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IR absorption spectra for chlorinated ethenes in water, calculated using density functional theory

  • L. Huang
  • S. G. Lambrakos
  • L. MassaEmail author
Original Paper
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Abstract

Calculations are presented of vibration absorption spectra for tetrachloroethene (PCE), trichloroethene (TCE), dichloroethene (DCE) and vinyl chloride (VC) molecules in water, using density function theory (DFT). DFT can provide interpretation of absorption spectra with respect to molecular structure for excitation by electromagnetic waves at frequencies within the IR range. The DFT-calculated absorption spectrum corresponding to vibration excitation states of these molecules in continuous water background provides quantitative estimates that can be correlated with additional information obtained from laboratory measurements. This case study provides proof of concept for using DFT-calculated spectra to construct templates, which are for spectral-feature comparison and, thus, detection of spectral-signature features associated with target materials.

Keywords

Chlorinated ethenes Water contaminants DFT IR spectra IR spectra data base Interpretation of IR spectra Computational quantum chemistry 

1 Introduction

Detection methodologies based on infrared (IR) spectroscopy are based on identification of unknown materials by comparison of measured spectra with reference spectra associated with known materials. In particular, that a pattern of frequencies, which is within an existing database of spectra corresponding to known molecular structures, can be compared to a measured spectrum for identification of the unknown molecules (see Haaland 1990) and references therein). Comparison of spectra for the purpose of identifying an unknown material is accomplished in principle using signal processing algorithms (Smith 1997), where signature structure within a measured signal is filtered using signal templates having patterns associated with known materials. These algorithms are typically based on least-squares (Lam 1983), Kalman-filter (Brown 1986; Cooper 1986) and cross-correlation methods (Mann et al. 1982; Mann and Vickers 1986), are statistical in nature, and can be used, in principle, together. In addition, for detection in practice, different types of databases can be referenced together, providing complementary information, as well as utilization of other types of information concerning interpretation of spectral features, e.g., knowledge of other measured chemical properties of the unknown material.

Historically, databases of spectra have been constructed using different types of spectroscopic measurements, which include different types of spectroscopy based on transmission and reflection (Hanick 1967; Griffiths and Christopher 2002), e.g., attenuated total reflection (ATR) spectroscopy. The present study demonstrates calculation of IR absorption spectra for materials in water, using density functional theory (DFT) and associated software technology (see Huang et al. 2015) for the case of pure water), which provides complementary information to that obtained from laboratory measurement. This complementary information should be in terms of the physical interpretation of spectral features with respect to molecular structure. In addition, this study provides proof of concept for constructing templates for spectral-feature comparison using DFT-calculated spectra, which can be used in filter algorithms for detection of spectral features associated with target materials.

This study presents calculation of IR spectra, using DFT, for tetrachloroethylene (PCE), trichloroethylene (TCE), dichloroethylene (DCE) and vinyl chloride (VC) within a continuous water background. The properties of PCE, TCE, DCE, and VC molecules are of major importance for monitoring and detection of chlorinated hydrocarbons in water. This follows in that PCE, TCE, DCE, and VC, which are part of a specific chemical transformation sequence ending in ethene, are among toxic and carcinogenic contaminants commonly found in the environment, e.g., ground water (Haaland 1990; Smith 1997; Lam 1983; Brown 1986; Cooper 1986; Mann et al. 1982; Mann and Vickers 1986; Hanick 1967; Holliger et al. 1993; Brennan et al. 2006; Freedman and Gossett 1989; Vogel and McCarthy 1985; de Bruin et al. 1992; DiStefano et al. 1992; Jablonski and Ferry 1992; Neumann et al. 1994). The transformation sequence for PCE to ethene is shown in Fig. 1. The detection of these hydrocarbons, especially in the presence of water, using methods based on infrared (IR) spectroscopy is of particular interest. Specifically, IR spectral signatures, i.e., fingerprint spectra, can be correlated with the presence of these hydrocarbons (see Lu et al. 2013). For example, detection methodologies using lasers require knowledge of IR absorption spectra associated with different types of ambient molecules, e.g., H2O, in order to apply background subtraction or spectral-signature-correlation algorithms, which would enhance spectral features associated with specific materials targeted for detection. Lu et al. (2013) describes well-poised sensor technology, based on Fourier-transform infrared spectroscopy–attenuated total reflectance (FTIR–ATR), for determining the presence of chlorinated hydrocarbons in water and gives further references concerning their detection using spectroscopy. The present study presents investigation of dielectric response properties of PCE, TCE, DCE and VC molecules using DFT. The molecular-level dielectric response of these molecules, within the IR range of frequencies for vibration excitation by electromagnetic waves, should be of interest for interpretation of spectral signatures associated with detection methodologies.
Fig. 1

