Excerpt

## Table of content

Preface

Acknowledgements

Chapter 1 Stochastic dynamic mass spectrometric diffusion parameters and 3D structural analysis of complexes of AgI–ion – experiment and theory

Abstract

1. Introductions

2. Experimental

2.1. Materials and methods

2.2. Synthesis

2.3. Figures of merit

2.3.1 Linearity and quantitation limits

2.3.2. Accuracy and precision

2.3.3. Intermediate precision conditions of measurements

2.3.4. Trueness of measurements and bias

2.3.5. Repeatability and reproducibility

2.4. Theory/computations

2.5. Chemometrics

3. Results and discussion

3.1. Experimental mass spectrometric data

3.1.1. Qualitative analysis

3.1.2. Quantitative analysis – figures of merit

3.1.3. Quantitative analysis – mass spectrometric diffusion parameters

3.2. Theoretical quantum chemical data

3.2.1. Quantum chemical treatment to mass spectrometric diffusion

3.2.2. Correlation between theoretical ionization potentials and experimental stochastic dynamic mass spectrometric diffusion parameters

4. Conclusion

Reference

Chapter 2 Mass spectrometric highly selective, sensitive, accurate and precise quantification of species of zinc(II) ion among other transition metal ions based on coordination with glycylhomopentapeptide – a stochastic dynamic approach

Abstract

1. Introductions

2. Experimental

2.1. Materials and methods

2.2. Synthesis

2.3. Theory/Computations

2.4. Chemometrics

3. Results and discussion

3.1. Mass spectrometric qualitative analysis

3.2. Quantitative mass spectrometric analysis

3.2.1. Accuracy and precision of collision induced spectra

3.2.2. Determination of stochastic dynamic diffusion coefficients

4. Conclusion

Reference

Chapter 3 Electrospray ionization and collision induced dissociation mass spectrometric quantitative conjunctions with experimental intensity of the analyte ions – a stochastic dynamic approach

Abstract

1. Introduction

2. Experimental

2.1. Materials and methods

2.2. Synthesis and sample pretreatment

2.2.1 Synthesis

2.2.2. Accuracy and precision

2.2.3. Repeatability and reproducibility

2.3. Chemometrics

3. Results and discussion

3.1. Mass spectrometric data – qualitative and semi–quantitative analysis

3.2. Quantitative analysis – figures of merit

3.3. Assessment of the correlation between experimental mass spectrometric parameters

3.4. Quantitative analysis – determination of stochastic dynamic diffusion parameters

3.4.1. Theory

3.4.2. Determination of mass spectrometric stochastic dynamic diffusion parameters in presence of external forced field

3.4.3. Correlative analysis between diffusion and kinetic parameters of collision induced dissociation reactions with respect to different forced field

Appendix A

Appendix B

Appendix C

## Preface

Throughout the chapters in this book we argue that the temporal behaviour of the experimental mass spectrometric intensity of analyte ions obeys a certain and universal law based on a stochastic dynamic approach. The content of the book evidences convincingly through a selected series of examples to molecular systems of metal–organic complexes of transition metal ions with electronic configuration d[10], for instance, AgI– and ZnII–ions, the validity of our model equation reported, more recently.

It needs to be underlined that, the comprehensive study that is provided, herein, is published, for first time in the literature. The book, therefore, represents monograph containing results from our research work, detailing correlatively experimental and theoretical mass spectrometric analyses of metal–organics using ultrahigh accuracy electrospray ionization and collision induced dissociation mass spectrometry. An enormous amount of effort is concentrated on a quantitative description of the relationships between experimental measurable parameter *“intensity”* and diffusion or kinetic parameters of analyte ions.

Chapter 1 assembles experimental facts about validity of our model equation, studying complexes of AgI–ion with simple inorganic ligands. We have chosen only to discuss aspects of species and fragment ions of coordination compounds that appear in the mass spectra, but are not observed in solution as far as there are known some anomalies of the electrospray ionization method. There are cases when the relative abundances to ions do not reflect exactly the ion concentration in solution. The chapter brings into consideration a set of aspects associated with ESI based quantification of analytes on the base on fragment processes of metal–organic complexes. They do not receive much attention, so far, or are not fully understood or both. In addressing further the lacuna of knowledge of this topic, Chapter 2 details through illustrative example to a ZnII–complex of oligopeptide, how our stochastic dynamic model equation can be used to quantify highly accurate, precise, selective and sensitive ZnII–ion among other transition metal ions looking at characteristic fragment collision induced dissociation reactions of the ligand. The stochastic dynamic diffusion parameters of the fragment species are quantified in chemometric terms. It represents an excellent contribution, demonstrating the powerful capability of the mass spectrometry of a highly selective quantification of mobile ZnII–ion in complex multicomponent mixture.

By applying our model equation, the last Chapter 3 puts forward a new quantitative model, accounting for the effect of the collision energy on the diffusion parameters under coupled electrospray ionization and collision induced mass spectrometric experimental conditions. A final aspect. We also approach both theoretically and experimentally the question in quantitative correlation between stochastic dynamic diffusion parameters and reaction kinetics obtained, again, within our model equation reported more recently. New model and quantitative relationships between these parameters are provided, as well.

