Quantitative collision induced mass spectrometry of substituted piperazines – A correlative analysis between theory and experiment

Journal of Molecular Structure 1149 (2017) 243e256

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Quantitative collision induced mass spectrometry of substituted piperazines e A correlative analysis between theory and experiment Bojidarka Ivanova*, Michael Spiteller €t für Chemie und Chemische Biologie, Universita €t Dortmund, Otto-Hahn-Straße 6, Lehrstuhl für Analytische Chemie, Institut für Umweltforschung, Fakulta 44221 Dortmund, Nordrhein-Westfalen, Germany

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 June 2017 Received in revised form 29 July 2017 Accepted 31 July 2017 Available online 2 August 2017

The present paper deals with quantitative kinetics and thermodynamics of collision induced dissociation (CID) reactions of piperazines under different experimental conditions together with a systematic description of effect of counter-ions on common MS fragment reactions of piperazines; and intramolecular effect of quaternary cyclization of substituted piperazines yielding to quaternary salts. There are discussed quantitative model equations of rate constants as well as free Gibbs energies of series of m eindependent CID fragment processes in GP, which have been evidenced experimentally. Both kinetic and thermodynamic parameters are also predicted by computational density functional theory (DFT) and ab initio both static and dynamic methods. The paper examines validity of MaxwelleBoltzmann distribution to noneBoltzmann CID processes in quantitatively as well. The experiments conducted within the latter framework yield to an excellent correspondence with theoretical quantum chemical modeling. The important property of presented model equations of reaction kinetics is the applicability in predicting unknown and assigning of known mass spectrometric (MS) patterns. The nature of “GP” continuum of CIDeMS coupled scheme of measurements with electrospray ionization (ESI) source is discussed, performing parallel computations in gasephase (GP) and polar continuum at different temperatures and ionic strengths. The effect of pressure is presented. The study contributes significantly to methodological and phenomenological developments of CIDeMS and its analytical implementations for quantitative and structural analyses. It also demonstrates great prospective of a complementary application of experimental CIDeMS and computational quantum chemistry studying chemical reactivity, among others. To a considerable extend this work underlies the place of computational quantum chemistry to the field of experimental analytical chemistry in particular highlighting the structural analysis. © 2017 Elsevier B.V. All rights reserved.

Keywords: Quantification Thermodynamics Kinetics Mass spectrometry Quantum chemistry

1. Introduction Mass spectrometry has become a major analytical approach over last few decades with irreplaceable trans-disciplinary application [1,2]. In order to capture the current trend in applied MS and variations among methods that are used in the analytical practice, it needs to be stressed that more recently major outstanding contributions are instrumental methodological newcomers associated with development of ionization methods, mass analyzers and detection approaches, among others [3,4]. Through combining different MS methods with a relevant software there is a clear trend

* Corresponding author. E-mail addresses: [email protected], (B. Ivanova). http://dx.doi.org/10.1016/j.molstruc.2017.07.107 0022-2860/© 2017 Elsevier B.V. All rights reserved.

[email protected]

in developing imaging technique as well [5,6]. The main goal of these innovations is improvement of method performances and instrumental characteristics [4]. The great advantage of MS is associated with capability to elicit high accurate and precise analytical information about single analyte of interest in a complex multicomponent mixture. Mass spectrometry exhibits: (i) flexible instrumental schemes, allowing improvement of instrumental design; (ii) ultraehigh resolving power; (iii) high accuracy, precision and selectivity; (iv) fast operating and detection times; (v) simple and limited number of sample pretreatments, including instrumental capability for direct assay; (vi) low concentration limits of detection and quantification of fmoleattomol concentrations; (vii) low instrumental and linear limits of detection and quantification; (viii) analysis of large scale of molecular weights from low molecular weight (LMW) analytes to (bio)macromolecules with weights 2 10e100 kDa; (ix) study of homogeneous and

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heterogeneous systems, including analysis of aerosols, semieliquid, liquid and solidestate phases [1e6]. There is important to underline that ones of central methodologies of analysis are based on soft ionization methods such as ESI and matrixeassisted laser desorption ionization (MALDI) mass spectrometry. Very particularly developments of imaging techniques has resulted to analytical information from living cells, whole organs and bodies [5,6]. This has led to implementation of MS to medicine, clinical diagnostics, clinical microbiology and structural biology [7,8]. Furthermore underlining great applicability of MS to metabolomics, including planteomics, it is not formal to distinguish LMW analysis of biological samples from quantification of LMW analytes in complex environmental samples. There is already becoming routine application of MS based methods coupled with chromatographic approaches to environmental analytical chemistry [9e14]. For the sake of brevity, we shall here only mention other trans-disciplinary research which also broadly employ MS like forensic chemistry, nuclear forensics, pharmacy, agricultural sciences, food sciences, archeology and more [15,16]. The physical phenomena of MS processes are different to different ionization methods [1e16]. They are among most important part determining a quantitative treatment of GP fragment reactions. Despite much greater contribution of MS to the science, developments to GP phenomena are rare. To the largest part of MS methods, phenomenology and molecular/ionic level interactions remain not well understood. It could be perceived that there is a rather lack of fundamental works devoted to theoretical and experimental analyses, depending on ionization methods. In particular, complementary application of computational quantum chemistry and MS is limited to effort mainly devoted to understanding of fundamental concepts of electron impact (EI) and chemical ionization (CI) MS [17e22]. A computational study has treated qualitatively relations between molecular conformation and relative intensities of MS peaks at ion mobility MS [19]. There are few more recent studies devoted to conformational analysis of fragment ions and nonecovalent interactions of MS species under ESIeexperimental conditions [20e22]. An essential part of them are relating to qualitative MS in GP employing capability of computational chemistry to predict highly accurate energetics depending on molecular conformations of the species. However, there has not been proposed quantitative equation-models correlating reaction kinetics. Following the latter line of reasons, one of the main goals of this research is development of quantitative relations of kinetics and thermodynamics of CIDeMS reactions, studying fragment patterns of substituted piperazines under different conditions (Scheme 1). Despite questions that such as formulation of this, first, goal has generated, we should point out that according to literature data, knowledge of fundamentals of CIDeMS processes is less understood quantitatively. The second strand of the work is quantitative correlation of experimental kinetics and thermodynamics with computationally predicted parameters on the base on a molecular design and prediction of electronic structure and properties of MS fragment species. As the analysis of references [18e22] shows and was mentioned above, major contributions of implementation of computational quantum chemistry to problematic of MS phenomenology are associated with EI and CI mass spectrometry. However, by contrast to CIDeMS phenomena, EI and CI ones are relatively well understood. At this point it is necessary to be underlined, that talking about ‘mass spectrometry’ as analytical method, it is important to note that it encompasses a set of different as theoretical physical backgrounds and phenomenology methods, including instrumental design and schemes; and processes of ion formation from bulk solids, surfaces, liquids and semieliquids upon various conditions. The ESIeMS is based on assumption about a

Scheme 1. Chemical diagrams of analytes (1)e(7); Atom labelling schemes.

