Molecular Spectroscopy E-Book
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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
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- Sprache: Englisch
Uniquely creates a strong bridge between molecular spectroscopy and quantum chemistry
This two-volume book consists of many reviews reporting new applications of quantum chemistry to molecular spectroscopy (Raman, infrared, near-infrared, terahertz, far-ultraviolet, etc.). It contains brief introductions to quantum chemistry for spectroscopists, and to the recent progress on molecular spectroscopy for quantum chemists.
Molecular Spectroscopy: A Quantum Chemistry Approach examines the recent progress made in the field of molecular spectroscopy; the state of the art of quantum chemistry for molecular spectroscopy; and more. It offers multiple chapters covering the application of quantum chemistry to: visible absorption and fluorescence, Raman spectroscopy, infrared spectroscopy, near-infrared spectroscopy, terahertz spectroscopy, and far-ultraviolet spectroscopy. It presents readers with hydrogen bonding studies by vibrational spectroscopy and quantum chemistry, as well as vibrational spectroscopy and quantum chemistry studies on both biological systems and nano science. The book also looks at vibrational anharmonicity and overtones, and nonlinear and time-resolved spectroscopy.
-Comprehensively covers existing and recent applications of quantum chemistry to molecular spectroscopy
-Introduces the quantum chemistry for the field of spectroscopy and the advancements being made on molecular spectroscopy for quantum chemistry
-Edited by world leading experts who have long standing, extensive experience and international standing in the field
Molecular Spectroscopy: A Quantum Chemistry Approach is an ideal book for analytical chemists, theoretical chemists, chemists, biochemists, materials scientists, biologists, and physicists interested in the subject.
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Veröffentlichungsjahr: 2019
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Table of Contents
Cover
Preface
Contents to Volume 1
1 Interpretability Meets Accuracy in Computational Spectroscopy: The Virtual Multifrequency Spectrometer
1.1 Introduction
1.2 The Virtual Multifrequency Spectrometer
1.3 The VMS Framework at Work
1.4 The VMS Framework: Applications
1.5 Conclusions
Acknowledgments
References
2 Excited State Dynamics in NTChem
2.1 NTChem
2.2 Electron Dynamics in a Molecular Aggregate Under a Light Field
2.3 Trajectory Surface Hopping Molecular Dynamics Simulation
2.4 Summary
Acknowledgment
References
3 Quantum Chemistry for Studying Electronic Spectroscopy and Dynamics of Complex Molecular Systems
3.1 Overview of Quantum Chemical Tools for Studying Electronic Spectroscopy
3.2 Examples: Quantum Chemical Calculations of Simple Systems
3.3 Spectral Line Shape
3.4 Examples: Complex Systems
References
4 Theoretical and Experimental Molecular Spectroscopy of the Far‐Ultraviolet Region
4.1 Introduction
4.2 Method
4.3 Results and Discussion
4.4 Summary
References
5 Weight Averaged Anharmonic Vibrational Calculations: Applications to Polypeptide, Lipid Bilayers, and Polymer Materials
5.1 Introduction
5.2 Method
5.3 Applications
5.4 Concluding Remarks and Outlook
Acknowledgments
References
6 Chiral Recognition by Molecular Spectroscopy
6.1 Introduction
6.2 The Physical Manifestation of Optical Activity in Chiroptical Spectroscopic Methods: Theory of the Chiroptical Properties
6.3 Selected Case Studies
6.4 Perspective
References
7 Quantum Approach of IR Line Shapes of Carboxylic Acids Using the Linear Response Theory
7.1 Introduction
7.2 The Characteristics of the Infrared Spectra of Hydrogen‐Bonded Species
7.3 The Strong Coupling Theory of Anharmonicity
7.4 Conclusion
References
8 Theoretical Calculations Are a Strong Tool in the Investigation of Strong Intramolecular Hydrogen Bonds
8.1 Introduction and Definition of Types of Intramolecular Hydrogen Bonds
8.2 Definitions of Strong Intramolecular Hydrogen Bonds
8.3 Calculation of Structural Parameters
8.4 Hydrogen Bond Strength
8.5 Calculation of Energies
8.6 Tautomerism
8.7 Calculation of IR Spectra of Strongly Hydrogen‐Bonded Systems
8.8 NMR
8.9 Principal Component Analysis
8.10 Solvent Effects
8.11 Conclusions
References
9 Spectral Simulation for Flexible Molecules in Solution with Quantum Chemical Calculations
9.1 Introduction
9.2 Selection of the Calculation Level for Spectral Simulations of Flexible Molecules