The examples in Chapters 1–3 indicate that the discussed stochastic dynamic concept is broadly applicable to the analytical practice treating quantitatively experimental mass spectrometric *“intensity”*. The figures of merit indicate a high reliability of the analytical information. The research on this problematic, so far, has shown that our model quantitative relationships appear universally applicable, empirically testable, verifiable and credible analytical approach to quantify experimental data. Therefore, the theoretical concept has stood up to empirical tests.

The book, in this context, seems to represent a bridge between experiment and theory. It gives to the reader a useful base line to further studies in many interdisciplinary fields and sub–areas of the Chemistry. The main research issues to grasp are that for: *(i)* “mass spectrometric based determination of 3D molecular and electronic structures” and *(ii)* “quantification of mass spectrometric intensity *via* stochastic dynamic diffusion parameter.” The contribution takes the view that the soft–ionization mass spectrometric methods, for instance, electrospray ionization and collision induced dissociation mass spectrometry represent not only robust, indispensable and irreplaceable methods for qualitative and quantitative analyses, but also have capability of providing exact 3D structural information about the analytes. This work, therefore, can be seen as essential for further methodological development into the mass spectrometry. It aims at pinpointing detail on methodology of application of mass spectrometry to the analytical practice as a robust approach to exact experimental 3D structural analysis. Throughout all chapters of the book we have insisted on the latter view, which, in general, is opposed to a common view to that, the methods of mass spectrometry cannot be used to multidimensional structural analysis.

The contribution provides methodology and outcomes of theoretical and empirical research conducted on metal–organic compounds of ions with electronic configuration d[10].

Since the content of the chapters covers a large number of aspects having fundamental or applied–oriented scientific characters, it might be of interest to many readers, who develop *into* mass spectrometry, methodologically; implement mass spectrometry as robust analytical instrumentation; or develop *into* analytical mass spectrometric instrumentation, respectively.

In one way or another, the book is directly related to MSc and PhD students’ research tasks for the “Chemistry”, in particular, looking at students in the sub–fields of the “coordination chemistry”, “analytical chemistry”, “environmental chemistry”, “computational chemistry”, “organic synthesis”, “catalysis” and more; also, interpenetrating with other interdisciplinary fields, for instance, “forensic chemistry”, “clinical diagnostics”, “toxicology”, “food technology” and more. It enables the students to look at in–depth study of the quantitative mass spectrometry based on stochastic dynamics.

## Acknowledgments

The authors thank the Deutsche Forschungsgemeinschaft (DFG, Germany), supporting their study in this research topic within a project grant 255/22–1; the Alexander von Humboldt Stiftung (Germany) for instrumental equipment (single crystal X–ray diffractometer); the *Deutscher Akademischer Austausch Dienst* (Germany) for a grant within the priority program “Stability Pact South-Eastern Europe” and for purchasing on Evolution 300 UV–VIS–NIS spectrometer *;* and central instrumental laboratories for structural analysis at Dortmund University of Technology (Federal State Nordrhein–Westfalen, Germany) as well as analytical and computational laboratory clusters at the Institute of Environmental Research at the same University.

The work was carefully carried out. Nevertheless, authors and publisher do not warrant the information therein to be free of errors. The work is being published in English aiming at a widest access to the scientific contributions. English is not native language of the authors, however. Stylistic rough edges might occur. The authors hope for understanding of the reader.

**Conflicts of interest**

Michael Spiteller has received research grant (255/22–1, DFG); Bojidarka Ivanova has received research grant (255/22–1, DFG).

**Address correspondence to the authors:**

Lehrstuhl für Analytische Chemie, Institut für Umweltforschung, Fakultät für Chemie und Chemische Biologie, Universität Dortmund, Otto–Hahn–Straße 6, 44221 Dortmund, Nordrhein–Westfalen, Deutschland.

## Keywords

Mass spectrometry; Electrospray ionization; Collision induced dissociation; Quantum chemistry; stochastic dynamics; Metal–organics; Quantification; 3D structural analysis; Diffusion; Kinetics; Transition metal ions

## Abbreviations AND acronyms

**ANOVA** – Analysis of variance; **APCI** – *Atmospheric pressure chemical ionization (mass spectrometry);* **B3LYP** – Becke 3–parameter exchange with Lee–Yang–Parr correlation; B3PW91 – Becke 3–parameter Perdew–Wang–1991; **BOMD** – Born Oppenheim Molecular Dynamics (quantum chemical method); **CASSCF** – Complete active space self-consistent field; **CC** – Coupled cluster (approach); **CCSD(T)** – Coupled–cluster theory (higher–order); **CID** – *Collision–induced dissociation (mass spectrometry)*; **DCMM** – diffusion parameter according to *“current monitoring method;“* **DQC** – quantum chemical diffusion parameter; **DSD** – stochastic dynamic diffusion; **DFT** – *Density functional theory;* **EOM** – Equations–of–motion; **ESI** – *Electrospray ionization (mass spectrometry)*; **G5** – glycylhomopentapeptide; **G6** – glycylhomohexapeptide; **GP –** Gas–phase; **GS** – Ground state; **HF** – *Hartree–Fock (method);* **IEF–PCM** – Integral–equation–formalism polarizable continuum model; **LANL2DZ** – Los Alamos National Laboratory (double–) pseudo-potentials; **LC– wPBE** – Long–range corrected Perdew-Burke-Ernzerhof (functional); **LOD** – (Concentration) limits of detection; **LOQ** – (Concentration) limits of quantitation; **M06–2X** (and M06) – Meta–hybrid GGA DFT functional(s); **MALDI** – *Matrix–assisted laser desorption ionization (mass spectrometry)*; **MD** – Molecular dynamics; **MM** – Molecular mechanics; **MS** – Mass spectrometry; **MS*** – Mean squares; ** m/z –** mass–to–charge (values);

