicals, Inc. Heteroatom Chem 24:138–145, 2013;View this article online at wileyonlinelibrary.com.DOI 10.1002/hc.21076

INTRODUCTION

Phosphoramidates belong to an amide class of phos-phoric acid. It has been found that these compoundshave particular importance most likely in medicine[1–4], having therapeutic applications due to anti-cancer, antiviral, anti-inflammatory activity, and intreatment of cardiovascular disease, in chemistry [5]often used as intermediates in organic synthesis [6]and to protect the amino group and as ligands forthe removal of metal cations [7], and in agricultureas pesticides and herbicides [8–10]. The interestingbiological properties [11,12] and also the study of co-ordination chemistry [7] of these compounds involvethe development of new methods for the synthesis ofphosphoramidates in organic chemistry.

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Synthesis and QSRR Study for a Series of Phosphoramidic Acid Derivatives 139

The standard synthesis method of phospho-ramidate derivatives elaborated by Todd and Ather-ton [13, 14] uses reactants, such as ammonia,primary/secondary amines, and a dialkyl/dibenzylphosphite, in the presence of a halogen source (car-bon tetrachloride). We described a new approachto the preparation of phosphoramidic acid deriva-tives from different aniline derivatives and dialkylphosphites in liquid–solid systems [15]. The synthe-sis and characterization of 11 new different phos-phoramidic acid derivatives from unsubstituted andpara-NO2 substituted aniline derivatives and dialkylphosphites in biphasic systems, liquid–liquid (meth-ods A and B) and liquid–solid (method C), are pre-sented in our previous work [15]. Our new methodC (in which potassium carbonate was used as base,and the catalyst was tetrabutylammonium bromide)is a simple method and with higher yield (50–81%).

In the present work, following our previousstudy, we have synthesized and characterized (byNMR and elemental analysis) some new phospho-ramidic acid derivatives from meta-NO2 anilinederivatives and dialkyl phosphites, in biphasic sys-tems, using the previously mentioned methods: theliquid–liquid (methods A and B) and liquid–solid(method C).

In this context, phosphoramidates represent aclass of organic compounds that show properties ofinterest for the application of quantitative structureretention relationships (QSRR) studies. The predic-tion of the retention factor from chemical structureswould be helpful in the estimation of some physico-chemical properties.

The retention factor was calculated accordingto the following equation: k′ = (tR − tM)

/tM, where

tR (the retention time) is measured from the timeat which the sample is injected to the point atwhich the display shows a maximum peak heightfor these 11 phosphoramidic acid derivatives [16]and tM (the dead time) is the retention time of anunretained species [17–20]. It is known that k′ ofa compound is related to the partition process, ad-sorption process, or both [21]. The application ofk′ in quantitative structure property/retention rela-tionships (QSPR/QSRR) studies provides significantinformation on the influence of the molecular struc-ture on the retention time [22, 23]. In general, theQSPR procedure is widely accepted and very use-ful in the prediction of physicochemical properties[24,25]. In the current study, we have applied multi-ple linear regression (MLR) and partial least square(PLS) techniques to a series of 11 phosphoramidicacid derivatives with the known retention factor [16]to establish the equation for the dependency of theretention factor and the molecular DRAGON de-

scriptors. The relevant QSPR/QSRR models for thisseries were constructed in the following steps: (i)generation of three-dimensional (3D) structures, (ii)geometry optimization, (iii) converting molecularstructures into mathematical descriptors that encap-sulate the key properties of the molecules, (iv) con-struction of the QSPR/QSRR models, and (v) modelvalidation. The advantages of these methodologiesare that they require only the knowledge of chemicalstructure and are not dependent on any experimen-tal properties [26].

Our goals were to synthesize and characterizesome new phosphoramidic acid derivatives and todevelop a robust model that meaningfully selects aset of variables that efficiently predict the retentionfactor for these compounds and analyze them in re-gard to the nature and position of substituents.

MATERIALS AND METHODS

Experimental

Synthesis. Six new meta-substituted phospho-ramidic acid derivatives were synthesized by threedifferent methods: the liquid–liquid (methods A andB) and liquid–solid (method C) [15].