9.3 Simulation of IR Spectra Observed in Solution Phase
9.4 Competition Between Intramolecular and Intermolecular Interactions
9.5 Conformational Diversity and Solvation in the Vibrational Spectrum
9.6 Conformational Diversity in the Vibrational Circular Dichroism Spectrum
9.7 Conformational Diversity in the Electronic Circular Dichroism
References
10 Combination Analysis of Matrix‐Isolation Spectroscopy and DFT Calculation
10.1 Introduction
10.2 Matrix‐Isolation Method
10.3 Adoption of Theory and Basis Set
10.4 Conformational Analysis
10.5 Identification for Unknown Species
10.6 Spectrum and Structure of Molecular Complex or Cluster
10.7 Photoinduced Transient Species
10.8 Conclusion
References
11 Role of Quantum Chemical Calculations in Elucidating Chemical Bond Orientation in Surface Spectroscopy
11.1 Introduction
11.2 Vibrational Sum‐Frequency Generation Spectroscopy
11.3 Determination of Bond Polarity
11.4 Quantum Chemical Calculations for Modeling the Molecular Hyperpolarizability
11.5 Example
11.6 Summary
Acknowledgments
References
Contents to Volume 2
12 Dynamic and Static Quantum Mechanical Studies of Vibrational Spectra of Hydrogen‐Bonded Crystals
12.1 Introduction
12.2 Historical and Theoretical Background
12.3 Applications
12.4 Summary and Perspectives
Acknowledgment
References
13 Quantum Mechanical Simulation of Near‐Infrared Spectra: Applications in Physical and Analytical Chemistry
13.1 Introduction
13.2 Overview of the Current Progress in Computational NIR Spectroscopy
13.3 Conclusions
References
14 Local Modes of Vibration: The Effect of Low‐Frequency Vibrations
14.1 Introduction
14.2 Local Mode (LM) Models
14.3 Effect of Low‐Frequency Modes
14.4 Local Mode Intensities
14.5 Summary
Appendix
References
15 Intra‐ and Intermolecular Vibrations of Organic Semiconductors and Their Role in Charge Transport
15.1 Introduction
15.2 Theoretical Treatment of Coupling Between Intra‐ and Intermolecular Vibrations in Low‐Frequency Region
15.3 The Role of Inter‐ and Intramolecular Vibrations in Charge Transport
15.4 Impact of Low‐Frequency Vibrations on Charge Transport in F
n
‐TCNQ Crystal Family
15.5 Conclusions
Acknowledgments
References
16 Effects of Non‐covalent Interactions on Molecular and Polymer Individuality in Crystals Studied by THz Spectroscopy and Solid‐State Density Functional Theory
16.1 A Historical Review of Phonon Modes
16.2 Theoretical Representation of Non‐covalent Interactions
16.3 A Mode Decomposition Method
16.4 Interpretation of the Nature of Optical Phonon Modes Controlled by Prototypical Non‐covalent Interactions
16.5 Application of the DFT‐D Method in a Material System scPLA
16.6 Experimental Evidence Supporting the Mode Assignments
16.7 Conclusion
References
17 Calculation of Vibrational Resonance Raman Spectra of Molecules Using Quantum Chemistry Methods
17.1 Introduction
17.2 Theory of Resonance Raman Scattering, Approximations, and Quantum Chemistry Methods
17.3 Illustrative Applications
17.4 Conclusions
References
18 Density Functional Theoretical Study on Surface‐Enhanced Raman Spectroscopy of CH
2
/NH
2
Wagging Modes in p–π Conjugated Molecules on Noble Metal Surfaces
18.1 Introduction
18.2 Brief Review of Wagging Vibrational Raman Spectra
18.3 Normal Mode Analysis
18.4 Density Functional Theoretical Calculations
18.5 Raman Intensity
18.6 Modeling Molecules
18.7 Chemical Enhancement Effect
18.8 The Reason of Broadbands
18.9 Conclusions
Acknowledgments
References
19 Modeling Plasmonic Optical Properties Using Semiempirical Electronic Structure Calculations
19.1 Introduction
19.2 INDO/CI vs. TD‐DFT: Absorption Spectra of Ag Nanoclusters
19.3 Higher‐Order Excitations: The Role of Double Excitations in Absorption
19.4 Identification of Quadrupolar Plasmonic Excited States
19.5 Electrochemical Charge Transfer
19.6 Voltage Effects and the Chemical Mechanism of Surface‐Enhanced Raman Scattering
19.7 Conclusions
Acknowledgment
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Equilibrium structure of pyrimidine (bond lengths in Å, angles ...
Table 1.2 Vertical excitation energies and oscillator strengths for the...
Chapter 2
Table 2.1 Excitation energies of coumarin.
a
Chapter 3
Table 3.1 Comparisons of TD‐DFT adiabatic excitation energies against e...
Chapter 4
Table 4.1 Transition energies (Δ
E
) and oscillator strengths (
f
) of
n
‐pe...
Table 4.2 Excitation energies (eV) of the center of the absorption band...
Table 4.3 Excitation energies (eV) of the π–π* transition of FA, NMF, N...