formation of quasi equilibrium ions based on unimolecular reactions [23,24]. On this view next developments have led to the concept about applicability of IribarneeThomson model equation of a quasi-equilibrium state giving a relation between rate constant (k) of reactions using Eyring's equation of transitions state theory [25e31]. The theory claims that relation between intensities of MS peaks at ESIeMS conditions and rate constant of these reactions at different times (t) is an exponential function, known as ‘survival yield’ [25,26]. It has been postulated that ions are produced in ground state, by contrast to EIeMS and internal energy is determined by distribution over vibrational/rotational states [31e34]. However, CID reactions, among most comprehensive theoretical studies along line ‘GP phenomenology’ are based on theoretical concepts treating noneBoltzmann GP phenomena under collision processes. Presumably, there is expected noneBoltzmann distribution of internal energy. In spite of MaxwelleBoltzmann distribution has been proposed to CID [25e31]. We will mention our more recent study, devoted to CID thermochemistry of peptides [32], where direct application of the theory stated above to ESI and correlating CID processes has resulted to a quantitative relation that rate constants of reactions obtained under one and the same experimental CID conditions and describing one and same type fragment processes are mutually connected quantitatively, furthermore, with a statistical significant confidence level 96.42%. Or these latter processes are expressed quantitatively by one and the same model equation. In this context, the first ultimate goal of this work, therefore, is to be seen a new theoretical concept treating quantitatively relations between kinetic parameters, but, within me(independent) CID experiments at different conditions and various analyte objects. We should now stress a certain generalization about ‘quantitative treatment of CIDeMS’. We distinguish between ‘quantitative mass spectrometry’ employing intensity ratios of MS peaks into linear calibration model (it already has a routine application to the field of analytical chemistry [35]) from quantitative statistical models of kinetic and thermodynamic parameters. Our study should be understood, therefore, as a quantitative treatment of latter quantities of CIDeMS reactions. We provide a correlative analysis between thermodynamic free Gibbs energetics of systems and molecular conformations stabilized as a result of CID. There are discussed new evidences supporting an assumption about stabilization of conformational states under CID processes, which are far from equilibrium ones. The results shed light on phenomenology of CIDeMS beyond classical understanding about thermodynamic stability of systems valid to spontaneous

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

process, however. This work contributes to applied aspects of CIDeMS as among rousts instrumentation of analytical chemistry. In addition, it contributes to fundamental phenomenology of GP processes and molecular structure and chemical reactivity of molecules/ions under CID MS conditions. 2. Experimental 2.1. Physical measurements HPLC
ESI
MS/MS measurements were carried out by TSQ 7000 instrument (Thermo Fisher Inc., Rockville, MD, USA). A triple quadruple mass spectrometer (TSQ 7000 Thermo Electron, Dreieich, Germany) equipped with an ESI 2 source were used for ESIeMS measurements (Table S1). A standard LTQ Orbitrap XL (Thermo Fisher Inc.) was also used. The quantification by ESIeMS was carried out via a combination of mass detectors (trap, linear ion trap and orbitrap), accumulating spectra for t ¼ 7e30 min. The selected reaction monitoring approach was used. The data were saved as individual files. The relative intensities of the species were obtained using QualBrowser software 2.7. The mass resolving power is R ¼ 90 904. The CID resolving power is R ¼ 23 604. The chromatographic analysis was carried out by Gynkotek (Germering, Germany) HPLC instrument, equipped with a preparative Kromasil 100 C18 column (250  20 mm, 7 mm; Eka Chemicals, Bohus, Sweden) and a UV detector set at 250 nm. The analytical HPLC was performed on a Phenomenex (Torrance, CA, USA) RP
18 column (Jupiter 300, 150  2 mm, 3 mm) under same chromatographic conditions. The analysis was performed on a Shimadzu UFLC XR (Kyoto, Japan) instrument. The chromatographic and MS measurements were conducted during synthesis in order to determine chemical purity of the substances used; control of their chemical reactivity under the shown experimental conditions in order obtaining of any chemically changed condensation/interaction product/s, as well as isolation of pure component/s system/s. 2.2. Synthesis Crystals of ZnIIecontaining organometallic compound (1); and the salts of dicationic 2-[4-(2-hydroxy-ethyl)-piperazin-1-yl]ethanol with the counter ions squarate dianion (2), mandelate anion (3) and {[ZnCl4]2
} (4) (Scheme 1) are obtained according [36e39]. The cyclic quaternary N-ethylmorpholine dichloride (5) and tetrachlorozincate(II) monohydrate (6) salts are obtained according [36e39], as well. Same is valid to tetrachlorozincate(II) salt of 4-(2-aminoethyl)morpholine (7) respectively which was synthesized according to [36e39]. Their crystallographic Xeray diffraction measurements and solution of crystallographic structures have been reported [36,37,39]. As far as molecular design and synthesis of these compounds is part of our systematic study on organic and metaleorganic nonelinear optical materials, experimental crystallographic geometry parameters, theoretical and experimental electronic absorption and fluorescence spectra have been presented in these works. The theoretical computations of optical excitations and emission in condense phase have been carried out [36,38,39]. In this context the paper herein involves quantitative kinetic and thermodynamics in GP both theoretical and experimental ones along with elucidation by fragmentation GP processes using various CID experimental conditions, such as solvents and voltage in order to investigate thermodynamics and kinetics of reactions occurring in GP. The MS measurements are carried out by direct dissolving of the crystals, which structure in solid e state has been determined according to [36e39]. Same structures are used for initial coordinates of the atoms for quantum chemical computations (See the next subesection 3).

245

3. Theory/calculations Quantum chemical computations were carried out by GAUSSIAN 98, 09; Dalton2011, GamesseUS program packages; visualization of data is done using GausView03 [40e43]. The thermodynamic parameters were calculated using Moltran v 2.5 program, as well [44]. Geometries were optimized at ab initio and DFT levels. The methods involved were Becke 3eparameter exchange with LeeeYangeParr correlation (B3LYP), Becke 3eparameter46 PerdeweWange1991 (B3PW91), uB97XeD, QCISD and longerange corrected (LC)euPBE (Perdew-Burke-Ernzerhof) as well as the Truhlar's M06, M06e2X and M06eHF functionals [40e42]. The Bernys' algorithm was utilized for ground state computations. The stationary points on potential energy hyper surfaces were obtained, using standard analytical harmonic vibrational analysis. The absence of imaginary frequencies and negative eigenvalues of second-derivative matrix confirmed the minima. Rotational constants were extracted by optimized geometries. When used in internal energy determinations via RiceeRamspergereKasseleMarcus (RRKM) calculations [43], the frequencies were scaled by 0.99. The Dunning's basis sets (cc-pVnZ) (n ¼ D,T and 5), 6e31þþG(2d, 2p), and quasirelativistic effective core pseudo potentials from StuttgarteDresden(eBonn) (SDD, SDDAll, http://www.cup.uni-muenchen.de/oc/zipse/los-alamosnational-laboratory-lanl-ecps.html) were employed. Evaluating excitation energies CIS, CIS(D) or timeedependent (TD)eDFT methods were employed, using GDIIS optimization. The choice of those methods was governed by known data about their accuracy as discussed in Refs. [32,54,55]. Species in solution were characterized using explicit super molecule and “mixed” approach of micro hydration and polarizable continuum model (PCM) (respectively, CPCM, and integraleequationeformalism polarizable continuum model (IEFPCM)) were utilized. The successful application of PCM for accurate prediction of IPs by DFT approaches has been shown as well. Solvation model using full solute electron density (SMD) was also used. For largest species was employed own Nelayer integrated molecular orbital and molecular mechanics (ONIOM) method, in which different parts of super molecule can be treated at different levels of accuracy, using different basis sets or different quantum methods. It was applied studying solvation effects by ONIOMPCM, as well. MM/MD computations of interacting molecular ensembles have been also carried out. Molecular mechanics calculations were performed, using consequently DREIDING and UFF force fields. The MD computations were carried out by ab initio BorneOppenheimer molecular dynamics (BOMD) and atomecentered density matrix propagation (ADMP) balancing between computational cost and accuracy. The BOMD was carried out at M06 and M062X functional as well as SDD and cc-pvDZ basis sets without to consider periodic boundary condition. BOMD computations with ONIOM for large molecular ensembles was carried out. The theoretical analysis obtains electrostatic potentials (ESPs) and natural bond orbital (NBO) charges predicting the protonation ability as well [45e53,56,57]. 4. Results and discussion 4.1. Mass spectrometric data Figs. 1 and 2 and S1 depict CID spectra of (1)e(7). Schemes 1 and 2 contain chemical diagrams, atom labelling and MS fragments discussed below. The fragment reactions of peak at m/z 131.12 of (1) yield to a MS peak at m/z 88.08. Such as observation has been reported studying MS spectra of crystals of protonated 2-[4-(2hydroxy-ethyl)-piperazin-1-yl]-ethanol [36] using MALDI method. Same is valid to (2). In work [37] we have assigned the peak at m/z