Transformation sequence for hydrocarbons PCE, TCE, DCE, and VC to ethene

Density functional theory (DFT) is applied to determine energy optimized structures and absorption spectra for isolated PCE, TCE, DCE and VC molecules within a continuous water background. DFT applied for the determination of equilibrium molecular structures and absorption spectra provides information complementary to that of experimental results. In this study, DFT-calculated vibration modes are associated with different molecules, which are part of a transformation sequence (see Fig. 1). In particular, DFT is used for calculation of ground-state resonance structure to enable physical interpretation of absorption spectra associated with molecules excited by IR electromagnetic waves. Such spectra are attributed to optically active vibration modes. In these studies, the DFT calculations were implemented using the computer program GAUSSIAN09 (G09) (Frisch et al. 2009a).

This report is organized as follows. First, issues motivating spectral database enhancement using DFT-calculated IR spectra are elucidated. Second, a general review of vibration analysis needed for calculation of absorption spectra is presented. Third, DFT calculations of energy-minimized geometries and IR spectra for isolated molecules of PCE, TCE, DCE, and VC within a water background are presented. The vibration resonance structure of these molecules provides estimates of their IR spectra and interpretation of spectral features with respect to specific molecules. Fourth, a discussion is given concerning the utilization of the DFT calculations. Finally, a conclusion is presented.

2 Background

Presented in this section are issues motivating the use of DFT-calculated IR spectra for spectral database enhancement, which are the following.

With respect to multidisciplinary-modeling issues:
  1. 1.

    Within the field of “computational quantum chemistry,” the calculation of spectra using DFT is considered a solved problem. Therefore, it should be expected that DFT calculation of spectra should be applied at production level for sensor applications.

     
  2. 2.

    Within the field of “spectroscopy”, DFT-calculated spectra should not be considered redundant information with respect to measurements, but rather complementary information, which is not always accessible via laboratory measurements.

     
  3. 3.

    Perspectives of the fields of computational quantum chemistry and applied spectroscopy should be linked, thus establishing a new perspective, adopting DFT-calculated spectra for database enhancement, i.e., adding DFT spectra to measured spectra for comparison with detector output.

     
With respect to detection issues:
  1. 1.

    It should be important to pose the problem of the practical feasibility of using DFT-calculated spectra to enhance databases used for detector reference and measured signal correlation. DFT-calculated spectra should add to measured spectra in that certain types of spectral features are not conveniently measurable, e.g., the water contaminants considered in this study.

     
  2. 2.

    Given the feasibility of using DFT-calculated spectra for spectral database enhancement, can these calculations be done efficiently as compared with spectral measurements in the laboratory? Significantly, computational capability has progressed such that DFT calculation of spectra can be undertaken efficiently, and applied at production level.

     
  3. 3.