Table 4.4 Excitation energies (eV) of the π–π* transition of FA, NMF, N...
Table 4.5 Interaction energies, excitation energies, and energy shifts ...
Chapter 9
Table 9.1
ν
C
O
obs
wavenumber observed under various condition...
Table 9.2 Relative energy Δ
E
(kJ/mol) from the energy of the most stabl...
Chapter 10
Table 10.1 The observed wavenumbers (in cm
−1
) of vanillin compare...
Chapter 13
Table 13.1 An exemplary comparison of total computational time for meth...
Table 13.2 Band assignments in NIR spectrum of rosmarinic acid, based o...
Chapter 14
Table 14.1 Typical LM parameters for different bond types.
Table 14.2 LM parameters (
) for 1,3‐butadiene.
Table 14.3 LM parameters (
) for propane.
Table 14.4 Calculated OH stretching intensities (oscillator strengths) ...
Chapter 15
Table 15.1 Relative contributions (%) of intra‐ and intermolecular vibr...
Table 15.2 Relative contributions (%) of intra‐ and intermolecular vibr...
Table 15.3 Main transfer integrals for TCNQ and F
2
‐TCNQ crystals.
Chapter 16
Table 16.1 Structural information of molecular crystals. The lattice pa...
Chapter 18
Table 18.1 Inversion angle (
α
, °), C-NH
2
bond length (Å), N-Ag bon...
Table 18.2 Inversion angle (
α
, °), C-C bond length (Å), C-Ag bond ...
Table 18.3 Selected parameters of optimized geometries, binding energy ...
Table 18.4 Inversion angle (α, °), C
C bond length (Å), calculated vibr...
Table 18.5 The six derivatives of polarizability components
, isotro...
Chapter 19
Table 19.1 Enhancement factors and frequency shifts of selected Raman m...
Table 19.2 Decomposition of the integrated enhancement factors for the ...
List of Illustrations
Chapter 1
Figure 1.1 The framework of the virtual multifrequency spectrometer.
Figure 1.2 Equivalence relations between the model property
P
and actua...
Figure 1.3 Assignment tool of VMS‐ROT. (a) Simulated spectrum window: t...
Figure 1.4 Comparison of the computed harmonic and anharmonic IR spectr...
Figure 1.5 The heat diagram for the semi‐diagonal cubic force constant,...
Figure 1.6 Comparison between the vibrationally resolved computed (red)...
Figure 1.7 The A
2
B
1
X
2
A
1
electronic transition of the phenyl rad...
Figure 1.8 Comparison between the computed and experimental spectra of ...
Figure 1.9 S
3
S
0
CPL spectrum of dimethyloxirane simulated by diff...
Figure 1.10 The 2,2,6,6‐tetramethyl‐4‐piperidone‐1‐oxyl radical, also k...
Figure 1.11 Two representative screenshots of the VMS‐EPR software: set...
Figure 1.12 The MSR software: (a) input panel, (b), visualization panel...
Figure 1.13 Simulated theoretical spectra: “ALL” (dark red) means the s...
Figure 1.14 Comparison of gas‐phase and chemisorbed glycine spectrum to...
Figure 1.15 Anharmonic IR spectra of methyloxirane in the 1600–2800 and...
Figure 1.16 Fully anharmonic ROA spectrum of (R)‐methyloxirane compared...
Figure 1.17 Performance of the B3LYP/SNSD, hybrid B2PLYP/B3LYP, and CCS...
Figure 1.18 Computed and experimental spectra for the S
1
S
0
transi...
Figure 1.19 Resonance forms of the TEMPO radical.
Figure 1.20 Fmoc‐(Aib‐Aib‐TOAC)
2
‐Aib‐OMe.
Figure 1.21 EPR spectra of Fmoc‐(Aib‐Aib‐TOAC)
2
‐Aib‐OMe in different so...
Chapter 2
Figure 2.1 (a) Schematics of the relative orientation of the monomers i...
Figure 2.2 Charge migration dynamics in a NPTL–TCNE dimer. The panels i...
Figure 2.3 Schematics of the relative positioning of a 20‐mer circle of...
Figure 2.4 Time‐dependent behaviors of quantities of unpaired electrons...
Figure 2.5 Schematics of the exciton dynamics in the circularly oriente...
Figure 2.6 Schematics of the exciton dynamics in the circularly oriente...
Figure 2.7 Molecular structure of coumarin.
Figure 2.8 Molecular orbitals of coumarin.
Figure 2.9 Time‐dependent population profiles of S
0
–S
3
states.
Figure 2.10 Representative trajectory that approaches to the S
0
/S
1
cros...
Figure 2.11 Representative trajectory that stays on the S
1
(
n
π*) state....
Chapter 3
Figure 3.1 Adapted TD‐DFT output example with selected excited states f...
Figure 3.2 The agreements of TD‐B3LYP (○) and CIS(D) (•) excitation ene...