**MP2**– Møller-Plesset theory on second order;

**ONIOM**– own N–layer integrated molecular orbital and molecular mechanics;

**OVGF**– Outer valence Green’s functions;

**PCM**– Polarizable continuum model;

**PES(s) –**Potential energy surface(s);

**RT**– Retention time;

**SD**– Standard deviation;

**SDD**– Stuttgart–Dresden (pseudo–potentials);

**SOS**– Scaled opposite–spin;

**SS***– Sum of squares;

**TDDFT**–

*Time – dependent density functional theory ;*

**TIC**– Total ion current;

**TS**– Transition state;

**UFF**– Universal force field;

**UV**– Ultraviolet (spectroscopy);

**ZPVE**– Zero–point vibrational energy.

## CHAPTER 1 Stochastic dynamic mass spectrometric diffusion parameters and 3D structural analysis of complexes of AgI–ion – experiment and theory

## Abstract

This work presents a quantification of mass spectrometric diffusion parameters based on our stochastic dynamic approach connecting experimental intensity of analyte ions with their diffusion parameters. The aim of this study is twofold. First, explicitly, the primary aim is to provide a new approach for analytical quantification of isotope MS shape of metal–organic complexes of AgI–ions allowing their unambiguous determination in complex mixture, quantitatively. In this context, the following aspects, which have hardly been considered so far, are taken into account for the purpose of the study the reproducibility of the intensity ratio of isotope shapes of metal–organic charged species over the time. Typical gas–phase reactions of a metal ion and its solvate complexes are described. Importantly, the analysis includes quantitative treatment to the correlation between mass spectrometric diffusion parameters based on our stochastic dynamic approach and quantum chemical diffusions of ions, obtained within the framework of Arrhenius’s approximation to the behavior of ions under mass spectrometric experimental conditions. These new results are in line with research evidences highlighting the capability of mass spectrometry to elicit exact 3D structure of analytes using a theory based on complementary employment of experimental high resolution mass spectrometry and high accuracy theoretical quantum chemical static and molecular dynamic approaches. As far as our research, so far, has been focused chiefly on determination of diffusion parameters of ions of organics, what we would like to argue with the study, herein, is that the discussed model equation for quantitative treatment to experimental mass spectrometric parameter *“intensity”* is applicable to high accuracy quantification of isotope compositions of metal–organics studying AgI–complexes of mandelic acid (1) and (3) and 2-hydroxy-4-sulfo-benzoic (2) acid and employing electrospray ionization mass spectrometry. The contributions to this work have provided a series of very important insights into the powerful application of experimental mass spectrometry to high accuracy 3D structural analysis of organics and metal–organics illustrating a great reproducibility of the data, quantitatively. The quantum chemical computations encompass static and molecular adiabatic and diabatic dynamics.