    It is an interesting and important fact that the spectrum of an isolated molecule, although perturbed by being embedded within a host environment, still retains and displays its identity and therefore can be detected as such. An atom in a molecule is perturbed by its environment within the molecule, but it retains its identity although its properties will be affected according to the strength of the perturbations it suffers. Analogously, a molecule retains its identity within its environment but will have its properties affected in accordance with the strength of the interactions it suffers within its environment. The particular properties of interest here are the IR spectra of a molecule. Of the ordinary three phases of matter, the interactions with the environment will increase in strength in the direction moving from gas to liquid to solid. In any of these environments, the interaction effects will grow with increasing pressure, which brings molecules into closer interaction. With regard to the effect of increasing temperature, within a fixed phase, higher temperature will affect the occupation of vibration levels and enhance a tendency towards a change of harmonic levels to an-harmonic levels. But the important point to be emphasized here is that molecules retain their IR spectral properties through the veil of all such changes. That spectral retention of identification can be quantified by means of mathematical cross correlations between database spectra for an ideal molecular environment and the spectra associated with the molecule in field measurements in which the molecule is perturbed by its environment, as discussed above.

     
With respect to multiscale issues:
  1. 1.

    Are DFT-calculated spectra, associated with small molecular clusters, scalable within reasonable approximation, for correlation with measured spectral features, which are associated with macroscopic molecular aggregates?

     
  2. 2.

    In principle, the scalability of DFT-calculated spectra to spectral features of molecular aggregates should be investigated with respect to specific cases and desired detection sensitivity.

     
  3. 3.

    What are considered small molecule clusters convenient for DFT calculation of spectra is based on the level of computational power available. Thus, as this power increases, the concept of smallness will adjust accordingly. In addition, the concept of small molecular clusters can be extended to include fragments of large clusters, for which DFT-based partitioning methodologies, e.g., the kernel energy method (Polkosnik and Massa 2017), can be applied.

     

The above issues establish a foundation supporting an approach for complementing sensor databases with DFT-calculated spectra, concerning all types of detection, e.g., detection with respect to airborne, surface deposited, water environments. Database enhancement using DFT for detection of water contaminants is an important example of this approach. It should be noted that the concept of database enhancement using DFT-calculated spectra is independent of specific types of detection technology. Methodologies for comparison of detected spectral features with database spectra represent a separate problem.

3 Calculation of absorption spectra using DFT

Although the topic of DFT calculation of IR spectra is well known within the field of computational quantum chemistry, its presentation within the multidisciplinary context of this paper is essential for completeness. We give here a brief description of the formalism underlying DFT calculation of IR spectra, and implementation of this formalism in terms of the DFT software GAUSSIAN09.

The commercial computer program GAUSSIAN09 (G09) is designed to compute the IR spectrum of a molecule, including the effect of a continuous solvent background (Frisch et al. 2009a, b). Second derivatives of the energy with respect to the Cartesian nuclear coordinates are calculated and subsequently changed to mass-weighted coordinates at the equilibrium geometry of the molecule. The IR spectrum is obtained from the ground-state energy surface calculated in the Born–Oppenheimer approximation by solving the DFT Kohn–Sham equations (Hohenberg and Kohn 1964; Kohn and Sham 1965; Jones and Gunnarson 1989; Martin 2004; Wilson et al. 1955; Ochterski 1999; Becke 1993). The electronic density, the potential energy V, and the equilibrium geometry are calculated. The details followed by Gaussian for IR analysis are given in references Frisch et al. (2009b) and Ochterski (1999).

The spectrum of vibration frequencies, i.e., the IR spectrum, requires the Hessian matrix fCART, defined in Eq. (1) in terms of second derivatives of V (the potential energy) with respect to displacements of the atoms. Elements of fCART are defined as:

$${\mathbf{f}}_{{{\text{CART}}ij}} = \left( {\frac{{\partial^{2} V}}{{\partial \xi_{i} \partial \xi_{j} }}} \right)_{0} ,$$
(1)
where \(\left\{ {\xi_{1} ,\xi_{2} ,\xi_{3} ,\xi_{4} ,\xi_{5} ,\xi_{6} , \ldots ,\xi_{3N} } \right\} = \{ \Delta x_{1} ,\Delta y_{1} ,\Delta z_{1} ,\Delta x_{2} ,\Delta y_{2} ,\Delta z_{2} , \ldots ,\Delta z_{n} \}\) are the Cartesian displacements, with N being the number of atoms. In Eq. (1), the subscript zero indicates that the derivatives are taken at the equilibrium positions of the atoms where the first derivatives are zero. To calculate the IR spectrum, the Hessian matrix is transformed to mass-weighted Cartesian coordinates according to
$${\mathbf{f}}_{{{\text{MWC}}ij}} = \frac{{{\mathbf{f}}_{{{\text{CART}}ij}} }}{{\sqrt {m_{i} m_{j} } }} = \left( {\frac{{\partial^{2} V}}{{\partial q_{i} \partial q_{j} }}} \right)_{0} ,$$
(2)
where \(\{ {q_{1} ,q_{2} ,q_{3} ,q_{4} ,q_{5} ,q_{6} , \ldots ,q_{3N} } \} = \{ \sqrt {m_{1} } \Delta x_{1} , \sqrt {m_{1} } \Delta y_{1} ,\sqrt {m_{1} } \Delta z_{1} ,\sqrt {m_{2} } \Delta x_{2} ,\sqrt {m_{2} } \Delta y_{2} ,\sqrt {m_{2} } \Delta z_{2} , \ldots ,\sqrt {m_{N} } \}\)\(\left. \Delta z_{N} \right\}\) are the mass-weighted Cartesian coordinates. Thus, the second derivatives of the energy deliver the forces associated with displacing atoms in Cartesian directions. The first derivatives of the dipole moment \({{\partial \vec{\mu }} \mathord{\left/ {\vphantom {{\partial \vec{\mu }} {\partial \xi_{i} }}} \right. \kern-0pt} {\partial \xi_{i} }}\) taken with respect to atomic positions lead to a peak in the IR spectrum at a normal mode eigen-frequency \(\nu_{n0}\). The intensity of a normal mode is calculated as:
$$I_{n} = \frac{\pi }{3c}\left| {\sum\limits_{i = 1}^{3N} {\frac{{\partial \vec{\mu }}}{{\partial \xi_{i} }}{\mathbf{l}}_{{{\text{CART}}in}} } } \right|^{2} .$$
(3)
The lCART matrix elements are the Cartesian atom displacements given by
$${\mathbf{l}}_{\text{CART}} = {\mathbf{Ml}}_{\text{MWC}} ,$$
(4)
where the matrix lMWC has elements that are atom displacements in mass-weighted Cartesian coordinates and the matrix M is diagonal with elements
$$M_{ii} = \frac{1}{{\sqrt {m_{i} } }}.$$
(5)
The matrix fMWC (Eq. 2) is diagonalized using lMWC, so that.
$$\left( {{\mathbf{l}}_{\text{MWC}} } \right)^{T} {\mathbf{f}}_{\text{MWC}} \left( {{\mathbf{l}}_{\text{MWC}} } \right) = \varLambda ,$$
(6)
with Λ diagonal having element eigenvalues \(\lambda_{i}\). Equation (6) is made diagonal by the sequential calculations
$${\mathbf{f}}_{\text{INT}} = \left( {\mathbf{D}} \right)^{T} {\mathbf{f}}_{\text{MWC}} \left( {\mathbf{D}} \right),$$
(7)
and
$$\left( {\mathbf{L}} \right)^{T} {\mathbf{f}}_{\text{MWC}} \left( {\mathbf{L}} \right) = \varLambda .$$
(8)
The matrix D delivers a transformation to coordinates in which translations and rotations have been separated. L is the matrix of eigenvectors given by Eq. (8). The eigenvalues \(\lambda_{n}\) deliver eigen frequencies (/cm) according to
$$\nu_{n0} = \frac{{\sqrt {\lambda_{n} } }}{2\pi c},$$
(9)
where c is the speed of light. The elements of lCART are
$${\mathbf{l}}_{{{\text{CARTk}}i}} = \sum\limits_{j = 1}^{3N} {\frac{{D_{kj} L_{{_{ji} }} }}{{\sqrt {m_{j} } }}} ,$$
(10)
with k, i = 1,…, 3N, and column vectors of these elements being Cartesian coordinate normal modes.