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Fig. 1. Chromatograms of (1)e(3) and (6); CIDeMS spectra of (2) and 35 and 65 V; Chemical diagram of the cation m/z 175.

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

247

Scheme 2. Proposed mechanisms of formation of morpholine from substituted piperazine; MS fragmentation pathways; Theoretical and experimental m/z values.

88.08 to protonated morpholine comparing MS spectra of crystals of mentioned above 2-[4-(2-hydroxy-ethyl)-piperazin-1-yl]ethanol cation(s) with crystals of 2-morpholin-4-yl-ethylamine. By contrast to MS/MS fragmentation pattern of set of compounds (2) [37], in MS spectra of (1), reported herein there is found a formation of ion with peak at m/z 113.12. The peak at m/z 131.12 is observed in CID spectra of (2) thus assuming that CeN and ZneN cleavage within 1-(2-hydroxy-ethyl)-piperazin-1-ium charged species can be regarded as a primary fragmentation process (Schemes 2 and S2). In general, fragmentation within cyclic molecular residue is a preferred pathway in MS spectra of molecular/ionic crystals containing 2-morpholin-4-yl-ethylamine [37]. The labeling of possible ionic fragments is shown in Schemes 3 and S1. As a reaction mechanism we have described a formation of m2b via cation diradical (m1b). Its significant molecular flexibility, comparing with m1a can explain a cyclization reaction associated with CeO bond formation. On this base we can propose a general mechanism of GP m1a þ Ar / m1b þ Ar* transition. This process causes for m1b / m2b þ m1d fragment together with CeO bond formation in m2b cation. In parallel, in (1) an m1a / m1c fragment pathway is found. The narrow ranges of operating experimental conditions towards pressure (~10
5 Torr (100 Pa or 9.8.10
4 atm), Table S1) prevent to evaluate the role of buffer gas on rate of reactions. In spite of this fact we are carried out computations of thermodynamic parameters of collision gas in a neutral and positively charged form (Table S2). The difference of free Gibbs energy (D(DG)) of both type species is j0.581097j a.u. (364.64 kcal mol
1). This fragment behavior is typical to (1)e(4) (Fig. 2). The structural analogue in (5) and (6) [36e39] exhibits MS fragment profile showing formation of MS ions at m/z 130, 112, 110 and 101 (Fig. 2). The MS peak at m/z 114 has been assigned to half of molecular weight of doubly charged quaternary N-ethylmorpholine dication [36]. The quantitative treatment of reaction kinetics is carried out using shown in the next scheme MS peaks in (1)e(4) and compounds (5)/(6):

The thermochemistry is based on assumption that ESI ion source has produced ions with internal energies, which can be expressed well by MaxwelleBoltzmann distribution using well known quasieequilibrium assumption. The energy transfer is associated with transfer to rovibrational states of molecules/ions. The energetics of systems studied is given within threshold regions of cross sections where low energy CID experiment is identified with threshold experiments and thus measured threshold corresponds to bond dissociation energy. The relation MS intensity of peak of cationics is given according [25]. The ratio intensities of cation at time t ¼ t (IM,t) and intensity at t ¼ 0 (IM,0) yields to dissociation rate constant k(E) and t, respectively. The t is time scale of experiment. The k(E) is a function of internal energy of a molecule, respectively, a fragment ion. Within an isolated ESIeMS experiment (Scheme 4) t is determined as flight time of an ion between MS source and analyzer. It depends on the instrumental setup configuration and the voltage [25]. But as it is written above t can be experimentally modified, so that at a shorter t, there should be obtained higher internal energies and larger dissociation rates of fragment reactions. Now, the direct application of the equation about ‘survival yield’ [25] to the shown in Scheme 4 experimental design is based on the followings. Nevertheless that the energetics of fragment reactions in ESI are less understood in general context, by contrast to EI mass spectrometry (the internal energy in EI is high, thus leading to the excitation of electronic and vibrational states causing to an electron ejection and formation of abundance fragment ion species) in ESI fragment ions should across a high pressure region where their internal energy is modified). This process is carried out before MS analyzing. However, once when the internal energy distribution of ions is builder up at mentioned above high pressure region, there is not further fragmentation. Within the theoretical treatment of CIDeMS thermodynamics and kinetics we have chosen as initial to

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Fig. 2. CIDeMS spectra of (1)e(7) within the range of molecular weigths m/z 100e130; Experimental and theoretical design of the performed correlation analyses between the rate constant producing the sown with pointers fragment MS ions.

CIDeMS experiment namely this, latter, ESI state (t ¼ 0), thus describing reaction kinetics of MS/MS processes. This determines that in our theoretical treatment t ¼ t depends on experimental time duration of CID experiment, not from time duration of ESI one. In this context the description here excludes from complexity of ion formation processes by ESI operating with experimentally observed selected set of fragment ions with a fixed within the ESI conditions initial internal energy distribution. Furthermore, the great capability of CIDeMS to treat precursor ion separately in its isolated state, thus generating highly reproducible fragment species [32] allows us not only to deduce the structure of this ion but in a combination with corresponding quantum chemical treatment to extract exact 3D molecular conformations through reported herein

modeling. Taking into consideration that by ESI intact molecular analyte ion is obtained with minimal fragmentation we have obtained in-fact direct structural information about analyte in solution. In addition to possible nonecovalent interacting oligomer species. As far as next theoretical treatment yields to quantitative statistical relations, there is provided direct evidence about high reproducibility and predictability of CID spectra, thus overcoming difficulties about interpretation of ESI MS spectra due to not well understood processes of ion formation which as it is well known depends on many environmental factors such as the nature of the solvent, pH, accelerating voltage, pressure and more. Furthermore, there is important to highlight that these quantitative relations, moreover, are applicable for correlation within class of compounds