Figure 3.3 The absorption spectrum of bacteriochlorophyll‐
a
from TD‐DFT...
Figure 3.4 Comparison between QM/MM simulated line shape (solid) and th...
Figure 3.5 Structure of bovine rhodopsin (left) and the embedded retina...
Figure 3.6 Structural evolution of the retinal chromophore minimal mode...
Figure 3.7 Excited state energy levels of rhodopsin at various geometri...
Figure 3.8 Chromophore structural model of the LH2 complex from
Rhodoba
...
Figure 3.9 (a) Comparison of computational and experimental absorption ...
Chapter 4
Figure 4.1 Schematic diagram of the ATR‐FUV spectrometer.
Figure 4.2 ATR‐FUV spectra of
n
‐alkanes (C
m
H
2
m
+2
,
m
= 5–9).
Figure 4.3 Theoretical spectra of
n
‐alkanes (C
m
H
2
m
+2
,
m
= 5–9) fr...
Figure 4.4 Theoretical spectra of
n
‐pentane calculated by (a) SAC‐CI an...
Figure 4.5 Temperature dependence of the ATR‐FUV spectrum of
n
‐tetradec...
Figure 4.6 Simulated electronic spectra of the
n
‐pentane monomer optimi...
Figure 4.7 Total density of states (TDOS) of the crystal structure (a) ...
Figure4.8 (a) Simulated spectra in the region of 120–220 nm of an
n
‐pen...
Figure 4.9 Changes in the orbital energy near the HOMO of the monomer a...
Figure 4.10 (a) Molecular structures and (b) ATR‐FUV spectra of FA, NMF...
Figure 4.11 Theoretical spectra of amides (a) in vacuum calculated by T...
Figure 4.12 (a) The optimized structure of the dimers of the five amide...
Figure 4.13 Peak shifts from vacuum to the liquid phase evaluated by AT...
Figure 4.14 SAC‐CI spectra of amides for (a) monomer and (b) dimer mode...
Figure 4.15 Optimized structures of the trimer, tetramer, and pentamer ...
Figure 4.16 Convergence of the peak shift along with the number of inte...
Figure 4.17 Chemical structures of (a) nylon 6, (b) nylon 11, (c) nylon...
Figure 4.18 (a) ATR‐FUV spectra of nylon 6, nylon 11, nylon 12, nylon 6...
Figure 4.19 (a) Tr‐FUV spectra of nylon 6, nylon 11, nylon 12, nylon 6/...
Figure 4.20 Correlation between the average alkyl chain and the intensi...
Figure 4.21 The peak position of the band near 195 nm for Tr spectra vs...
Figure 4.22 Calculated spectra of model compounds of nylon 6, nylon 11,...
Figure 4.23 Computational trimer models with the transition dipole stre...
Figure 4.24 Typical MOs relevant to the π–π* transition in the trimer m...
Figure 4.25 Distribution of the π–π* transitions with relatively strong...
Chapter 5
Figure 5.1 Schematic representation of (a) harmonic and anharmonic pote...
Figure 5.2 A group of atoms (O, C, N, and H in blue) that gives the vib...
Figure 5.3 (a) The structure and the HB pattern of five lowest energy c...
Figure 5.4 Plots of the NH stretching frequency of the amide group free...
Figure 5.5 (a) The chemical structure of
N
‐acyl sphingomyelin (SM). (b)...
Figure 5.6 (a) The HB connectivity of the amide group (A), hydroxyl gro...
Figure 5.7 (a) The chemical formulas of model molecules used for repres...
Figure 5.8 (a, b) Raman spectrum of an SM bilayer in the LC and gel pha...
Figure 5.9 (a) The chemical structure of nylon 6. (b) Snapshots of a un...
Figure 5.10 (a) The harmonic and anharmonic difference IR spectrum of w...
Chapter 6
Figure 6.1 Comparison of the Raman (upper graph) and ROA (lower graph) ...
Figure 6.2 (a) Experimental IR and VCD spectra of PO in the fingerprint...
Figure 6.3 (a) Experimental VCD spectra of S‐PO in various solvents. Do...
Chapter 7
Figure 7.1 Hydrogen‐bonded system.
Figure 7.2 Cyclic H‐bonded dimers. The action of the parity operator ...
Figure 7.3 Structure of the “Davydov” Hamiltonian. The Davydov coupling...
Figure 7.4 Connections between the different theories of IR spectra of ...
Figure 7.5 IR spectrum of the
dimer in the gas phase at room temper...
Figure 7.6 Application of the theory to several isotopic species of for...
Chapter 8
Figure 8.1 H‐bond motifs without indication of inter‐ or intramolecular...
Figure 8.2 Intramolecular H‐bonds with a “double” bond linking the hydr...
Figure 8.4 Compounds with single bond corresponding to salicylaldehyde....
Figure 8.3 Plot of calculated H⋯O distance vs. calculated O⋯O distance,...