The spectral intensity, assuming non-interacting molecules, is obtained by multiplication of the intensity, Eq. (3), by the molecular number density. In this way, the spectrum is calculated as a sum of delta functions, whose positions correspond to IR transition frequencies and whose coefficients correspond to spectral intensities. Were these spectra to be further refined they would be broadened by anharmonic effects, not here considered. In the discussion below, we consider comparison of calculated and measured IR spectral features.

4 DFT calculation of IR spectra

Results of a computational investigation using DFT concerning PCE, TCE, DCE, and VC molecules in water are presented. These results include the energy-minimized configuration of these molecules within a water background, and their ground-state oscillation frequencies and IR intensities. For these calculations, geometry energy optimization and vibration analysis were affected using the DFT model B3LYP (Becke 1993; Miehlich et al. 1989) and basis functions 6-311 + G(d) (McLean and Chandler 1980; Clark et al. 1983). These basis functions designate the 6-311G basis set supplemented by diffuse functions on non-hydrogen atoms, indicated by the sign +, and polarization functions (d), having one set of d functions on heavy atoms (Frisch et al. 1984). Graphical representations of molecular geometries for stable molecules of PCE, TCE, DCE, and VC within a water background, their ground-state energies and IR spectra, are shown in Figs. 2, 3, 4, 5, 6, 7. Values of the IR intensities as a function of frequency for these molecules (within water) are given in Table 1.
Fig. 2

DFT-calculated equilibrium geometry, minimal energy and IR spectra of isolated PCE molecule with water background

Fig. 3

DFT-calculated equilibrium geometry, minimal energy and IR spectra of isolated TCE molecule with water background

Fig. 4

DFT-calculated equilibrium geometry, minimal energy and IR spectra of isolated DCE1 molecule with water background

Fig. 5

DFT-calculated equilibrium geometry, minimal energy and IR spectra of isolated DCE2 molecule with water background

Fig. 6

DFT-calculated equilibrium geometry, minimal energy and IR spectra of isolated DCE3 molecule with water background

Fig. 7

DFT-calculated equilibrium geometry, minimal energy and IR spectra of isolated VC molecule with water background

Table 1

DFT-calculated absorption spectra [frequency (/cm), and intensity (km/mol)]

 

PCE-water

TCE-water

DCE1-water

Frequency

Intensity

Frequency

Intensity

Frequency

Intensity

1

176.4991

1.5875

171.0988

1.5166

167.9167

0.4428

2

291.6681

0.4443

202.7956

0.7714

563.1017

16.3969

3

311.9159

0.1131

274.0988

0.3871

689.7511

36.0586

4

344.5236

0.0001

382.0636

0.1544

711.9485

88.0086

5

442.9880

0.0001

473.6879

6.7270

824.6902

151.2395

6

562.4911

0.0001

617.0884

28.6720

917.7529

0.0002

7

756.7441

142.2207

807.4960

224.0390

1210.8771

0.0289

8

857.6000

371.1108

819.6176

37.0979

1310.6727

48.4690

9

946.9446

0.0117

891.3541

165.4903

1642.5854

63.2315

10

  

1269.5649

16.6776

3220.4785

31.6794

11

  

1636.8470

20.4494

3239.1296

0.2904

12

  

3242.2332

25.9618

  
 

DCE2-water

DCE3-water

VC-water

Frequency

Intensity

Frequency

Intensity

Frequency

Intensity

1

211.4155

0.4683

295.2784

0.0231

395.9996

0.6330

2

235.3571

5.3435

376.2886

0.3495

633.0379

22.1395

3

781.1868

239.6248

470.3112

10.0193

678.2792

84.9151

4

805.5179

0.0002

584.7642

29.8594

944.6993

60.4071

5

830.1527

0.0013

743.4598

192.6792

972.5149

43.5243

6

927.7733

94.8059

920.4420

66.3164

1034.8925

30.3397

7

1223.3744

33.2094

1081.7848

150.7204

1298.6516

22.6790

8

1638.7527

0.0001

1406.6536

0.1224

1404.6418

15.7280

9

3236.8621

24.2607

1653.7823

140.6795

1655.3824

100.3569

10

3239.7190

0.0275

3174.2524

4.8113

3156.3096

0.1352

11

  