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

(below) thus extending the current mainly qualitative or semiquantitative treatment of reaction kinetics and thermodynamics to statistically significant quantification. Various arguments can be presented towards applicability of IribarneeThomson model equation to CIDeMS. One series of argumentation focuses on nature of GP continuum in CIDeMS accounting for that the experimental scheme is based on initial ESI, which is directly coupled with CID mass spectrometry (Scheme 4). The nature of ESI has been extensively studied [58e63] thus providing a comprehensive understanding about formation of charged ions in GP as result of evaporation of charged droplets of solution of analyte, describing the initial molecular ions as a hydrate {[M(H2O)2]þ} molecular cation [64,65]. For this reason IribarneeThomson model is based on transition state theory (TST) applicable to ion mobility MS of charged hydrate species, where major dissociation process is cleavage of solvent H2O molecules [64,65]. At this point we could assume that initial solvent environment should be taken treating CIDeMS spectra as well (See section 4.2). Nevertheless under ESIeMS conditions there are obtained as final stage free charged ions in GP [58e63], the ESI measurements frequently have yielded to stabilization of solvation complexes [58e63], cause of the soecalled GP environment contains as well as fragment solvent molecules like for example H2O, CH3CH3OH, CH3OH, etc., together with solvent molecules from the solution analytes. A further related insight into quantitative relationships between MS intensities of CID reactions and kinetics and thermodynamics of processes can be derived studying fragment patters under different CID voltages. As we could expect there is obtained different intensities of ions at time t. For example, if we describe an MS intensity (I0 ) at time t which is characterized with t0 at given CID voltage and a second experiment involving different CID voltage then there is observed intensity of the ion I00 at t00 . In both cases the initial intensity IM,t¼0 is one and the same. Then it should be valid the relationship Equations (1)e(3). 00

0 IM;t¼t

¼ ek ðEÞ$t 0

0

0

0

0 IM;t¼t 00

IM;t¼t

ln

00

e

k0 ðEÞ$t0

$e

¼

¼

e
k ðEÞ$t e
k

0 IM;t¼t

0

0

00

ðEÞ$t00

have not physical meaning. All aboveementioned theoretical assumptions and relations (Equations (1)e(5)) can only be settled once we obtain quantities about k00 and k0 of a fragment reaction observed under different CID conditions. A direct quantitative evidence about validity of our theoretical concept above follows studying CIDeMS data of (2) (Figs. 1 and S1) at m/z 175 (Scheme 3). The intensity ratios IM,t¼t/ IM,t¼0 are 0.98592 (CID ¼ 35 eV) and 0.0018381 (CID ¼ 65 eV). According to Equation (4) there is found a theoretical value 0.00349158 (t ¼ 30 min ¼ 1800 s) about k00
k0 . The employment of equation about ‘survival yield’ [9(a)] lead to obtaining of corresponding experimental values about the rate constant of the same reaction at both CIDeMS experimental conditions (CID ¼ 35 and 65 eV) of k’ ¼ 7.87764.10
6 s
1 (CID ¼ 35 eV) and k00 ¼ 0.00349946 s
1. The difference between these experimental quantities yields to k00
k0 ¼ 0.00349158. Or there is 100% confidence between rate constant differences obtained using ‘survival yield’ equation in Ref. [25] and our Equation (4). The main importance of this result is due to the fact that it unambiguously shows applicability of MaxwelleBoltzmann distribution equation to noneBoltzmann processes like CIDereactions, furthermore quantitatively. The relations have a statistical representativeness. In order to illustrate the last statement, let us describe the CID reactions at 35, 55 and 85 eV to the MS peak at m/z 113.12 (Fig. S1). The experimental k0 , k00 and k000 rate constants according to equation of survival yield [25] are 3.17908.10
5 s
1
4
1 (CID ¼ 85 V),
2.736637.10 s (CID ¼ 35) and
3.917102.10
4 s
1 (CID ¼ 55 V), respectively. The employment of Equation (4) in predicting the {k00
k0 } using MS intensity ratios of peak at m/z 113.11 in both CID spectra results to {k00
k0 } ¼
3.054544 (Fig. S1). As can be seen from the data above {k00
k0 } ¼
2.736637.10
4 e 3.17908.10
5 ¼ 3.054544. Or there is, again, a 100% correspondence. Within CID experiments, next development of Equations (4) and (5) should result to Equations (6) and (7) valid for three independent CIDeMS measurements.

0=$ek ðEÞ:t 0 0

00

k ðEÞ$t

0

(1)

00

I0M;t¼t ek ðEÞ$t

IM;t¼t

249

IM;t¼t 00

ek

00

ðEÞ$t

$e

k0 ðEÞ$t0

(2)

!

00

IM;t¼t

00

00

00

¼ k ðEÞ$t
k ðEÞ$t0

(3)

As far as t0 and t00 are time scales of the experiments, they can be chosen by the operator as t0 ¼ t00 . In this case there should be valid Equation (4).

1

t

$ln

0 IM;t¼t

! 00

¼ k
k0

00

IM;t¼t

(4)

For a common case of n experiments, there should be applied an Equation (5), where i  1 and m  0, respectively.

1

t

$ln

i IM;t¼t n
m IM;t¼t

! ¼ kn
m
ki

(5)

As we could deduce negative values of m and i should cause to negative MS intensities, which within the positive operation mode

Scheme 3. Fragment patter of the cation of (2); Chemical diagrams of the proposed fragment ions.

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Scheme 4. Experimental design of the coupled ESI and CIDemass spectrometry.

0

0

00

k ,t ¼ k $t
ln

000

0 IM;t¼t 0

00

000

(6)

00

IM;t¼t 00

k0 $t0 ¼ k $t
ln

0 IM;t¼t 0 0 IM;t¼t 000 00

:

(7)

Equation (8), therefore, gives a relation between k00 and k000 . 00

00

000

000

k $t ¼ k $t ¼ ln

0 IM;t¼t 0 00

IM;t¼t 00


ln

0 IM;t¼t 0 0 IM;t¼t 000 00

:

(8)

Within independent CIDeMS measurements at t00 ¼ t000 ¼ t, there should be valid Equation (9).

! 0 0 IM;t¼t IM;t¼t 0 0 00 000 1 k
k ¼ $ ln 00
ln 00 0 : t IM;t¼t 00 IM;t¼t 000

(9)