Figure 8.5 A plot of the calculated O⋯O distances vs. the calculated OH...
Figure 8.6 Hydrogen‐bonded system.
Figure 8.7 1,3,5‐Triacetyl‐2,4,6‐trihydroxybenzene.
Figure 8.8 Calculated O⋯O distance (Å) vs. calculated HB‐out MP2 energi...
Figure 8.9 Hydrogen bond energies (MP2) in kcal/mol vs. calculated O⋯O ...
Figure 8.10 Illustration of the MTA fragmentation method.
Figure 8.11 Observed
two‐bond deuterium isotope effect
s (
TBDIE
s) ...
Figure 8.12 Naphthalene Schiff bases. The shown structure refers to S3 ...
Figure 8.13 Potential energy curves for S1 [2‐(
E
)‐(methylimino)methy]ph...
Figure 8.14 Molecular structures of selected investigated
o
‐hydroxyaryl...
Figure 8.15 A two‐dimensional free energy map reconstructed from the CP...
Figure 8.16 Correlation of proton motions in double bridges of the zwit...
Figure 8.17 The IR spectrum of dibenzoylmethane enol has puzzled spectr...
Figure 8.18 Linear regression of OH stretching wavenumbers computed wit...
Figure 8.19 Atomic velocity power spectra for 2‐(
N
‐methyliminomethyl)‐4...
Figure 8.20 Plot of
13
C nuclear shieldings vs.
13
C measured chemical sh...
Figure 8.21 Calculated OH bond lengths in Angstroms vs. OH chemical shi...
Figure 8.22 Visualization of the spatial magnetic properties (TSNMRS) o...
Figure 8.23 Calculated ring current effects for salicylaldehyde and thi...
Figure 8.24 (a) 10‐Hydroxybenzo[h]quinoline; (b) 4′‐substituted 2′‐hydr...
Figure 8.25 Resonance structures of thiophenoxyketenimines.
Figure 8.26 Deuterium isotope effect transmission coefficients.
Figure 8.27 Deuterium isotope effects on
13
C chemical shifts for picoli...
Chapter 9
Figure 9.2 IR spectra of NdMAm (a) in Ar matrix at 12 K, (b) in cyclohe...
Figure 9.1 Chemical structures of NdMAm and NMAm.
Figure 9.3 Comparison between the IR spectrum of NdMAm measured in Ar m...
Figure 9.4
ν
C
O
band of NdMAm measured in various solvents at 2...
Figure 9.5 Correlation between
ν
C
O
calc
and 〈
ν
C
O
〉 expe...
Figure 9.6 Optimized structures for the complex of NdMAm and the solven...
Figure 9.7 Correlation between
ν
C
O
calc
for NdMAm/solvent comp...
Figure 9.8 Chemical structures of PNiPAm and its dimer model (dNiPAm‐c1...
Figure 9.9 IR spectra in the amide I and II region for PNiPAm and dNiPA...
Figure 9.10 Optimized geometries of trans and gauche conformers of dNiP...
Figure 9.11 (a) Simulated IR spectra for the trans (solid line) and gau...
Figure 9.12 Chemical structure of EDMPAm.
Figure 9.13 Experimental IR spectra of EDMPAm (a) in CCl
4
and (b) in th...
Figure 9.14 Optimized geometries of the representative conformers of ED...
Figure 9.15 Experimental Raman spectrum of EDMPAm in the neat liquid (a...
Figure 9.16 (a) Experimental IR spectra of EDMPAm in CCl
4
and D
2
O solut...
Figure 9.17 Optimized conformers of (
S
)‐1‐phenylethanol obtained at the...
Figure 9.18 (a) IR spectrum of
DL
‐1‐phenylethanol (racemic mixture) in ...
Figure 9.19 (a) VCD spectrum of (−)‐1‐phenylethanol observed in the CS
2
Figure 9.20 Structures of the dimers of (
S
)‐1‐phenylethanol optimized a...
Figure 9.21 (a) Observed VCD spectrum of (−)‐1‐phenylethanol in the CS
2
Figure 9.22 Chemical structure of Cl/I‐Im.
Figure 9.23 (Top) ECD spectra of (−)‐ and (+)‐Cl/I‐Im in methanol. (Bot...
Figure 9.24 Simulated ECD spectra for several conformers of (aR)‐ and (...
Chapter 10
Figure 10.1 Schematic diagram of matrix‐isolation method. Sample molecu...
Figure 10.2 Comparison of experimental spectra of acetic acid in CCl
4
s...
Figure 10.3 Comparison of the matrix IR spectrum of H‐TFSI in a Ne matr...
Figure 10.4 Matrix‐isolation spectra of 1,2‐dichloroethane isolated in ...
Figure 10.5 Matrix‐isolation IR spectra of 2‐chlorobenzaldehyde measure...