## INTRODUCTION

The methods of mass spectrometry appear precise and accurate analytical instrumentation, amongst others. On the base on the superior instrumental characteristics these methods are broadly implicated in the analytical practice in quantification. As we have pointed out more recently in contributions devoted to methodological developments of methods for quantitative treatment to experimental mass spectrometric parameters [1–4], the MS approaches, in particular, highlighting soft ionization methods possess a large scale of unique instrumental features consisting of: *(a)* ultrahigh resolving power, allowing an accurate detection of a single analyte in complex multicomponent mixture; *(b)* low concentration limits of detection and quantification ranging from *fmol* to *attomol* levels; *(c)* a large number rapid, cheap and simple procedures for sample pretreatment; *(d)* a capability of direct assay; *(e)* quantification of masses of analytes ranging low molecular weight compounds to (*bio*)macromolecules (~ 100 kDa); *(f)* imaging techniques for assay; *(g)* analysis of homogeneous and heterogeneous phases; *(h)* flexible instrumental design, allowing coupling instrumental schemes, which improve significantly the method performances, and more [5–38]. The ultrahigh mass resolving power using Orbitrap analyzer has been demonstrated more recently, studying complex biomacromolecules [39–43]. The reason for emphasis of superior instrumental characteristics of the MS methods, in general, is that points *(i)–(h)* determine their wide application to many interdisciplinary research areas such as the analytical chemistry; environmental chemistry; clinical diagnostics; medicinal chemistry; forensic chemistry; nuclear forensics; pharmacy; food chemistry and technology; agricultural science; archeology; and more. Despite the broad application of MS methods to the research practice, their application does not differ mostly in context of what they produce as analytical information. In other words, in studies with a highlighted applied–oriented goal and implementations the MS provides mainly quantitative information about the analytes. Thus, its potential contribution to our understanding of the exact 3D molecular structures of analytes is thus limited. One common strategy to bypass the understanding of the MS as method chiefly employed for quantitative purposes is the methodological development of MS based methods for exact 3D structural analysis. In context application of MS to structural determination we do not know very much yet about it. Nevertheless, it has great capability of implementation, namely, as an absolute and unique method for experimental 3D structural analysis. As yet there are only fragmentary insights into quantitative treatment to many experimental parameters, because of, in general, fundamental aspects of ionization desorption mechanisms of different MS methods are still far from well understood. There is, therefore, a related practical problem in methodological development of MS protocols for 3D structural analysis connected, on the one hand, with the different physical phenomena of ionization approaches; and, on the other, hand with the quantitative treatment to experimental MS parameters, thus producing exact model equations connecting experimental MS parameters with the electronic structure of the analytes. Despite the available apparent convergence of research interests in context of an understanding of 3D conformation and electronic structures of molecules employing great instrumental capability of MS methods, many research difficulties, so far, confront a common view to a MS protocol for experimental structural analysis. Therefore, we need a practical methodology for treatment to experimental MS parameters yielding to information about exact 3D structures of the analytes. Over decades there are few important contributions, which should be pointed out in order to underline our new methodology for quantitative treatment to experimental MS intensity, based on stochastic dynamics [3,4]. It is, in general, agreed today, that the fundamental understanding of the behavior of MS intensity of fragment ions under MS experimental conditions in expressed quantitatively using the Iribarne-Thomson’s theory [44–47] (Appendix A, equation (1)). Our contributions in this domain have brought out two model equations connecting experimental MS intensity with reaction kinetics of fragment reactions under ESI– or APCI–MS experimental schemes coupled with CID mass spectrometry [1,2] (equations (3)–(5)). Furthermore, we have shown that on the base on the Iribarne-Thomson’s theory there can be obtained 3D structural information about the analytes, using the Arrhenius’s approximation within the framework of the transition state theory (Consider work [2] and equations (6)–(8)). On the other hand, in a resent paper [48] the authors argue with that the temporal behavior of the analyte MS intensity in solution can be expressed quantitatively using the diffusion of MS ions (Appendix A, equations (9) and (10)). The latter paper sets out an account of ion mobility called further in this work *“current monitoring method.”* In the discussion we shall adopt the latter theory as starting point validating our stochastic dynamic concept for quantitative treatment to MS intensity [3,4] (Appendix A, equations (11)–(14)). Moreover, more recently we argue with that the comparative analysis with our quantitative model equations and formalism of the *“current monitoring method”* is a very useful basis for evidencing the validity of our new theoretical concept accounting for the fact about that the chemometrics of organic compounds [2,4] shows excellent agreement on the datasets. The coefficients of correlation across the data vary *r* = 0.96027–0.9944. In the light of these studies mainly devoted to organics and the facts about that model equation (14) expresses quantitatively relationship with experimental MS intensity and DSD as well as experimental 3D structure and theoretical DQC obtained within the Arrhenius’s formalism, in a similar fashion we apply the equations studying temporal behavior of analyte MS intensity of aforementioned metal–organic complexes of silver ion (**Figure 1**). Therefore, the foci of our study may be further detailed. Nevertheless, we hope that it may have become clear in this introductory part that the main goal exploited our new stochastic dynamic concept of quantitative treatment to experimental MS intensity (equation (14)) and determination of 3D structure of analytes using the functional relationship between DSD parameters obtained on the base on our formalism and the DQC parameters according to the Arrhenius’s theory.

Abbildung in dieser Leseprobe nicht enthalten

**Figure 1**. Chemical diagrams of analytes **(1)–(3)** (Authors’ own work).

In sum, we pursue the answers to the following research questions: *(i)* whether equation (14) becomes applicable to metal–organics and *(ii)* can we distinguish quantitatively between 3D structures and coordination modes in complexes with subtle metal–to–ligand interactions like, for example, cases of M…NºC–R coordination bond and cation p–interactions of type M+…p(NºC)–R? Accounting for the fact that, on the one hand, the latter interactions play a significant role in biological systems associated with folding of proteins, neurological signaling, and many more, and on the other hand, there is frequently competitive metal–to–ligand bonding mode of the former type besides weak forces governing cation p–interactions in a general context, to distinguish by mass spectrometry between these two type of coordination fashion represent a significant research challenge. In this context, one could wonder whether the mass spectrometry can provide argument towards such as subtle interactions in metal–organic complexes accounting for the fact about that very frequently the unambiguous determination represent challenge even within the framework of the crystallographic electron density analysis (Consider [1–4]). With regard to, the latter opinion we argue with that the MS within the framework of our stochastic dynamic approach can not only provide 3D molecular and electronic structures of analyte, but also can distinguish experimentally; furthermore, quantitatively between subtle metal–to–ligand interactions examining the temporal behavior of MS intensity of isotope clusters of AgI–complexes. The largest part of known methodological contributions to MS based analytical protocols have not yet caught up with a so significant challenge to use mass spectrometry for 3D structural determination posed by our new theoretical concept expressed exactly by model equation (14). Therefore, the discussed new research contributions and significant results in this work dealing with quantitative treatment to MS intensities of isotope compositions show that our stochastic dynamic concept is fundamental in experimental treatment to mass spectrometric data; it is applicable to organics and metal–organics over a wide range of MS methods, such as CID–, ESI–, APCI– and MALDI–MS methods [3,4].