Method A. A solution of 0.011 mol dialkyl phos-phite and 0.01 mol of the corresponding meta-nitroaniline in 5 mL ethyl acetate was prepared.This solution was dropwise added to a stirredtwo-phase system, which was formed with 5 mLof dichloromethane/5 mL tetrachloromethane/5 mLsodium hydroxide, 25% (w/v), and 0.02 g of the cata-lyst. The temperature was kept at 0–10◦C by externalcooling. After completion of addition, the mixturewas stirred for 1 h at 0–10◦C and then for another2 h at room temperature. The organic layer was sepa-rated, washed with 3% hydrochloric acid (2 × 10 mL)and water (2 × 10 mL), and dried over anhydrousmagnesium sulfate.

Method B. To a stirred and cooled (0–10◦C)mixture of dialkyl phosphite (0.011 mol), corre-sponding meta-nitroaniline in 5 mL of ethyl acetate,tetrachloromethane (5 mL), and a catalyst (0.02g), asolution of 25% aqueous sodium hydroxide (5 mL)was added dropwise. After completion of addition,stirring was continued for 1 h at 0–10◦C and then foranother 3 h at room temperature. Then, the organiclayer was separated, washed with 3% hydrochloricacid (2 × 10 mL) and water (2 × 10 mL), and driedover anhydrous magnesium sulfate.

Method C. To a stirred two-phase systemof dichloromethane (5 mL), tetrachloromethane

Heteroatom Chemistry DOI 10.1002/hc

140 Petric et al.

(5 mL), potassium carbonate (3 g), and a catalyst(0.02 g), a solution of dialkyl phosphite (0.01 mol)and the corresponding meta-nitroaniline in 5 mL ofethyl acetate was added dropwise. The temperaturewas kept at 0–10◦C by external cooling. After comple-tion of addition, stirring was continued for 1 h at 0–10◦C and then for another 3 h at room temperature.The potassium carbonate and potassium chloridewere filtered, and the organic layer was separated,washed with 3% hydrochloric acid (2 × 10 mL) andwater (2 × 10 mL), and then dried over anhydrousmagnesium sulfate, and the solvent evaporated.

All NMR spectra were recorded with a BrukerDRX 400 MHz spectrometer, in deuterated chloro-form, at 298 K. All chemical shifts were measuredusing the XSI scale and TMS as the internal stan-dard [27]

Elemental analysis was performed using Kjel-dahl and Schoniger methods.

C10H15N2O5P (3*). Yield: method A 66%,method B 55%, method C 85%; mp = 122◦C. Anal.Calcd.: N, 10.22; P, 11.3. Found: N, 10.34; P, 11.02;1H NMR (400 MHz, CDCl3, 25◦C): δ = 7.61–7.33 (m,4H, Ph), 4.53–4.45 (m, 4H, CH2OP), 4.05 (s, 1H, NH),1.19 (t, 6H, CH3); 13C NMR (100 MHz, CDCl3, 25◦C):δ = 146.6, 138.5, 128.3, 123.3, 111.8, 107.1, 60, 13.9.

C14H23N2O5P (6*). Yield: method A 63%,method B 55%, method C 82%; mp = 127–128◦C.Anal. Calcd.: N, 8.48; P, 9.38. Found: N, 8.62; P, 9.54;1H RMN (400 MHz, CDCl3, 25◦C): δ = 7.50–7.02 (m,4H, Ph), 4.15 (m, 4H, CH2OP), 4.02 (s, 1H, NH),1.75–1.42 (m, 8H, CH2), 0.88 (t, 6H, CH3); 13C RMN(100 MHz, CDCl3, 25◦C): δ = 147.2, 139.1, 128.9,123.9, 112.4, 107.7, 63.1, 30, 17, 12.3.

C18H15N2O5P (9*). Yield: method A 32%,method B 25%, method C 47%; mp = 131–132◦C.Anal. Calcd.: N, 7.57; P, 8.36. Found: N, 7.75; P,8.04; 1H RMN (400 MHz, CDCl3, 25◦C): δ = 7.58–6.95(m, 14H, Ph), 4.0 (s, 1H, NH); 13C RMN (100 MHz,CDCl3, 25◦C): δ = 151, 149.5, 141.4, 131.2, 130.9,126.2, 122.1, 121.1, 114.7, 110.