3268.4785

1.1432

3225.9724

3.8986

12

    

3248.6128

1.5513

5 Discussion

Given a detection methodology that is well poised for measurement of spectral-signature structure associated with PCE, TCE, DCE, and VC, the experimental isolation of spectral features associated with these molecules, individually, may be difficult in that these molecules are part of a transformation sequence, where separate rates of transformation within this sequence may vary with environmental conditions. Accordingly, DFT provides an approach for estimating IR absorption spectra of isolated molecules. As discussed, identification of unknown molecules by comparison of spectra is accomplished using signal templates having patterns associated with known materials, which are adopted by different types of filter algorithms (Lam 1983; Brown 1986; Cooper 1986; Mann et al. 1982; Mann and Vickers 1986). In practice, because spectral features of target molecules are within complex spectral-signature backgrounds, filter algorithms associated with detection require reasonable estimates of target spectral features for construction of comparison templates, e.g., cross-correlation. In addition, one would expect small shifts of measured spectra maxima relative to those of template spectra due to different types of detector designs and ambient environments, which would result in different levels of coupling between molecular vibration modes and intermolecular interactions. This coupling of molecular and intermolecular modes, depending on the detection scenario, implies the need for “lag” parameters in application of spectrum-comparison algorithms, e.g., cross-correlation (Smith 1997). In particular, the DFT-calculated spectra in Table 1 were calculated for isolated molecules within a weakly interacting background and are, therefore, quite similar to spectra of isolated molecules in space, where there are no shifts due to intermolecular couplings.

It follows that the DFT-calculated IR spectra calculated here, given in Table 1, should provide a reasonable template for filtering of IR spectral measurements associated with different types of detector schemes. In principle, this template can be a linear combination of the spectra given in Table 1, having adjustable weight coefficients of the component spectra, as well as correlation-lag parameters for adjustment of absorption maxima frequencies. A qualitative analysis of prototypical spectral features as would occur in a realistic detection environment, using DFT-calculated spectra (Table 1), may be applied to the measurements (VC IR Spectrum from NIST Standard Reference Database 69: NIST Chemistry Webbook 2017). Shown in Fig. 8 is a comparison of IR absorption spectra for VC in condensed phase, which was measured using FTIR as described in VC IR Spectrum from NIST Standard Reference Database 69: NIST Chemistry Webbook (2017), with DFT-calculated spectra for an isolated VC molecule weakly interacting with a water background. Further a comparison of the measured spectral features shown in Fig. 8, and those given in Table 1 for VC show good correlation within a small correlation lag, i.e., frequency shift of absorption maxima.
Fig. 8

Comparison of DFT-calculated and FTIR measured (Frisch et al. 1984) IR absorption spectra for VC

6 Conclusion

The DFT-calculated absorption spectra given here provide information concerning molecular level dielectric response structure. The calculations of IR spectra associated with PCE, TCE, DCE, and VC molecules within a water background using DFT are meant to serve as reasonable estimates of molecular level response characteristics, providing interpretation of dielectric response features for comparison with experimental measurements. Specifically, the DFT-calculated IR spectra calculated here should provide a reasonable template for filtering of IR spectral measurements associated with different types of detector schemes. Also it is worth emphasizing the scalability of the DFT calculations relevant to individual molecules as against their presence in a macroscopic environment. This may be seen for example in Fig. 8.