## 2. Experimental

### 2.1. Materials and methods

Mass spectrometric 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 ESI–MS and APCI–MS measurements (**Table S1**). A standard LTQ Orbitrap XL (Thermo Fisher Inc.) was employed. The quantification using the lastly mentioned instrument was carried out *via* a combination of mass detectors (trap, linear ion trap and orbitrap), accumulating spectra for t = 7–30 mins (420–1800 s). The data were saved as individual files. The absolute and relative intensities to the species studied were obtained using QualBrowser software 2.7. The program packages ProteoWizard 3.0.11565.0 (2017) and AMDIS 2.71 (2012) were used, as well. The mass resolving power at R > 1.10[6]. The ESI, APCI and CID resolving powers are R > 1.10[5], respectively. The ImageQuest 1.0.1 program package was used for data processing (Thermo Fisher Inc.). The chromatographic analysis was carried out by Gynkotek (Germering, Germany) HPLC instrument, equipped with a preparative Kromasil 100 C18 column (250×20 mm, 7 μm; 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 μm) 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 the chemical purity of the starting 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 compounds (1)–(3) were obtained according to [49,50]. Compound (3) is obtained under heating at T = 200oC for t = 1h of crystalline compound (1). As far as their design and synthesis were based on our ongoing research on new metal – organic nonlinear optical materials of ions with electronic configuration d[10], the structural determination of the analytes in solid state, using single crystal X–ray diffraction has been reported to the mentioned above works. The contributions [49,50] also contain detail analysis of the optical properties and vibrational assignment of the complexes in solid–state. In this context, the presented herein paper deals with new analytical mass spectrometric quantitative information of compounds (1)–(3) reported for first time in the literature.

### 2.3. Figures of merit

#### 2.3.1. Linearity and quantitation limits

The linear range has been determined by standard procedure. The crystalline complex (2) which molecular and crystal structures have been determined in [49,50] was dissolved in the solvent mixtures CH3CH2OH:H2O and CH3OH:CH3CN at molar ratio 1:1. The concentrations range from 50 ng.(mL)-[1] to 5000 mg.(L)-[1]. Linear correlations and quantitation concentration limits have been obtained using the abundance isotope shapes at *m/z* 189/191 and 148/150 together with the characteristic MS peaks of the organic ligands.

#### 2.3.2. Accuracy and precision

The accuracy has been evaluated using three replicates and solvent mixture CH3OH:CH3CN at molar ratios 1:1 at concentration 2 mg.(mL)-[1]. The evaluation has been carried out by means of multiple measurements. The accuracy and the precision of the measurements have been estimated by multiple measurements of standard samples of (1)–(3) and by evaluation of the closeness of the agreement on the independent result and an accepted reference value. The reference values in our case are those mass spectrometric parameters, which have been obtained by measurements of the standard samples of analytes (1) and (2). As standard samples of crystals (1)–(3) there have been used crystallographically determined analytes according [49,50] where the X–ray diffraction measurements and structural solutions have involved a statistically representative set of data and corresponding chemometric analysis. In addition, the structural determination of the standard samples has included solid–state conventional and linear polarized infrared spectroscopy.

#### 2.3.3. Intermediate precision conditions of measurements

The intermediate precision conditions of experimental measurements have been described as a set of conditions, including identical measurements procedures and replicate measurements over an extended time period. Thus, measurements over different period of time have been carried out.

#### 2.3.4. Trueness of measurements and bias

The closeness of agreement on average data has been obtained of replicated measurements and compared with the true value of reference samples. As mentioned before, the reference samples are those analytes (1) and (2), which absolute molecular and crystal structures have been determined crystallographically according to [49,50]. The measurement trueness is inversely related to SME, which estimated the measurement bias.

#### 2.3.5. Repeatability and reproducibility

The repeatability of measurements is evaluated using the following procedure: *(i)* data of three independent measurements of two replicated samples have been collected and compared with the data of the standard samples of crystals of (1) and (2); and *(ii)* a chemometric analysis has been carried out. The calculation of *„reproducibility”* is according to equation: 2.(2)[1]/[2].SD2. The SD2 represents the long-time standard deviation.