A direct evidence about its validity follows studying intensity ratios of peak at m/z 113.11 at CIDeMS measurements at 85, 35 and 0 55 V (Fig. S1). According Equation (9) ln{(I M,t¼t0 )/ 00 0 (I m,t¼t00 )} ¼
0.549818. The corresponding value about ln{(I M,t¼t0 )/ 000 (I m,t¼t000 )} is
0.7623017. Then at t ¼ 1800 s, we obtain {k00
k000 } ¼ 1.18046.10
4. Now, turning in stated above values of experimental rate constants subtraction of k000 from k00 yields exactly to the quantity 0.0001180465. Or, again, there is 100% correspondence between the data. From the results about free Gibbs energies of species in GP under CIDeMS reactions and our analytical discussion we may also conclude that depending on experimental CID conditions there would be possible stabilization of molecular conformations of fragment ions which are far from equilibrium state (See the next section 4.2). This assumption goes beyond the classical understanding about stabilization of conformation corresponding to minimum of potential energy surface. In general, this is valid to spontaneous process. However, there is unable to address CIDeMS reaction to such as spontaneous stabilization of given molecular and electronic structures of fragment ions. A direct confirmation follows from frequently obtained “negative” rate constants studying fragment patterns of ions (above). The physical meaning of such as “negative rate constants” reflects in fact a system characterizing with a positive free Gibbs energy according the IribarneeThomson model and Eyring's equation [25,26,32]. Similarly, this conclusion goes beyond classical concept about the thermodynamic stability of species under spontaneous reactions. Or we can assume that under CIDeMS reactions there would be possible stabilization of species with positive free Gibbs energy values (See the next part of the work). In addition, we evidence, here, that studying reaction kinetics

and thermodynamics of CIDeMS processes employing computational quantum chemistry allow us a highly reliable prediction of MS patterns as far as corresponding kinetic, respectively, thermodynamic parameters are exactly determined within the known model equations [25,32] and Equations (4) and (5), presented in this paper. Or these model equations clearly have implications for theoretical prediction of CIDeMS spectra. Once when we have obtained thermodynamic free Gibbs energy parameters of reactions and corresponding derivate kinetic ones, then using Equations (4) and (5) we can obtain intensity IM,t. A semieempirical treatment should involve measurements of the MS spectra at t ¼ 0 in order to gain information about IM,t¼0. Or employing parallel measurements under CID conditions employing Equation (5) in order to predict IM,t¼0, respectively. The analysis of CIDeMS data of (1) shows the rate constants k for reactions of m1b and m2b′ ions: k ¼ 1.7615.10
4 s
1 and 1.50264.10
4 s
1 (m/z 113) as well as k ¼ 0.002433 s
1 (m/z 88). Those data agreed excellent with boundary condition that k  0.01/ t [25]. If we compare the data about (1) and corresponding ones for same process of fragmentation observed in another set of piperidineecontaining derivatives discussed above [36e39], then for reaction monitoring towards m/z 88 a k ¼ 0.00186 s
1 value is obtained, using the same kinetic mode. Those data indicate that the mechanism of the ion formation of m2b′ via m1b is same in both substances (1) and those set piperazine containing compounds as they have been reported in Ref. [37] (Compare the data here and in Ref. [37]). In order to illustrate unambiguously the validity of discussed treatment of CID fragment kinetics quantitatively, let us correlate rate constants of CID reactions of (12) at different energies 35 and 65eV (Fig. 3). Fragment ions typical for piperazines at m/z 131, 114, 113, 116, 102 and 101 are studied (Fig. 2). As can be seen from the data in Fig. 3 and Table 1 there is obtained confidence level 98.829%, which illustrates a high reliability of our models. On the other hand, this result assumes that within the one and the same type of cleavage process in “GP” under CID conditions CID CE percentage of energy effects on abundance of fragment ions, but a lack of effect on reaction kinetics occurs. There is important to underline that experimental studies on ESIeMS have shown that solvent polarity of analyte solution plays important role on fragmentation efficiency of MS spectra and MS fragment patterns [58e63]. The later observations provide direct evidences about a polar continuum environment, rather than a GP one. In general, these data agree with a concept that intensity of MS peaks under ESIeconditions depends on parameters accounting for fraction of charges on droplets, in addition to rate constants and ion samplingeefficiency [58e63]. The fact that our data indicate same behavior under CIDeMS conditions, additionally support the concept of polar continuum environment. Furthermore, a correlative analysis between rate constants of one and same type of

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

251

Fig. 3. ESIeMS spectra of (1) within the range of molecular weigths m/z 290e345 of ZnIIecontaining inorganic complex species, observed in parallel to the discussed MS ions of the piperazine-containing organics.

Table 1 Chemometric analysis of the data in Figs. 2 and 3. (1)/(2) A B

Value
1.5099.10 1.25582

Error
4

5.7138.10 0.25174

r
4

0.96209

SD 4.5469.10e5

p 0.03791

fragment reactions, but observed within two different substances (Analysis of (1) and (2)) under different experimental conditions yields to confidence level 96.209% studying same set of MS ions (Figs. 2e4 and Table 1). The latter result indicates that CIDeMS can be used for structural analysis and unambiguous identification of analytes in complex mixture using selected set of common to given molecular fragment kinetic parameters. Preliminary we could write, that this statement is valid to experimental thermodynamics as well (below).

(2)

Value

A B

3.08404.10 0.94932

(2), ki,j

Mean 0.00438 0.00212 0.00106 0.00319

Error
5

r

2.99359.10e5 0.10362

0.98829

SD(yEr±) 2.98399.10e5 3.62378.10e4 3.36371.10e5 7.37866.10e5

SE(yEr±) 2.11.10e5 2.5624.10e4 2.3785.10e5 5.2175.10e5

SD 2.61179.10

p
5

0.01171

The correlation between theoretical quantum chemical thermodynamics and experimental MS energetics is carried out using Eyring's equation [66]. Early work on CIDeMS has assumed that ion source produces ions in quasi-equilibrium state [67]. Ensembles of interacting nonecovalently bonded species in GP occur. In this context the free Gibbs energy in the discussed equation is associated with a transition state (TS). And thus the employment of Eyring's equation allows us to extract high accurate information about internal energies of MS fragment ions via high resolution MS

Fig. 4. Correlation analyses between kli,j rate constants of CID reactions of (11) at different experimental conditions; and between (1) and (2) at one and the same experimental conditions, but applied CIDeMS to different parent ions (kli,j denotes the rate constant of ith compound (i ¼ 1 or 2); lemolecular weigth of the fragment ions and j e applied energy).

252

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

measurements computing experimentally rate constants of unimolecular reactions [68,69]. There is important to discuss however per-exponential parameter (k) in the original equation along with employment of Wigner correction describing processes within the conventional TST [69] (Equation (10)). In latter equation, the jnj accounts for imaginary frequency of TS energetics, which direct application to molecular ensembles exhibiting permanent stability (or systems at stationary states) has led to discrepancy between theory and experiment about reaction rates [67e71].



 k¼

1þ

1 hPnR 24 kB $T

2 

DG k $T $ B $e
RT h

(10)

In general, deviation from “universal frequency” in original Arrhenius' theory of TS has been broadly discussed [70,71]. In this context our correlation between experimental and theoretical quantum chemical data (next subesection) uses an assumption that CIDeMS fragment species are at their stationary state. As it has been already shown [32], obtaining of high reproducibility of CIDeMS spectra assumes that at MS-analyzer measured intensities of fragment ions corresponds to their most stable electronic structures and interacting ensembles. Our optimizations correspond to computation of most stable geometries, thus excluding from calculation of energetics on the base on TS energies. Or in Equation (10) we neglect the parameter 1/24.{[hjnj/kB.T]2}, because of a stationary state jnj ¼ 0. Furthermore we have described systems optimized in polar continuum, nevertheless, that our initial geometry parameters of the analytes are those determined crystallographically in Refs. [36e39]. On the base of this approximation calculated free Gibbs energies of above CID processes show DG(m/z 113) ¼ 22737.54 J mol
1 (or 5.4344 kcal mol
1) and DG (m/z 88) ¼ 21082.90 J mol
1 (5.03893 kcal mol
1). The data about DG (m/z 131) is 22643.08 J mol
1 (5.41183 kcal mol
1). The analysis of fragment CIDeMS reactions of ion at m/z 175 in (12) shows k ¼
2.225.10e4 s
1. The application of Equation (10) within the stated above approximation yields to DG ¼ 22828.27 J mol
1 (5.456 kcal mol
1). The corresponding theoretical data are shown in the next section.