Figure 10.6 Conformers of vanillin with their related energies in kJ/mo...
Figure 10.7 Matrix‐isolation IR spectrum of vanillin (a) and simulated ...
Figure 10.8 A difference IR spectrum of vanillin measured between after...
Figure 10.9 Eight enol conformers and keto tautomer of acetylacetone.
Figure 10.10 Isomers of cytosine with their relative energies (in kJ/mo...
Figure 10.11 Matrix‐isolation IR spectrum of cytosine (a), photoinduced...
Figure 10.12 Photoinduced isomerization between 1,8‐aminonaphthylnitren...
Figure 10.13 Matrix IR spectra related with photoinduced isomerization ...
Figure 10.14 Photolysis of
s
‐triazine to make cyclic (HCN)
3
in a matrix...
Figure 10.15 IR spectra of hydroquinone (a), UV‐induced transient speci...
Figure 10.16 A difference IR spectrum of 1,4‐dicyanobenzene measured be...
Figure 10.17 Bond length changing of 1,4‐dicyanobenzene in the S
0
to th...
Chapter 11
Figure 11.1 Some basic co‐propagating geometries for a visible–infrared...
Figure 11.2 (a)
spectra of ethanol obtained from an ATR‐IR absorpti...
Figure 11.3 (a) Energy level diagram illustrating a vibrationally reson...
Figure 11.4 (a) Schematic of a heterodyne SFG experiment, where the vis...
Figure 11.5 Relationship between the polar orientation of the surface c...
Figure 11.6 Values of the dipole moment vector elements
for the CH
3
Figure 11.7 Values of the linear polarizability tensor elements
for...
Figure 11.8 Relationship between the direction of the observed band in ...
Figure 11.9 (a) SFG
phase response of PMMA methyl ester symmetric s...
Chapter 12
Figure 12.1 Definition of pathways for one‐dimensional proton potential...
Figure 12.2 (a) Subsystems ABCD and A′B′C′D′ in crystal structure of ic...
Figure 12.3 Structure (a) and atom labeling (b) in crystal unit cell of...
Figure 12.4 Infrared spectrum of oxalic acid dihydrate crystal calculat...
Figure 12.5 O-H stretching band contours of oxalic acid dihydrate: blac...
Figure 12.6 Ascorbic acid molecules − labeling of atoms and crystal str...
Figure 12.7 Infrared spectra of
L
‐ascorbic acid. (a) Experimental spect...
Figure 12.8 The power spectra of the atoms in the O-H bonds obtained fr...
Figure 12.9 The band contours calculated from individual fundamental vi...
Figure 12.10 (a) Structure of cyclic dimer of aspirin. (b,c) Form I and...
Figure 12.11 (a) Position of second cyclic dimers in form I and form II...
Figure 12.12 Panel (a) presents the chemical structure of tropolone. Th...
Figure 12.13 Results of the analysis of the electronic structure for a ...
Chapter 13
Figure 13.3 Band assignments in the experimental and calculated NIR spe...
Figure 13.1 NIR spectra of diluted methanol; experimental (5 × 10
−3
...
Figure 13.2 Band assignments of methanol diluted in CCl
4
determined thr...
Figure 13.4 Experimental and simulated (harmonic: B2PLYP/def2‐TZVP; VPT...
Figure 13.5 Experimental (0.2 M; CCl
4
) and simulated (VPT2//B3LYP/SNST+...
Figure 13.6 Experimental (solution; CCl
4
) and modeled spectrum of aceti...
Figure 13.7 Molecular structures of the major conformational isomers of...
Figure 13.8 Experimental and simulated NIR spectra of MCFAs: (a) propio...
Figure 13.9 Band assignments proposed for NIR spectra of MCFAs in mediu...
Figure 13.10 The experimental FT‐NIR spectrum of aqueous malic acid in ...
Figure 13.11 The experimental (powder) and theoretical NIR spectrum of ...
Figure 13.12 Simulated NIR spectra of CXXXOX (X = H, D) molecules.
Figure 13.13 Contributions due to first and second overtones, as well a...
Figure 13.14 Convolution of NIR bands on the example of spectra simulat...
Figure 13.15 Vibrational potential and vibrational states [B3LYP/6‐311G...
Figure 13.16 The slopes of solvent shifts of phenol, 2,6‐difluorophenol...
Figure 13.17 (a) Dependences on the dielectric constant of the potentia...
Figure 13.18 Vibrational wavefunctions and dipole moment functions alon...
Chapter 14
Figure 14.1 The observed OH stretching transitions of
for
and 2...
Figure 14.2 2D HCAO Hamiltonian. The same basis states as shown on the ...
Figure 14.3 Spectrum of CH stretching transitions of 1,3‐butadiene in t...
Figure 14.4 HCAO Hamiltonian for 1,3‐butadiene. The same basis states (
Figure 14.5
region of 1,3‐butadiene‐
(top trace) and 1,3‐butadi...