### 2.4. Theory/computations

The quantum chemical program packages that we use in this work are GAUSSIAN 98, 09; Dalton2011 and Gamess–US. The visualization of the output data was performed using GausView03 [51–54]. The thermodynamic was calculated using Moltran v 2.5 program, as well [55]. Geometries were optimized by *ab initio* and DFT methods. The B3LYP, B3PW91, wB97X–D, QCISD, LC–wPBE, MP2, MP4, and CASSCF [56–63] as well as the Truhlar’s M06, M06–2X and M06–HF functional were used [65,66]. The Bernys’ algorithm was utilized for ground state computations. The stationary points on PES were obtained from standard analytical harmonic vibrational analysis. The absence of imaginary frequencies and negative eigenvalues of second-derivative matrix confirmed the minima. When used in internal energy determinations *via* RRKM calculations, the frequencies were scaled by 0.99. The Dunning's basis sets (cc-pVnZ) (n=D,T and 5), 6–31++G(2d,2p), and quasirelativistic effective core (or small core relativistic) pseudo potentials from *Stuttgart* – *Dresden(* – *Bonn) (SDD, SDDAll, http://www.cup.uni-muenchen.de/oc/zipse/los-alamos-national-laboratory-lanl-ecps.html) were employed [56–63]*. The doubly polarized triple- *z -* basis sets augmented by diffuse functions (6-311+G(2df,2p) or aug-cc-pVTZ) were used. The computations of enthalpies at MP4/6-31+G(2d,2p) and MP2/aug-cc-VDZ have shown a good reproduction and support of the experiment. On the other hand, studies on organics have shown that employment of B3LYP/6-31+G(d,p) level of theory has been able to approach in a balanced way towards computational cost and accuracy theoretical data obtained from more expensive method such as CCSD(T) /aug-cc-pVTZ. The scalar relativistic effects were taken into account using the DKH Hamiltonian. Nevertheless, the analysis of {[Ag(H2O)]+} in [64] based on B3LYP/SDD and four component relativistic computations involving Dirac-HS and Dirac-B3LYP (Data about all electrons) have shown difference in the complexation energy in DE = |0.1| a.u., indicating an excellent accounting for the relativistic effects the lastly mentioned DFT functional applied to SDD. The correction of the energy based on BSSE approach has been accounted for DE = |1.1| a.u. Evaluating excitation energies CIS, CIS(D) or TD–DFT methods were employed, using GDIIS optimization. The energy improvement was achieved using W1BD and G4 methods. The choice of those method was governed by known reports about accuracy of theoretical data obtained from *ab initio* thermo chemistry using W1 (Weizmann **–** 1), W2 (Weizmann **–** 2), Gaussian **–** n (Gn) and CBS approaches [65–86]. The W1 has provided more accurate data about IPs comparing with Gn (n = 2,3 and 4) and CBS methods studying organics [65–86]. W2 has provided weak improvements towards computation of EA but insignificantly affects the IPs. The analysis of G3 and G4 has shown that the latter method shows a higher accuracy [65–86], but it is comparable with the W1BD one. For analysis of organics, there has been found that distinction between methods towards predicting of adiabatic IPs varies Î 0.00–0.04 eV. The distinction between theory and experiment has been on account of Î 0.01–0.08 eV. A general deviation between theory and experiment *per* method is EA Î (–0.001)–(0.051) (W1), Î (–0.001)–(0.039) (W2), Î (–0.010)–(0.110) (G2), Î (–0.006)–(0.175) (G3) and Î (–0.009)–(0.121) eV (CBS–QB3), respectively. The CBS predicting AIPs were used CBS such as CBS–Q, CBS–QB3 and APNO. IPs and EAs were obtained from quasiparticle approximations to electron propagator theory. A correlation analysis with Koopmans’, OVGF, EOM–CC and P3 values was carried out. The AIPs according to Koopmans’ theorem have been obtained. Total atomization energy for cationic and neutral molecules were obtained from T = 0K, at their optimized geometries. DFT methods have been successfully used in accurate prediction of energetic of molecules, involving IPs as well as long-range corrected hybrid functional such as for example (LC–wPBE) and hybrid functional B3LYP, BHandHLYP, M06-2X and M06-HX. The M06 as local exchange functional has been tested towards accuracy to predict IPs as well. There has been found that, generally, DFT approaches under esteem the IPs values. Despite this fact, the correlation study with theoretical IPs obtained from B3LYP/6-31G** approach and the experimental values of representative set aromatic conjugated molecules has shown a reliability of the method 98.4 % (*r* [2] = 0.9843). There has been found a good correlation with theoretical energetic of the fragment ions of peptide systems and their MS intensities, employing M06–2X and wB97X–D functional. Comparing theoretical with experimental IPs is important for taking into consideration that methods based on GW calculations have provided information of vertical IPs, while experimentally mostly data are about adiabatic IPs. So that the measured values are different with ZPE and vibrational contribution, in terms of first ionization potential values. The obtained ZPE values by MP2/cc-pVDz approach are scaled by a factor 0.95. The shifting of IPs comparing theoretical with experimental values due to last discussed contributions can be up to 0.3 eV. The thermodynamic parameters about the species in GP have been obtained from hindered internal rotor approximation. Species in solution were characterized using explicit super molecule and "mixed" approach of micro hydration and PCM (respectively, CPCM and IPCM) were utilized. The successful application of PCM for accurate prediction of IPs by DFT approaches has been shown in work as well. For largest species was employed ONIOM method, in which different parts of super molecule can be treated to different levels of accuracy, using different basis sets or different quantum methods. The theoretical analysis obtains ESPs and NBO charges predicting the protonation ability as well. The Eckart’s based approach employing analytical potential-energy function along with an adiabatic minimum-energy path or IRC analysis was carried out in order to provide further insights into the PESs (energetic), reaction mechanisms and electronic structures of interacting/reacting systems [65–88]. The step size was 0.010 a0.amu[1]/[2]. The equilibrium or stationary point and the transition states were confirmed using frequency analysis. The MD computations were done by classical approaches, *ab initio* BOMD and ADMP ones. The BOMD was carried out at M06 and M062X functional; and CASSCF as well as SDD and cc-pvDZ basis sets without any consideration of the periodic boundary condition. BOMD computations with ONIOM for large molecular ensembles were carried out. The trajectories were integrated using Hessian-based predictor-corrector approach with Hessian updating for each step on BO PES. The step sizes were 0.3 and 0.25 amu[1]/[2]Bohr. The trajectory analysis stops when: *(a)* centres of mass of a dissociating fragment are different at 15 Bohr, or *(b)* when the number of steps exceed the given to as input parameter maximal number of points. The total energy was conserved during the computations within at least 0.1 kcalmol-[1]. The computations were carried out using fixed trajectory time speed (*t* = 0.025 or fs) starting from initial velocities. The velocity Verlet and Bulirsch-Stoer integration approaches were used. The dynamics of the processes of molecular/ion collisions, charge transfer, intramolecular proton transfer, molecular rearrangement and chemical reactions associated with the made or broken chemical bonds were further studied using diabatic computations based on trajectory surface hopping method, as well [65–88]. The method by Tully and Preston was employed [65–88]. The nonadiabatic transitions are described as vertical transitions between adiabatic potential energy surfaces [65–88] at concrete localized regions. The nuclear trajectory was propagated adiabatically using Born–Oppenheim approximation, which in the surface hopping region the electronic forces were treated using stochastic hopping. The conservation of the total electron–nuclear energy after the hope is achieved using rescaling of the nuclear velocity. The empirical decoherense correction was 0.1 a.u. The time step for the nuclear motion was 0.1 fs, while for the electronic propagation there was used time step 0.0005 fs (More detail can be found in reference [65–88] and the cited literature sources). The solution properties were computed by TDDFT and PCMs approaches. The effect of ionic strengths on energetic in solution was studied by IEF–PCM approach. Part of the computations was carried out using SMD parameterization of non–electrostatic terms. There were compared to models of changing the cavity topology, too, including Merz-Kollman atomic radii and heavy atoms UFF topological models. Explicit super molecule and micro–hydration approach, includes several *n* = 1–3 water molecules coordinated to a solute were used. The effect of pH was evaluated computing properties in neutral, cationic and anionic forms. It was applied studying solvation effects by ONIOMPCM, as well. The AIM methods were utilized as well. The crystallographic data were used as input coordinates for the theoretical computations as well.