C20H19N2O5P (12*). Yield: method A 30%,method B 23%, method C 45%; mp = . Anal. Calcd.:N, 7.03; P, 7.78. Found: N, 6.93; P, 7.34; 1H RMN(400 MHz, CDCl3, 25◦C): δ = 7.72–7.15 (m, 14H, Ph,)5.38–5.25 (d, 4H, CH2), 4.0 (s, 1H, NH); 13C RMN(100 MHz, CDCl3, 25◦C): δ = 151.2, 143.1, 137.9,132.9, 131.4, 130.1, 129.6, 127.9, 116.4, 111.7, 73.

C22H39N2O5P (15*). Yield: method A 55%,method B 30%, method C 64%; mp = . Anal. Calcd.:N, 6.33; P, 7%. Found: N, 6.21; P, 6.95%; 1H RMN

(400 MHz, CDCl3, 25◦C): δ = 7.6–7.01 (m, 4H, Ph.),4.21–4.02 (m, 4H, CH2OP), 4.01 (s, 1H, NH), 1.81–1.46 (m, 24H, CH2), 0.98 (t, 6H, CH3); 13C RMN(100 MHz, CDCl3, 25◦C): δ = 150, 141.1, 131.1, 127.3,116.8, 114.9, 64.3, 32.5, 31.2, 30, 23.2, 17.2.

C26H47N2O5P (17*). Yield: method A 54%,method B 29%, method C 62%; mp = . Anal. Calcd.:N, 5.62; P, 6.21%. Found: N, 5.44; P, 6.02%; 1H RMN(400 MHz, CDCl3, 25◦C): δ = 7.41–7.03 (m, 4H, Ph.),4.32–4.22 (m, 4H, CH2OP), 4.01 (s, 1H, NH), 1.71–1.25 (m, 32H, CH2), 0.94 (t, 6H, CH3); 13C RMN(100 MHz, CDCl3, 25◦C): δ = 151.3, 143.2, 132.2,128, 117.5, 112.8, 68.3, 34.5, 33.6, 32, 25.3, 16.7.

Data Set

The Data set used in QSRR analysis includes 11different phosphoramidic acid derivatives [16] as atraining set and six new phosphoramidic acid deriva-tives (see Table 1) as a test set. Their structure, reten-tion factor (experimental and predicted), and signif-icant selected descriptor variables calculated on thebasis of the MLR equation are listed in Table 1.

Chromatography

High-performance liquid chromatography (HPLC)is the most common separation method, and it hasbeen frequently used in analytical chemistry and bio-chemistry to identify, separate, and quantify com-pounds [28]. HPLC analysis was performed using aJASCO HPLC system, which is composed of a PU-1580 intelligent HPLC pump and the MD-1510 UV–vis detector. The sample was injected through an in-jector (Reodyne model 7725) with a 10-μL externalloop. The separation was performed on a NucleosilC18 column (25 cm × 4 mm) in conjunction with amobile phase of methanol at a flow rate of 1 mL/min.All the experimental runs in this study were carriedout at a room temperature (23 ± 2◦C). The deadtime (tM) was determined as the retention volume ofuracil. The chromatographic data were collected andprocessed with a Borwin chromatography worksta-tion, version 1.5 (for values of the retention factor,see Table 1).