Figure 14.6 Absorbance from the CH stretching vibrations of propane in ...
Figure 14.7 The coordinate system used to describe a rotating methyl gr...
Figure 14.8 Potential (
), frequency (
), and anharmonicity (
) o...
Figure 14.9 Illustration of the two most significant intermolecular mod...
Figure 14.10 Observed and calculated HF stretching frequencies for the ...
Figure 14.11
stretching fundamental transition in MeOH complexes. ...
Figure 14.12 Observed NH stretching transitions of DMA and the DMF for ...
Figure 14.13 Simulated (top) and observed (bottom) spectra of the methy...
Figure 14.14 Absorption from the fundamental OH stretching and second o...
Chapter 15
Figure 15.1 Crystal packing of crystalline TCNQ (a), F2‐TCNQ (b), and F...
Figure 15.2 Low‐frequency Raman spectra for polycrystalline TCNQ (upper...
Figure 15.3 Calculated vibrational frequencies in crystals (blue) and t...
Figure 15.4 The three mechanisms underlying the impact of electron–phon...
Figure 15.5 The effect of molecular size on local (a) and nonlocal (b) ...
Figure 15.6 Local and nonlocal electron–phonon couplings in pentacene c...
Figure 15.7 Main charge transfer directions of TCNQ (a) and F
2
‐TCNQ (b)...
Figure 15.8 Contribution of various vibrational modes to the nonlocal e...
Figure 15.9 Illustration of intermolecular charge delocalization respon...
Figure 15.10 The impact of representative LF vibrations on Dimers 1 and...
Chapter 16
Figure 16.1 Molecular structures of urea: (a)
C
2
v
conformation in t...
Figure 16.2 Structural information of the C
60
(a), anthracene (b), aden...
Figure 16.3 The simulation results for the C
60
crystal. (a) The simulat...
Figure 16.4 The simulation results for the anthracene crystal. (a) Comp...
Figure 16.5 The simulation results for the adenine crystal. (a) Compare...
Figure 16.6 The simulation results for the
α
‐glycine crystal. (a) ...
Figure 16.7 The simulation results for the
L
‐alanine crystal. (a) The s...
Figure 16.8 Comparison of the molecule weights and the average of the m...
Figure 16.9 Crystal structure of scPLA with
R
3
c
space group symmetry. T...
Figure 16.10 Simulation results for scPLA. Panel (a) shows a THz spectr...
Figure 16.11 Examination of the symmetry breaking extents for PLLA and ...
Figure 16.12 Examination of the effect of crystallinity of scPLA on the...
Figure 16.13 Examination of the effect of crystallinity of adenosine on...
Chapter 17
Figure 17.1 (a) Normal (non‐resonant) Raman scattering, (b) resonance R...
Figure 17.2 (a) RR spectra of JM calculated with different XC functiona...
Figure 17.3 (a) Molecule of R6G, (b) theoretical (B3LYP) and experiment...
Figure 17.4 Calculated (B3LYP) and experimental RR spectra of the [(tbb...
Figure 17.5 Calculated (B3LYP) and experimental RR spectra of R6G (a) a...
Chapter 18
Figure 18.1 Character vibrational modes related to the NH
2
group in fre...
Figure 18.2 Optimized structures of molecules interacting with Ag
4
clus...
Figure 18.3 Energy levels (ranging from −11.63 to 0 in eV unit) of mole...
Figure 18.4 Dependence of amino wagging frequencies on bonding energy (...
Figure 18.5 Calculated Raman spectra of aniline interacting with coinag...
Figure 18.6 Simulated Raman spectra of aniline adsorbed on silver elect...
Figure 18.7 Simulated surface Raman spectra of PABA (a), PABN (b), and ...
Figure 18.8 Simulated Raman spectra of benzyl anion adsorbed on silver ...
Figure 18.9 Simulated Raman spectra of ethylene interacted with cationi...
Figure 18.10 The polarizability components (unit in Bohr
3
) along the am...
Figure 18.11 The molecule‐silver cluster complexes in their rectangular...
Figure 18.12 The variation of molecular orbital energies (in atomic uni...
Chapter 19
Figure 19.1 INDO/SCI absorption spectra of the tetrahedral Ag
20
cluster...
Figure 19.2 Absorption spectra of several Ag clusters. Solid lines indi...
Figure 19.3 Transition quadrupole moments
Q
zz
(magnitudes) along th...
Figure 19.4 (a) Molecular orbital energies and (b) excited state energi...
Figure 19.5 (a, b) Normal and (c, d) resonance Raman spectra for the (a...
Figure 19.6 Integrated enhancement factors as a function of photon ener...
Figure 19.7 (a, b) Normal and (c, d) resonance Raman spectra for the (a...