### 2.5. Chemometrics

Chemometric analysis is applied to experimental and theoretical data. It was **done by R4Cal OpenOffice STATISTICs for Windows 7 program packages [18].** The statistical significance of each regression coefficient was checked by *t* –test. The model adequacy was determined by *F* -test for goodness-of-fit and lack-of-fit, respectively. **ANOVA methods were used. The nonlinear fitting of experimental MS data was carried out using searching method based on** Levenberg-Marquardt algorithm [ **89–94** ].

## 3. Results and discussion

### 3.1. Experimental mass spectrometric data

#### 3.1.1. Qualitative analysis

In this short sub–section we will begin the discussion by addressing a central issue associated with common MS peaks to complexes of AgI–ion, typically of CH3CN solution of the metal ion due to an effect of coordination of the AgI–ion with solvent molecules. The fragment reaction of loss of ligand: {[AgI(CH3CN)2]+} ® {[AgI(CH3CN)]+} + CH3CN, however, is a gas–phase reaction. Thus, despite the different experimental conditions in solution, the reproducibility of the latter data is determined on the base on the experimental instrumental conditions. Nevertheless, ESI is the softest mass spectrometric ionization method based on measurements of solutions. Therefore, the energy states of detected MS ions, in general, correspond to their states in solution. In other words, the structure of analyte MS ion, in this case the complex {[AgI(CH3CN)2]+}, is kept in course of an ESI–analysis as it is in the initial solution. Thus, depending on the experimental conditions, for instance, pH, ionic strengths, T, P, type of the solvent, and more, there can be studied in detail and can be modelled mechanistic aspects of bonds or binding interactions of different complexes of AgI–ions.

**Figure 2** depicts experimental ESI–MS spectra of (1)–(3) together with chromatographic data. As can be seen MS peaks at *m/z* 148/150 and 189/191 appear characteristic fragment peaks of all MS spectra, which have been assigned {[AgI(CH3CN)]+} and {[AgI(CH3CN)2]+} solvate complexes of AgI–ion [95].

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(Continued **Figure 2**; authors’ own work)

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(Continued **Figure 2**; authors’ own work)

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**Figure 2**. Chromatographic, electronic absorption and ESI–MS data of (1)–(3) in solution; theoretical MS data; qualitative assignment of selected MS peaks; curve–fitting of chromatographic data of (3), using Gaussian function (Authors’ own work).

However, the knowledge how to gain 3D structural information is, in particular, essential in both quantitative and structural analyses based on MS, because of, as is well–known AgI–ion exhibits a great variety of coordination fashion. At this point it is worth noting the capability of AgI–ion to form ion–p complexes as we have demonstrated more recently in a crystallographic study of coordination ability of the discussed metal ion to 1H-indole-5-carboxylic acid [95]. It appears, therefore, that to the shown above mass contents of complexes {[AgI(CH3CN)]+} and {[AgI(CH3CN)2]+} there could correspond different 3D structures of analytes depending on AgI–ligand bonding modes (below). Looking at MS spectra of (1)–(3) (**Figure 2**) there arises the following questions: *(i)* How do we relate quantitatively elemental compositions of complex species {[AgI(CH3CN)]+} and {[AgI(CH3CN)2]+} to corresponding 3D molecular and electronic structures using MS methods? And *(ii)* can we distinguish quantitatively using soft–ionization MS methods between subtle metal–to–ligand coordination fashions such as AgI…NºC–CH3 and AgI…p(NºC)–CH3 bonds modes? Despite the significant analytical challenge to study the coordination manner in metal–organics in the next sub–section we answer to these questions using explicit quantitative criteria based on equation (14) in order to make up such judgment reliably from the perspective of quantitative and structural analytical chemistry in context chemometrics.