4.2. Theoretical quantum chemical data Let us start this section with evidences confirming validity of the later statement from the previous subesection. In this context, now, we describe CIDeMS fragment reaction of (12) to ion at m/z 175 within the reaction (11):

  2: m175 /m1a þ m2b00 þ md0 þ 2:C2 H5 OH

(11)

As far as both precursor (m175) and fragment ions could exhibit series of conformational situations with close energies due to flexibility of aliphatic chains as well as Neheterocyclic aliphatic residue we describe comprehensively set of possible conformations (Schemes 1, S4 and Fig. S3). To all closely dispose as energies molecular conformations and optimization in GP and solution is performed in order to determine precisely error contribution to free Gibbs energy of reaction (11) due to effect of molecular conformation and possible intra-molecular hydrogen bonding. The obtained energies are listed in Table 2. The computations of solvent CH3CH2OH in polar continuum yield to DG ¼
6.5 kcal mol
1. The summing up of energies of fragment ions (Table 2) result to DG of reaction (11) 4.87 kcal mol
1. As can be seen from a correlative analysis with experimental thermodynamic free Gibbs energy obtained on the base on CIDeMS spectra (DG ¼ 5.456 kcal mol
1) a difference between theory and experiment D(DG) ¼ j0.586j kcal mol
1 is obtained. This excellent correspondence between theoretical quantum chemical and experimental CIDeMS thermodynamics unambiguously confirm validity of Equation (10) within the approximation discussed above. In addition, this result clearly indicates that the thermodynamics computations of molecular 3D structures of analytes and their typical fragment reactions depending on concrete CIDeMS conditions allow to assign not only qualitatively, but quantitatively 3D structure of analytes using MS CID spectral as well as; to predict profile of unknown and/or chemically substituted derivatives to piperazine skeleton, studied in this paper. Towards mechanistic aspects of CID induced reaction of formation of morpholine scaffold from corresponding piperazine skeleton we have proposed formation of cation diradical (m1b),

Table 2 Thermodynamics by DFT, using LCeuPBE, B3PW91 and B3LYP functionals with SDD and ccePVnZ, augeccePVnZ basis sets in polar continuum.

ET S DEUPSS DEPSS DESP DET DED DER DETNS DG

E

T

S

DEUPSS DEPSS DESP DET DED DER DETNS DG

m1a

m1b

m1c0

m1c00

m1e0

m1e00

m2b0

m2b00


422.126815
62.40
65.79 1.80
64.00
28.33 9.78
1.17 ¡65.16


421.908608
86.03
67.75
105.98
173.73
26.36 8.76 1.72 ¡172.01


345.710385
64.27
71.50 4.00
67.50
23.74 7.20
0.12 ¡67.62


345.694377
59.19
63.45 2.40
61.05
23.99 7.87 0.13 ¡60.91


422.090861
76.23
88.87 6.72
82.15
29.35 11.33
0.44 ¡82.59


422.118765
63.76
71.28 4.21
67.07
27.73 8.94
1.11 ¡68.18


288.168542
76.18
84.94 4.65
80.29
21.28 8.42
0.96 ¡81.25


288.193814
66.79
72.55 3.25
69.31
19.99 6.25
1.65 ¡70.96

m131b-conf. (a)

m131 b-conf. (b)

m1d000

m175-conf. (a)

m175-conf. (b)

m1d0

m1d00


414.4401
76.34
84.04 3.94
80.10
29.49 11.45
0.61 ¡80.71


421.9825
79.38
89.60 5.16
84.44
29.31 11.21
0.67 ¡85.11


133.919125
5.31
6.56 0.64
5.92
10.32 2.43 1.21 ¡4.71


575.7457
85.59
98.32 6.52
91.80
35.70 13.69 0.27 ¡91.52


575.750415
101.64
120.35 9.77
110.57
36.41 14.26 0.17 ¡110.40


133.727474
66.67
68.04 0.75
67.29
11.12 3.02 0.48 ¡66.81


133.652737
68.94
72.58 1.98
70.61
10.07 2.11 1.36 ¡69.25

ETS e total free energy in solution [a.u.]; DEUPSS e Unpolar solute/Solvent interaction energy [kcal mol
1]; DEPSS e Polar solute/Solvent interaction energy [kcal mol
1]; DESP e solute polarization energy [kcal mol
1]; DET e Total electrostatic energy [kcal mol
1]; DED e Dispersion energy [kcal mol
1]; DER e Repulsion energy [kcal mol
1]; DETNS e Total nonelectrostatic energy [kcal mol
1]; DG e free Gibbs energy [kcal mol
1]. The free Gibbs energy values are highlighted.

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

particularly proposing eNH and eO radical formation (Scheme 2). The quantum chemical data are summarized in Tables S2 and S4. The molecular flexibility of ionic species m1a, m1b and m0 allows stabilization of a set conformations of molecular scaffold, thus leading to conformational analysis (Scheme S2, Table S3), showing three possible molecular geometries of m1b ion (Schemes S3 and S4). Most stable from a thermodynamic standpoint appears conformation m1b (a). The energy difference between species m1b (b) and m1b (c) is D(DE) ¼ j5.8892j and j3.7242j eV, respectively (Scheme S3). Comparing with m1a ion a higher energy D(DE) ¼ j7.6472j eV is found. This result supports the assumption about stabilization of diradical cation (m1b) in GP, to which we assign MS peak at m/z 131.12. The thermodynamic and kinetic data (Table S4) at DFT level of theory both in GP and in continuum are shown as supporting information. The ab initio results are summarized in Table S4. The NBO analysis and DFT thermochemistry is summarized in Tables S5eS7. The comparative analysis between ccpvdz and SDD basis sets towards prediction of thermochemical data yields to DET 2 j0.004jej0.0428j Hartree.(particle)
1 (Table S7). Or, values DET 2 j2.51jej26.86j kcal mol
1. While the effect of diffusion and polarization functions to the first basis set comparing cc-pvdz and cc-pvdzþd is accounted for j0.0352j Hartree.(particle)
1, respectively. The analysis of aug-cc-pvdz and aug-cc-pvdzþ2df exhibit DET ¼ j0.531j Hartree.(particle)
1. Accounting for the values of the free Gibbs energies of the reactions studied, there can be concluded that DFT methods and employment of effective core potentials provide reliable information about thermochemistry of processes examined herein, i.e. DG 2 (j216547.91j±j2.51j)e(j216547.91j±j26.86j) kcal mol
1 (Tables S2 and S4). The cleavage of H2O molecule and formation of m1c ions from corresponding m1a we associate with formation of two possible cationic species labeled as m1c0 and m1c00 , respectively (Scheme 2). The thermodynamic data both in GP and in solution have shown that m1a is less stable from thermodynamic standpoint (DG (m1c0 ) < DG (m1c00 )) (Tables S3 and S4). Or, it can be proposed a m1a/m1c0 fragmentation pathway, whit thermodynamic parameters accounting for the process: 



m1a /m1c0 þ H2 O

(12)
1

DrH (299.15) ¼ 6.46147 kcal mol and DrG (299.15) ¼ e 4.300323 kcal mol
1, respectively (Tables S3 and S4). The data about H2O are ε0 ¼
0.022076, εZPE ¼ 0.021484, ε0 þ ETot ¼
76.380278, ε0 þ Hcorr ¼
76.379334, ε0 þ Gcorr ¼
76.401410, ETot ¼ 0.024320, Hcorr ¼ 0.025264 and Gcorr ¼ 0.003188 Hartree.(Particle)
1 at same theoretical level. The thermodynamic data both in gas phase and polar continuum show that m1a has lower stability, then m1b (D(DG) ¼ j106.85j kcal mol
1). This result assumes a highly probable formation of cationdiradical m1b, thus explaining the formation of morpholine scaffold via: 0

m1b /m1c0 þ H2 O

0

(13)