As emphasized in this study, IR spectra of PCE, TCE, DCE and VC are of major importance for monitoring and detection of chlorinated hydrocarbons in water. In particular, these chlorinated hydrocarbons are among the most toxic and carcinogenic contaminants commonly found in the environment. This work provides proof of concept for using DFT-calculated spectra to construct templates, which are for spectral-feature comparison, and thus detection of spectral-signature features associated with target materials. And in addition, it is perhaps obvious that exactly the same detection techniques which have been focused in this paper on halogen hydrocarbons would apply in exactly the same way with any other molecular contaminants of a water supply.

Finally, it is significant to note that placement of this work within a particular and specific field (and associated community) represents an issue in itself. Accordingly, this study attempts to convey the underlying issue that this problem is multidisciplinary. Within theoretical chemistry density functional theory is well defined and thought of as a complete theory. But its practical, one might say engineering applicability, is hardly a matter for consideration. On the other hand, where practical matters, such as those which are the subject of our paper, are the problems under consideration, engineers while aware of DFT have not realized its practical importance in solution of engineering problems. This study highlights the benefits of bringing these two fields together. Strictly theoretical quantum mechanical density functional theory has a role to play in solving practical problems such as detection and analysis of deadly water contaminants.

Notes

Acknowledgements

Funding for this project was provided by the Office of Naval Research (ONR) through the Naval Research Laboratory’s Basic Research Program.