Structural Calculations

To calculate the theoretical descriptors, the two-dimensional (2D) structures of phosphoramidicacid derivatives were drawn using the HyperChem,version 7.52 [29]. In the first step, a molecular me-chanics force field was used to optimize the geom-etry of the molecules. The resulted structures were



TABLE 1 Chemical Structure, Retention Factor, and Selected Descriptor Variables by the MLR Equation of PhosphoramidicAcid Derivatives

No. R1 R2 k′ (e) HPLC k′ (p) PLS k′ (p) MLR RDF130p GATS3p

1 C2H5- – 1.46 1.49 1.44 0 1.272 -p-NO2 1.38 1.34 1.38 0 1.3153* -m-NO2 1.38 1.38 0 1.3154 C4H9- – 1.83 1.76 1.56 0 1.1975 -p-NO2 1.36 1.60 1.49 0 1.2376* -m-NO2 1.35 1.50 0.002 1.2377 C6H5- – 1.86 1.83 1.86 0.001 0.9998 -p-NO2 1.72 1.70 1.81 0.001 1.0339* -m-NO2 1.70 1.81 0 1.03310 C6H5-

CH2-– 1.37 1.19 1.24 0.076 1.414

11 -p-NO2 1.03 1.13 1.21 0.134 1.44512* -m-NO2 1.56 1.29 0.511 1.44513 C8H17- – 3.14 3.29 3.28 7.251 1.114 -p-NO2 3.73 3.49 3.64 9.099 1.12915* -m-NO2 3.92 3.63 9.102 1.12916 C10H21- – 4.20 4.27 4.19 11.181 1.06517* -m-NO2 4.12 4.09 11.035 1.104

*New synthesized compounds.

further refined using the semiempirical PM3 Hamil-tonian, applying a root mean square (RMS) gradientnorm limit as a stopping criterion at 0.01 kcal/A.

Molecular Descriptors Calculation

A set of 1145 molecular descriptors of differentkinds, resulting from DRAGON [30] software, wereused to build the X-matrix suitable for QSPR anal-ysis and are as follows: 27 constitutional descrip-tors, 219 topological descriptors, 14 walk and pathcounts, 64 BCUT (Burden - CAS - University ofTexas eigenvalues) descriptors, 18 Galvez topolog-ical charge index, 90 2D autocorrelations, 3 func-tional group counts, 11 Atom-centered fragments,2 empirical descriptors, 3 properties, 14 charge de-scriptors, 41 randic molecular profiles, 17 topo-logical charge indices, 40 geometrical descriptors,150 radial distribution factor (RDF) descriptors, 1603D-MoRSE (3D-Molecule Representation of Struc-ture based on Electron diffraction) descriptors, 99WHIM (Weighted Holistic Invariant Molecular) de-scriptors, and 190 GETAWAY (GEometry, Topology,and Atom-Weights AssemblY) descriptors. The com-plete list of these molecular descriptors and theirmeanings is provided in the literature [31].

MLR Method. MLR is the statistical methodused to analyze the relationship between single re-sponse variable (dependent variable) with calculatedvariables (independent variables) [32]. Because of

the great number of calculated descriptors (X =1145) in comparison with the number of compounds(N = 11), a reliable variable selection method and acorrelation check for the descriptors are required[33]. By applying multicollinearity tests with a cut-off value of 0.95, the number of descriptors was re-duced to 284. The statistical software package STA-TISTICA [34] was used to develop a forward stepwiseselection. The analysis was restricted to constructonly two descriptor equations.

PLS Method. PLS is a regression technique thatworks with two matrices, X (independent variables)and Y (dependent variables), and has two objectivesto well approximate X and Y and to model the rela-tionship between them [35]. This methodology hasadvantages over MLR because it works with inter-correlated variables [36]. The relation between thechemical descriptors and the dependent data is de-scribed as a linear model in the space described bythe latent variables [37].

Model Validity

Validation is a crucial aspect of any QSAR/QSPRmodeling [38]. To avoid chance correlations, whichare possible because of a large number of gener-ated descriptors and to certify the predictive abilityof our models, the Y-randomization (Y-scrambling)test and R2

pred for the test set were used. In thistechnique, Y values (dependent variable) are


142 Petric et al.

randomly interchanged, keeping the original in-dependent variable as such, and new modelsQSAR/QSPR are constructed, by the same procedureas for the real Y values. The obtained models, afterrandomizations, must provide the minimal R2 andQ2 values [39]. The exclusion of chance correlationof a QSAR model can be quantitatively assessed bythe penalty parameter R2

p that amend the squaredcorrelation coefficient by subtracting the averagesquared correlation coefficient (R2

r ) of the random-ized models from the squared correlation coefficientof the non randomized model (R2) as follows:

R2p = R2

√R2 − R2

r (1)

Roy et al. [39] considered that R2p should be greater

than 0.5 for a statistically adequate model that ex-clude chance correlation.