The thermochemistry of fragmentation process: DrH0 (299.15) ¼
119.04922 kcal mol
1 and DrG0 (299.15) ¼
130.033774 kcal mol
1, respectively (Tables S3 and S4). The obtained energies of formation of cationdiradical m1b and stabilization of 4-vinyl-piperazin-1-ium ion (m1c0 ) ion in GP (m/z 113.11) via shown above fragmentation pathway appears a competitive from a thermodynamic point of view reaction, by contrast, to a process of direct cleavage of H2O molecule from 1-(2hydroxy-ethyl)-piperazin-1-ium cation (m1a) (D(DrG0 (299.15)) ¼ j125.73j kcal mol
1). The data about stability of species m1d0 , m1d00 and m1d000 have shown that in GP more stable is m1d0 ,

253

while in continuum there is higher probability for stabilization of m1d00 . In this context the thermodynamic data about following two processes of fragmentation:

m1b /m2b0 þ m1d0

(14)

m1b /m2b0 þ m1d00

(15)

are DrG0 (299.15) ¼ 104.72506 kcal mol
1 for first process and, respectively, 127.73897 kcal mol
1 for the second one in the GP. The involvement of solvent H2O in reaction 13 is based on the assumption that in polar continuum under initial soft ionization ESIeconditions where the cations are formed from the charge droplets of the analyte solution frequently there are found a stabilization of the hydrate, respectively, solvate coordination complexes [39,58e63] as it was already pointed out above. Furthermore the stabilization of the charged hydrate species, together with the well-known alkali ion and NHþ 4 adducts and/or hydrogen bonded analyte oligomers depends on the relative proton accepting ability or basicity of the analytes in a general context, including the fragment ions, which however vary from the GP to continuum [58]. As far as we operate with an experimental scheme (Scheme 2) involving direct coupling between ESI and CIDeMS, associated with a general complexity of the ESI processes, followed after by the not well understood CIDeMS ones there is unable to neglect a possible formation of {[m1c0 .H2O]þ} charged species as well. As far as a closely associated to CID is the phenomenology of dissociation of molecules/ions due to preliminary activation [34], then the participation of the H2O molecule in the TS of dissociation would contribute to the common energetics of the process, determining the free Gibbs energy at the TS according the IribarneeThomson model equation. Moreover operating with low energy CID mass spectrometry, the collision phenomenology includes MS fragmentation a result of multiple collisions. This presumably means a multi-step cleavage reactions [34]. Thus, in order to account comprehensively for different possible reaction transitions states we perform parallel computations in the presence and without small molecular neutral fragment molecules like for example H2O, CH3OH, CO, CO2, etc. The energetics balance of reactions shown in Scheme 2 accounting, however, internal energy contribution to the free Gibbs energy (Table S2) shows the following results. Towards the fragmentation pattern shown as “Reaction 12” D(DG) ¼ j12.08j kcal mol
1 comparing DGs of m1c0 and m1c00 . In this respect DG1 of “Reaction 12” is j47946.06j kcal mol
1. Toward “Reaction 14” the D(DG) of m2b0 and m2b00 is j21.09j kcal mol
1, so that we describe m2b00 and m1d00 fragments formation. Thus, DG1 ¼ j7.99j kcal mol
1. Given that DG is j47954.05j kcal mol
1. The comparative analysis with the experimental data shows D(DG) ¼ j3005.60j kcal mol
1 (see subesection 4.1). This deviation can be associated with entropy contribution and/or originating due to difference between the experimental and theoretically predicted conformational preferences of the fragment ions, which are characterized with a significant molecular flexibility. In this context, there should be stressed that to determine the accurate molecular and electronic structure of the fragment ion represent the crucial step of the theoretical modeling of the fragment MS patterns. Because of the extreme CID condition frequently cause for unpredictable chemical reactivity following the classical concepts of the interaction of organics at ambient conditions in solution. It needs significant efforts in predicting the fragment patterns when set of competitive reactions occurs. Generally, here is important to highlight that the model of charged species in polar continuum, accounting to the contribution of the internal energy (Table S2) described well the

254

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

thermochemistry observed under CID mass spectrometric experimental conditions [10]. Those results confirm the assumption that despite the fact that the during the CID experimental conditions the species are not at thermal equilibrium, and thus presumably should be valid the noneBoltzmann distribution, there have been obtained essentially same relationship using the noneequilibrium models [28]. In this context as it was already written equilibrium thermodynamic models have shown a high reliable application studying CID fragmentation reactions. The contribution of formation of azetidinium fragment to energetics of the reactions is accounted for a total energy value
108923.95 a.u., which should be take into consideration studying fragmentation pattern under CID ¼ 55 and 85 eV. The computations show that consideration of contribution of collision gas to energy balance of reaction fragmentation pathways can be neglected (Tables S2 and S1). The conformational analysis of mj ion (Scheme S5) reveals a series of conformers with energies < 0.24 kcal mol
1 (0.01 eV) (Fig. S3, Table S9). The NBO analysis yields to a positive value (qC(NBO) ¼ þ 0.135) of C(H2) ¼ Nþ center and a negative one to OHecenter (qO(NBO) ¼
0.785), thus determining strong electrostatic interaction within the cation. Such as reaction should yield to oxazolidin-3-ium cation (m/z 74.06). This can explain experimentally observed low abundance MS peak at m/z 74.70. The involvement of mj and ml in “Reaction 15” leads to DG values j84618.44j and j83860.06j kcal mol
1. By contrast, energy balance according to “Reaction 16” and involving mg0 cation yields to DG ¼ j24915.25j and j25673.63j kcal mol
1.

mj ðml Þ/m2b0 þ mg0

(16)

Comparing with experimental data D(DG) ¼ j1229.89j and j4410.68j kcal mol
1 are obtained These data highlight reaction mechanism via cation formation of mj and ml ions as competitive to “Reaction 15”. As far as potential energy distribution is a function of ionization potentials (IPs) and internal energy of species a quantum chemical prediction of these quantities computing both vertical and adiabatic IPs is carried out (Tables 1 and S8). Figs. 5, S4 and Table S11 reveal energetics of MS fragment ions of (2). The molecular optimization of m52 ion shows a skeleton transformation (Figs. S4 and 5). Table S9 illustrates optimized geometry parameters. Natural ionicity values [56] i12 and i34 of 0.26/ 0.455 and
0.188/e0.3 are obtained (Tables S5 and S6). A deviation from pure covalent character (iij ¼ þ/
0.5) occurs. The bond orders and hybrid overlap integral values are summarized in Tables S12 and S13. The directionality analysis and deviations from line nuclear centers are listed in Table S14. The orbital character of N1eC2 (Fig. 1) is spl as far as N1exhibits s(32.64%)p2.06(67.36%), while C2

s(25.50%)p2.92(74.50%) hybrid configurations (Table S6). This conclusion is supported studying natural ‘bond bending; or ‘strain’ (Table S14) showing ‘Dev’evalue of 0.0 or a s e character of the bond. Nevertheless, there is obtained Dev ¼ 90.0 for the second bond, thus indicating a p-bond nature. The data in Table S14 summarizes polar and azimuthal angles in spherical coordinates. They determine line of centre direction and hybrid direction. The ‘Dev’ denotes the angular deviation [56]. When the quantities are small (<1 ), there is a small strain.