References

  1. Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648–5652CrossRefGoogle Scholar
  2. Brennan RA, Sanford RA, Werth CJ (2006) Biodegradation of tetrachloroethene by chitin fermentation products in a continuous flow column system. J Environ Eng ASCE 132:664–673CrossRefGoogle Scholar
  3. Brown SD (1986) The Kalman filter in analytical chemistry. Anal Chim Acta 181:1–26CrossRefGoogle Scholar
  4. Clark T, Chandrasekhar J, Spitznagel GW, Schleyer PVR (1983) Efficient diffuse function-augmented basis-sets for anion calculations, 3, the 3–21 + G basis set for 1st-row elements, Li-F. J Comp Chem 4:294–301CrossRefGoogle Scholar
  5. Cooper WS (1986) Use of optimal estimation theory-in particular the Kalman filter-in data analysis and signal processing. Rev Sci Instrum 57(11):2862–2869CrossRefGoogle Scholar
  6. de Bruin WP, Kotterman MJJ, Posthumus MA, Schraa G, Zehnder AJB (1992) Complete biological reductive transformation of tetrachloroethene to ethane. Appl Environ Microbiol 58(6):1996–2000Google Scholar
  7. Distefano TD, Gossett JM, Zinder SH (1992) Hydrogen asan electron donor for dechlorination of tetrachloroethene by anaerobic mixed culture. Appl Environ Microbiol 58(11):3622–3629Google Scholar
  8. Freedman DL, Gossett JM (1989) Biological reductive dechlorination of tetrachlororthylene and trichloroethylene to ethylene under methanogenic conditions. Appl Environ Microbiol 55(9):2144–2151Google Scholar
  9. Frisch MJ, Pople JA, Binkley JS (1984) Self-consistent molecular orbital methods. 25. Supplementary functions for Gaussian basis sets. J Chem Phys 80:3265–3269CrossRefGoogle Scholar
  10. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009a) Gaussian 09, revision A.1. Gaussian Inc., Wallingford CTGoogle Scholar
  11. Frisch A, Frisch MJ, Clemente FR, Trucks GW (2009) Gaussian 09 user’s reference. Gaussian Inc., p 105–106. www.gaussian.com/g_tech/g_ur/g09help.htm
  12. Griffiths PR, Christopher CC (2002) Handbook of vibrational spectroscopy. Wiley, New YorkGoogle Scholar
  13. Haaland DM (1990) Multivariate calibration methods applied to quantitative FT-IR analyses, Chapter 8. In: Ferraro JR, Krishnan K (eds) Practical fourier transform infrared spectroscopy. Academic Press Inc, San DiegoGoogle Scholar
  14. Hanick NJ (1967) Internal reflection spectroscopy. Interscience Publishers, New YorkGoogle Scholar
  15. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864MathSciNetCrossRefGoogle Scholar
  16. Holliger C, Schraa G, Stams AJM, Zehnder AJB (1993) A highly purified enrichment culture couples the reductive dechlorination of tetrachloroethene to growth. Appl Environ Microbiol 9(9):2991–2997Google Scholar
  17. Huang L, Lambrakos SG, Shabaev A, Bernstein N, Massa L (2015) Molecular analysis of water clusters: calculation of the cluster structures and vibrational spectrum using density functional theory. Comptes Rendus Chim 18(5):516–524CrossRefGoogle Scholar
  18. Jablonski PE, Ferry JG (1992) Reductive dechlorination of trichloroethylene by the CO-reduced CO dehydrgenase enzyme complex from methanosarcina thermophile. FEMS Microbiol Lett 96:55–60CrossRefGoogle Scholar
  19. Jones RO, Gunnarson O (1989) The density functional formalism, its applications and prospects. Rev Mod Phys 61:689CrossRefGoogle Scholar
  20. Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133MathSciNetCrossRefGoogle Scholar
  21. Lam RB (1983) On the relationship of least squares to cross-correlation quantitative spectral analysis. Appl Spectros 37:567–569CrossRefGoogle Scholar
  22. Lu R, Mizaikoff B, Li W-W, Qian C, Katzir A, Raichlin Y, Sheng G-P, Yu H-Q (2013) determination of chlorinated hydrocarbons in water using highly sensitive mid-infrared sensor technology. Sci Rep 3:2525.  https://doi.org/10.1038/srep02525 CrossRefGoogle Scholar
  23. Mann CK, Goleniewski JR, Sismanidis CA (1982) Spectrophotometric analysis by cross-correlation. Appl Spectros 36:223–227CrossRefGoogle Scholar
  24. Mann CK, Vickers TJ (1986) Signal enhancement by data domain averaging. Appl Spectros 40(4):525–531CrossRefGoogle Scholar
  25. Martin RM (2004) Electronic structures basic theory and practical methods. Cambridge University Press, Cambridge, p 25CrossRefGoogle Scholar
  26. McLean AD, Chandler GS (1980) Contracted Gaussian-basis sets for molecular calculations. 1. 2nd row atoms, Z = 11-18. J Chem Phys 72:5639–5648CrossRefGoogle Scholar
  27. Miehlich B, Savin A, Stoll H, Preuss H (1989) Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr. Chem Phys Lett 157:200–206CrossRefGoogle Scholar
  28. Neumann A, Schloz-Muramatsu H, Diekert G (1994) Tetrachloroethene metabolism of Dehalospirillum multivorans. Arch Microbiol 162:295–301CrossRefGoogle Scholar
  29. Ochterski JW (1999) Vibrational analysis in Gaussian. (help@gaussian.com)Google Scholar
  30. Polkosnik W, Massa L (2017) Single determinant N-representability and the kernel energy method applied to water clusters. JCC 39(17):1038–1043Google Scholar
  31. Smith SW (1997) The scientist and engineer’s guide to digital signal processing, chapter 7: properties of convolution, correlation. California Technical Publishing, San DiegoGoogle Scholar
  32. VC IR Spectrum from NIST Standard Reference Database 69: NIST Chemistry Webbook (2017) US Secretary of Commerce on behalf of the USAGoogle Scholar
  33. Vogel TM, McCarthy PL (1985) Biotransformation of tetrachlororthylene to trichloroethylene, dichloroethylene, vinyl chloride, and carbon dioxide under methanogenic conditions. Appl Environ Microbiol 49(5):1080–1083Google Scholar
  34. Wilson EB, Decius JC, Cross PC (1955) Molecular vibrations. McGraw-Hill, New YorkGoogle Scholar

Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019

Authors and Affiliations

  1. 1.Volunteer Emeritus Naval Research LaboratoryWashingtonUSA
  2. 2.Naval Research LaboratoryWashingtonUSA
  3. 3.Hunter College and the Graduate SchoolCUNYNew YorkUSA

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