RESULTS AND DISCUSSION

Synthesis

In the present study, six novel phosphoramidates(marked with an asterisk (*) in Table 1) from meta-NO2 aniline derivatives and dialkyl phosphites weresynthesized in biphasic systems, using three differ-ent methods. The method C (Scheme 1) for the syn-thesis of these compounds gives higher yields, com-pared with the other two methods (A and B) (seeExperimental). Method C is more convenient for ob-taining a wide range of phosphoramidates than theclassical methods used in literature.

The 1H NMR spectra of the analyzed compoundsshow a mutiplet in the range of 7–8 ppm for thearomatic hydrogens, one singlet around 4 ppm forthe NH, the CH2-O-P appears at 4–4.21 ppm. Thealiphatic hydrogens show a multiplet for the CH2

groups at 1.2–1.8 ppm and a triplet for the CH3

around 1 ppm, respectively. The 13C NMR spectraof the analyzed compounds show a singlet in therange of 151–107 ppm for the aromatic carbons, asinglet at 73–60 ppm for CH2-O-P, and a singlet inthe range of 34.5–12.3 ppm for aliphatic carbons.The structure of the products was confirmed by 1Hand 13C NMR.

SCHEME 1 Synthesis of new phosphoramidates.

TABLE 2 Correlation Matrix for MLR Model, Eq. (2).

RDF130p GATS3p

RDF130p 1.00GATS3p 0.43 1.00

MLR Results

The stepwise forward regression routine was usedto develop the linear model for the prediction of theretention factor of phosphoramidic acid derivativesusing 284 selected structural descriptors. The case-wise plot of outliers was analyzed, but based on val-ues of standard deviation (±2 SD) no compoundsshould be removed from the data set as outliers.

The best linear model contained two moleculardescriptors (RDF130p in the RDF descriptor classand GATS3p in the 2D autocorrelation class) and ispresented in Eq. (2).

k′ = 3.386 (±0.432) + 0.217 (±0.012) RDF130p

− 1.529 (±0.346) GATS3p (2)

R2 = 0.985; N = 11; t(8) = 7.839; F = 257.528; stan-dard error of estimate (SEE) = 0.149; SD (RDF130p)= 4.364; SD (GATS3p) = 0.151.

For Eq. (2), SEE is less than 0.2. The standard er-rors of regression coefficients are given within paren-thesis. The intercorrelation (r) among RDF130p (ra-dial distribution function–130/weighted by polariz-ability) and GATS3p (Geary autocorrelation of lag 3weighted by polarizability) descriptors is presentedin Table 2, which suggests the absence of high in-tercorrelation, which justifies the appearance of theparameters in the equation. Positive values in theregression coefficients show that the RDF130p de-scriptors contribute positively to the value of k′,whereas negative values indicate that the greaterthe value of the GATS3p descriptor the lower is thevalue of k′. The higher standard deviation value [40]for RDF130p indicates a higher influence on the re-tention factor than GATS3p. In addition, for com-pounds 13, 14 and 16, the high values for RDF130pcorrespond to the high value of the retention factor(Table 2). The same observation can be highlightedfor new synthesized compounds 15 and 17 with thepredicted retention factor 3.63 and 4.09, respectively(Table 1).

Because 861 descriptor variables were elimi-nated via multicollinearity tests to test whetherchemically pertinent information has been lost, aPLS approach was applied. The PLS methodology,by the adequate handling of the intercorrelated vari-ables, is able to manage this insuperable problem inthe MLR.