#### 3.1.2. Quantitative analysis – figures of merit

As the previous sub–section underlined, this study takes the view that the crucial experimental MS parameter DSD according to equation (14) accounts very sensitively even perturbation of 3D molecular conformation and electronic structure of analyte ions. The equation shows that the temporal behavior of the analyte MS ions obeys a certain and universal law applicable to any analyte; any span of time of measurements; and any of the aforementioned mass spectrometric methods. In order to provide an empirical evidence for the later claim, it should be argued with by a critical test the most important MS method performances associated with accuracy and precision of measurements; their repeatability and reproducibility. The results from the test which has been specifically designed for evaluating contributions of random and systematic errors to the absolute quantities of experimental MS parameters [93,94]. The former type of errors causes for different replicate results and affect on precision of measurements or reproducibility [93]. In this context, **Table 1** contains mass–to–charge values of MS peaks of isotope shapes at *m/z* 189/191 and 148/150 measured in multiplications. The analysis was carried out within a span of time t = 6 days, as well. The chemometrics based on ANOVA and descriptive statistics are summarized in **Tables 2** and **3**.

**Table 1.** The *m/z* –values of the sub–components of the isotope shapes at *m/z* 189/191 and 148/150 of analyte (1) and (2) measured in multiplication.

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**Table 2**. Descriptive statistics of the experimental dataset in **Table 1**.

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**Table 3**. ANOVA test of the experimental dataset of (2) measured in multiplication and compared with the standard values of the crystalline sample of (2).

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As the data in the latter tables clearly show there is a lack of contribution of random and total systematic errors of measurements or bias to experimental MS parameters of isotope shape components over the show period of time. The standard deviations are at the five decimal sign. The ANOVA test produces absolute *P* value P = 1 and *F* –parameter F » 3.10-[13], which is much closed to zero. The populations at a probability level 0.001 are identical. Using the equations determining reproducibility and repeatability of measurements as given above and reference [94] there are obtained the following statistical parameters: SD1 = 2.36718.10-[5] and SD2 = 4.34729.10-[5]. Looking at the latter values, it is more than clear that our experimental results are highly accurate, precise and reproducible, respectively.

As far as the MS intensity, in fact, reflects a concrete unique 3D structure of the analyte ions and in parallel equation (14) accounts for temporal behavior of analyte MS intensity *per* different spans of times of measurements the accuracy and precision of experimental parameters with respect to the whole time of the measurements should be evaluated, as well. **Table S2** shows the temporal behavior of the peak position of the isotope peaks at *m/z* 107 and 189 of (1) as well as *m/z* 189 and 150 of (2). **Figure 3** presents temporal behavior of MS peak position, the corresponding intensity and total ion current *per* span of time. Again, the descriptive statistics shows a standard deviation at the five decimal sign as far as, herein, are obtained the following values: *m/z* 106.60982 ± 1.75276.10-[5] and 188.95774 ± 2.32891.10-[5] (1) as well as *m/z* 188.95774 ± 3.08139.10-[5] and 150.06814 ± 2.05397.10-[5].

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(Continued **Figure 3**; authors’ own work)

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**Figure 3**. Relationships between experimental *m/z* values of MS peaks at *m/z* 107 and 189 of (1) or *m/z* 189 and 150 of (2) with respect to the time of measurement [mins]; relationships between absolute peak intensity and total ion current [arb.units] *versus* time [mins]; correlative analysis between absolute peak intensity and total ion current; chemometrics (Authors’ own work).

The latter figure depicts correlative analysis between temporal behavior of MS intensity of peaks of isotope shapes and total ion current. As the chemometric data show there is a deviation from the absolute linear correlation (coefficient of correlation *r* = 1). The corresponding coefficients of correlation are *r* = 0.92–0.98. This result assumes that an evaluation of the method performances based on absolute total intensity of a MS peak with respect to the whole time of a measurement, for instance, let us describe the MS intensities of the peaks at *m/z* 107 and 189 of (1) is suspect. The method performances should be accounted for looking at peak positions or *m/z* –values, or DSD parameters, but, with respect to different short spans of time as we have carried out (below). Because of, as aforementioned, the results from our small–scale research on this field [1–4] have shown that the DSD parameter reflects concrete – unique – 3D molecular and electronic structures. In parallel, the behavior of MS ions in MS polar continuum is described as a Wiener process. The latter process is determined mainly on fluctuation of the MS continuum. There are in this context two point for serious reconsideration. First, there is important for determining adequately the nature of the MS continuum in context, polarity, solvent type, ionic strength, and more, together with experimental parameters such as temperature, pressure and so on. Second, due to fluctuations of the continuum there is perturbation of DSD parameters *per* span of time. In other words, when perturbation or even change of DSD parameters occur, this means that change of 3D molecular and electronic structures *per* span of time of a measurement also occur. The DiSD parameters according to equation (14) are defined *per* ith span of time. The total DSDtot parameter of the whole measurement time should be given as a sum of n-number of DiSD parameters, where *i* = 1…n (equation (1)). From the perspective of a 3D structural analysis, however, the DtotSD should correspond to an average, but not the absolute 3D structure. Because of, if a DiSD parameter of ith span of time is determined using very low abundance peak comparable with uncertainty of the method at or below its LOD, then the error contribution to DiSD parameter should affect on the DtotSD value.

**[...]**

- Quote paper
- Prof. Dr. Bojidarka Ivanova (Author)Michael Spiteller (Author), 2019, Electrospray Ionization and Collision Induced Dissociation Mass Spectrometric Quantitative Conjunctions with the Experimental Intensity of the Analyte Ions of Metal-Organics- Stochastic Dynamics, Munich, GRIN Verlag, https://www.grin.com/document/458723

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