5. Conclusion Shortly, with this work we thus not only describe, but rather explain quantitatively GP phenomena of reaction kinetics and thermodynamics of CID mass spectrometric processes. We have provided statistically representative examples about validity of new concept and model equations connecting rate constants of one and the same reactions, typical for different analytes, within the framework of menumber of different independent CID reactions yielding to 98.83% reliability of the compared rate constants of fragment MS reactions. The results unambiguously illustrate validity of MaxwelleBoltzmann distribution treating noneBoltzmann CIDeMS phenomena, Iribarne-Thomson's model and Eyring's model equations. In this work as well as we have begun to insight into GP phenomenology of CIDeMS e quantitatively e associated with kinetic and thermodynamic behavior of collision induced fragments. We have shown how are correlated experimental kinetic parameters as well as those ones corresponding to our model equations thus establishing a 100% correspondence between the data. There is obtained a difference D(DG) ¼ 0.58 kcal mol
1, between experimental MS thermodynamics and theoretical quantum chemical data, studying a representative set of molecular conformations of parent and fragment CIDeMS ions. As far as CIDeMS spectrometry, and in general, methods of mass spectrometry represent robust and irreplaceable analytical tools for qualitative, quantitative and structural analysis, which have already found place to many interdisciplinary branches of analytical sciences, we are now in position to say here that our theoretical treatment of experimental CIDeMS spectra and model equations and their more than satisfying support obtained on the base on quantum chemical methodology, clearly illustrate that the complementary application of these approaches enable development of CID mass spectrometry beyond its routine application for quantification within the wellknown linear calibration model. A systematic further research involving quantitative kinetic and thermodynamic both experimental CID mass spectrometric and theoretical quantum chemical treatment allows us to predict CIDeMS spectra of analytes,

Fig. 5. BOMD data of fragment ions at m/z 52 and 113; Chemical diagrams and the optimized structure of ion m52.

B. Ivanova, M. Spiteller / Journal of Molecular Structure 1149 (2017) 243e256

quantitatively. This represents an important and crucial methodological step into development of CIDeMS for structural analysis. As far as structural analysis represents the third branch of the analytical chemistry, such as methodological contributions directly impact the field of analytical chemistry and its applied interdisciplinary aspects. In addition, there is provided a great prospective for development of fundamental knowledge and understanding about relations between molecular structure, electronic structure, kinetics, thermodynamics and chemical reactivity, which essentially has outstanding contribution to development of the fundamentals of the chemistry in a general context. Acknowledgments The authors thank the Deutscher Akademischer Austausch Dienst, Deutsche Forschungsgemeinschaft, central instrumental laboratories for structural analysis at Dortmund University (Federal State NordrheineWestfalen, Germany) and analytical and computational laboratory clusters at the Institute of Environmental Research at the same University. Conflict of interests: Michael Spiteller has received research grants (Deutsche Forschungsgemeinschaft, 255/21e1 and 255/22e1); Bojidarka Ivanova has received research grants (Deutsche Forschungsgemeinschaft, 255/22e1, Alexander von Humboldt Foundation, research fellowship). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.molstruc.2017.07.107. References [1] R. Zenobi, Ionization methods in mass spectrometry, Anal. Chem. (2017), http://dx.doi.org/10.1021/acs.analchem.5b01062. [2] T. Nakashima, H. Wada, S. Morita, R. Erra-Balsells, K. Hiraoka, H. Nonami, Single-cell metabolite profiling of stalk and glandular cells of intact trichomes with internal electrode capillary pressure probe electrospray ionization mass spectrometry, Anal. Chem. 88 (2016) 3049e3057. [3] R. Zubarev, A. Makarov, Orbitrap mass spectrometry, Anal. Chem. 85 (2013) 5288e5296. [4] F. Xian, C. Hendrickson, A. Marshall, High resolution mass spectrometry, Anal. Chem. 84 (2012) 708e719. [5] E. Seeley, R. Caprioli, 3D imaging by mass spectrometry: a new frontier, Anal. Chem. 84 (2012) 2105e2110. [6] L. Qiao, E. Tobolkina, A. Lesch, A. Bondarenko, X. Zhong, B. Liu, H. Pick, H. Vogel, H. Girault, Electrostatic spray ionization mass spectrometry imaging, Anal. Chem. 86 (2014). [7] S. Dunham, J. Ellis, B. Li, J. Sweedler, Mass spectrometry imaging of complex microbial communities, Accts. Chem. Res. 50 (2017) 96e104. [8] E. Michelucci, G. Pieraccini, G. Moneti, C. Gabbiani, A. Pratesi, L. Messori, Mass spectrometry and metallomics: a general protocol to assess stability of metallodrug-protein adducts in bottom-up MS experiments, Talanta 167 (2017) 30e38. [9] N. Ul'yanovskii, D. Kosyakov, I. Pikovskoi, Y. Khabarov, Characterisation of oxidation products of 1,1-dimethylhydrazine by high-resolution orbitrap mass spectrometry, Chemosphere 174 (2017) 66e75. [10] L. Jia, A. Dufour, Y. Le Brech, O. Authier, G. Mauviel, On-line analysis of primary tars from biomass pyrolysis by single photoionization mass spectrometry: experiments and detailed modelling, Chem. Eng. J. 313 (2017) 270e282. [11] A. Nebbioso, A. Piccolo, M. Lamshoeft, M. Spiteller, Molecular characterization of an end-residue of humeomics applied to a soil humic acid, RSC Adv. 4 (2014) 23658e23665. [12] M. Schluesener, M. Spiteller, K. Bester, Determination of antibiotics from soil by pressurized liquid extraction and liquid chromatographyetandem mass spectrometry, J. Chromatogr. A 1003 (2003) 21e28. [13] M. Bahadir, H. Parlar, M. Spiteller, Springer Umweltlexikon, Springer verlag, Auflage, Berlin Heidelberd, 2000, pp. 1e1447. [14] M. Spiteller, Extraction of soil organic matter by supercritical fluids, Org. Geochem 8 (1985) 111e113. [15] H. Katayama, Y. Tatemichi, A. Nakajima, Simultaneous quantification of twenty Amadori products in soy sauce using liquid chromatography-tandem mass spectrometry, Food Chem. 228 (2017) 279e286. [16] Z. Zhou, R. Zare, Personal information from latent fingerprints using desorption electrospray ionization mass spectrometry and machine learning, Anal.

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