TABLE 3 First 10 Coefficients in Order of Descending VIP Values for the Final Model

No. X VIP [2] CoeffCS [2] Descriptor Classes Descriptor Significance

1 GATS3p 1.062 –0.041 2D autocorrelations Geary autocorrelation of lag 3 weighted bypolarizability

2 RDF130v 1.061 0.014 RDF descriptors Radial distribution function–130/weighted byvan der Waals volume

3 RDF130p 1.060 0.014 RDF descriptors Radial distribution function–130/weighted bypolarizability

4 Mor31m 1.060 0.026 3D-MoRSE descriptors Signal 31/weighted by mass5 RDF130u 1.055 0.013 RDF descriptors Radial distribution function–130/unweighted6 RDF130e 1.054 0.013 RDF descriptors Radial distribution function–130/weighted by

Sanderson electronegativity7 RDF130m 1.054 0.018 RDF descriptors Radial distribution function–130/weighted by

mass8 L2s 1.052 0.012 WHIM descriptors Second component size directional WHIM

index/weighted by I-state9 RDF135e 1.051 0.013 RDF descriptors Radial distribution function–135/weighted by

Sanderson electronegativity10 RDF135u 1.049 0.013 RDF descriptors Radial distribution function–135/unweighted

PLS Results

To identify different descriptors, which correlatedwith the retention factor, the PLS calculations withthe SIMCA P09 [41] were performed. In a first step,a principal component analysis model was usedto investigate the correlation structure of the de-scriptor matrix X. The model (M1) was constructedfor the whole X matrix (N = 11 rows/compounds,and K = 1145 columns/descriptors). A five princi-pal component model was resulted, but the firsttwo components already explain 72.9% of the in-formation of the QSPR matrix. In the next stage,a PLS method was used to identify the relation-ship between the retention factor values (Y vec-tor) and the molecular descriptors (X matrix) [37].In SIMCA program, all X variables were centeredand scaled to unit variance before to the analy-ses. So, all variables had an equal weight in themodel. The first PLS model was constructed us-ing the same X matrix (N = 11 rows/compoundsand K = 1145 columns/descriptors). Afterward, avariable selection was performed, preserving in thenew model only the descriptors significantly differ-ent from zero (elimination of noise). Thereby, a finalrobust model with two principal components, whichexplains 90.9% of the information content of the Xmatrix and 117 significant variables, was obtained.The statistical qualities for this model are R2

Y(CUM)

= 0.984 and Q2(CUM) = 0.971. In PLS, a measure

of the importance of an X variable for both mod-eling of X and Y is the variable importance in theprojection (VIP) value. The descriptors with higherVIP score are the most relevant for a model. InTable 3 VIP values for the final model are presented

in a descending order for the first 10 most importantvariables.

Validity Tests for the Models

The high R2 (MLR) and R2Y(CUM) and Q2

(CUM) (PLS)values do not automatically imply a high predictivepower of the model. The absence of chance corre-lation in our models is tested in the next step bythe randomization validation (Table 4). It consistsof scrambling the experimental property (k′ for ourstudy) a number of times (20 randomly permuted)in such a way that the retention factor does not cor-respond to the respective compounds. The low val-ues for the statistical parameters indicate that thegood results in our models are not due to a chancecorrelation or structural dependency of the data set.In addition, the Rp

2 (see Table 4) parameter valuesgreater than 0.5 for our models confirm that we haveobtained a reliable quantitative structure–propertyrelationship.

The final models for both methodologies haveexcellent statistical parameters and good predictivecapacity. The correlation coefficient calculated forthe experimental versus predicted retention factorhas been determined for the training set (1, 2, 4, 5,7, 8, 10, 11, 13, 14, 16 compounds) and shows sim-ilar statistical performances for both methods used:R2

fit = 0.946 (MLR) and R2fit = 0.984 (PLS). Because

the MLR method is simple and easily interpretable,it was selected to predict the retention factor fornew phosphoramidic acid derivatives synthesized(Table 1). For this method, R2

pred was calculated us-ing the retention factor (experimental vs. predicted)


144 Petric et al.

TABLE 4 Statistical Qualities of MLR* and PLS* Models after20 Randomly Permuted Y Values

No. R2 SEE A R2Y(CUM) Q2

(CUM)

1 0.261 1.034 2 0.48 0.092 0.190 1.020 2 0.33 –0.093 0.086 1.150 2 0.25 –0.214 0.297 0.951 2 0.60 0.035 0.292 1.022 2 0.27 –0.216 0.320 0.935 2 0.46 –0.117 0.220 1.001 2 0.48 0.168 0.423 0.913 2 0.34 –0.139 0.290 0.955 2 0.54 0.1910 0.469 0.876 2 0.53 0.1611 0.292 0.954 2 0.55 –0.0412 0.225 0.998 2 0.56 0.3213 0.203 1.012 2 0.31 –0.2114 0.268 0.969 2 0.60 0.3015 0.102 1.075 2 0.38 –0.216 0.520 0.833 2 0.58 –0.2117 0.230 1.009 2 0.43 –0.0218 0.230 0.876 2 0.45 0.0719 0.164 1.037 2 0.36 0.0120 0.296 0.951 2 0.38 –0.21R2

r 0.227 0.443R2

p 0.843 0.723

*R2, squares of the correlation coefficient; SEE, standard error ofestimate (the MLR model); R2

Y(CUM), the cumulative sum of squaresof all the Y values; Q2

(CUM), the fraction of the total variation of theY values that can be predicted for all the A extracted principal com-ponents in the cross-validation procedure (seven rounds) used toestablish the number of significant principal components; A (the PLSmodel).

of new synthesized compounds 3, 6, 9, 12, 15, 17as test set. The value 0.982 for R2

pred confirmed thepredictivity ability power for our MLR model.

Interpretation

The most important variables in our models areweighted with the atomic masses, van der Waalsvolumes, Sanderson electronegativity, and atomicpolarizabilities. The comparison of the descriptorspresent in the MLR equations and the PLS modelascertains that RDF130p and GATS3p are most im-portant to explain the correlation between the re-tention factor and molecular descriptors for this se-ries of phosphoramidic acid derivatives. To studythe sign of the coefficients for these two descriptors(RDF130p and GATS3p), we have observed that theircontribution to the retention factor for both modelsis identical.

In conclusion the retention factor profile ofphosphoramidic acid derivatives and the identifieddescriptors display a direct proportionality relation-ship for RDF130p and an inverse proportionality re-lationship for GATS3p. Based on Eq. (2), the sub-stituents R1 and R2 influence values of the retention

factor, increasing with the number of carbon atomsfor aliphatic substituents (Table 1).

CONCLUSIONS

Using a new and simple synthesis method, six novelphosphoramidic acid derivatives were synthesized.The operational simplicity of synthesis method Cand the good yield of the products make it valuablefor a wide range of phosphoramidates. As a futureproject, we intend to use the synthesized phospho-ramidates as ligands in coordinative chemistry.

The statistically significant models are based onMLR and PLS regression using the 2D and 3D de-scriptors based on squares of the correlation co-efficient (R2 = 0.985), SEE = 0.149, Fischer test(F = 257.528) for the MLR model, respectively, theinternal fit and the internal predictive power forthe PLS model (R2

Y(CUM) = 0.984, Q2(CUM) = 0.971).

The absence of chance correlation for these modelshas been confirmed by the values greater than 0.5for the R2

p parameter (0.843 for the MLR model and0.762 for the PLS model). In PLS, a measure of theXj variable importance for both modeling of X and Yis the VIP value. The descriptors with VIP >1 are themost relevant for a model. The molecular descrip-tors appearing in the final models merge 2D and 3Daspects of the molecular structure and are becomingan attractive tool for the efficient phosphoramidatedesign process. These MLR and PLS models can alsobe used successfully to estimate the retention factorfor new compounds or for diverse compounds whoseexperimental values are unknown.

A good predictive QSRR model was obtained todescribe and predict the chromatographic behav-ior of new phosphoramidic acid derivatives usingmolecular descriptors.

ACKNOWLEDGMENTS

We thank Dr. Erik Johansson (Umetrics, Sweden) forkindly providing the SIMCA P 9.0 program package(L. Kurunczi laboratory). The authors are indebtedto Prof. Mircea Mracec for giving access to Hyper-Chem software and to Dr. Simona Funar-Timofei forthe access to STATISTICA software.

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synthesis and qsrr study for a series of phosphoramidic acid derivatives

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