Guide
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Molecular Spectroscopy
A Quantum Chemistry Approach
Edited by
Yukihiro OzakiMarek Janusz WójcikJürgen Popp
Volume 1
Molecular Spectroscopy
A Quantum Chemistry Approach
Edited by
Yukihiro OzakiMarek Janusz WójcikJürgen Popp
Volume 2
Copyright
Editors
Yukihiro Ozaki
Kwansei Gakuin University
Department of Chemistry
2‐1 Gakuen
Kobe Sanda Campus
669‐1337 Sanda, Hyogo
Japan
Marek Janusz Wójcik
Jagiellonian University
Department of Chemistry
Ingardena 3
30‐060 Kraków
Poland
Jürgen Popp
Leibniz‐Institut für Photonische Technol
Albert‐Einstein‐Str. 9
07745 Jena
Germany
Cover Image: Kindly provided by Yukihiro Ozaki, Kwansei Gakuin University, Japan; © Sirinarth Mekvorawuth/EyeEm/Getty Images (Background)
All books published by Wiley‐VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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© 2019 Wiley‐VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
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Print ISBN: 978‐3‐527‐34461‐1
ePDF ISBN: 978‐3‐527‐81462‐6
ePub ISBN: 978‐3‐527‐81460‐2
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Cover Design: Wiley
Preface
The purpose of this book is to outline the state‐of‐the‐art quantum chemical approach to molecular spectroscopy. Over the last two decades or so, molecular spectroscopy has made remarkable progress; several novel spectroscopies such as terahertz spectroscopy, tip‐enhanced Raman scattering (TERS), and far‐ultraviolet (FUV) spectroscopy in condensed phase have emerged. Moreover, existing spectroscopies have shown prominent advances in this period. The advances in spectroscopies lie in the development of theory, instruments, spectral analysis, and applications. In spectral analysis quantum chemical approach is particularly important. It is useful not only for spectral analysis such as band assignments but also for studies of structure, reactions, and physical and chemical properties of molecules.
This book aims at making a strong bridge between molecular spectroscopy and quantum chemistry. For the last quarter of a century quantum chemistry has been extensively used for various spectroscopies such as vibrational spectroscopy, electronic spectroscopy, and nuclear magnetic resonance spectroscopy. However, one cannot find a good book that connects spectroscopy and quantum chemistry. This book may be the first one that explains comprehensively how quantum chemical approach can be applied to molecular spectroscopy. It covers FUV spectroscopy, UV–visible spectroscopy, near‐infrared (NIR) spectroscopy, IR spectroscopy, far‐IR spectroscopy/terahertz spectroscopy, Raman spectroscopy, and NMR spectroscopy. Almost all kinds of molecular spectroscopies are presented in this book. For quantum chemical approaches various new calculation methods are introduced. The recent rapid progress in supercomputers has made it possible to utilize these new methods. For example, anharmonic quantum chemical calculations are becoming popular due to advances in supercomputers. In applications many chapters deal with studies of hydrogen bonding and inter‐ and intramolecular interactions. In this book, we invited front runners from many countries who are currently very active in the molecular spectroscopy–quantum chemistry field.
This book is very useful not only for chemistry but also for applied physics, material sciences, biosciences, and industrial applications. It is suitable for molecular spectroscopists who are interested in quantum chemistry and quantum chemists who are interested in molecular spectroscopy. We hope this book will find many readers among students at graduate level as well as researchers and engineers in academia and industry.
Last but not the least, we would be most grateful if the book can inspire readers to use novel quantum chemistry approaches for molecular spectroscopy studies and/or to attempt to develop new approaches by themselves.
In closing, we would like to thank Dr. Lifen Yang, Ms. Shirly Samuel, and Mr. Jayakumar Ramprasad of Wiley for their continuous efforts in publishing this book.
April 2019
Yukihiro Ozaki, Sanda, Japan
Marek Janusz Wójcik, Krakow, Poland
Jürgen Popp, Jena, Germany
1Interpretability Meets Accuracy in Computational Spectroscopy: The Virtual Multifrequency Spectrometer
Vincenzo Barone1 and Cristina Puzzarini2
1Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
2Università di Bologna, Dipartimento di Chimica “Giacomo Ciamician”, Via Selmi 2, 40126 Bologna, Italy
The virtual multifrequency spectrometer (VMS), under active development in our laboratories over the last few years, is shortly described in this chapter by means of selected spectroscopic techniques and a few representative case studies. The VMS project aims to offer an answer to the following question: is it possible to turn strongly specialized research in the field of computational spectroscopy into robust and user‐friendly aids to experiments and industrial applications? VMS contains a number of tools devised to increase the interaction between researchers with different background and to push toward new frontiers in computational chemistry. As a matter of fact, the terrific advancements in computational spectroscopy and the wide availability of computational and analytic tools are paving the route toward the study of problems that were previously too difficult or impossible to be solved and let imagine even more ambitious targets for fundamental and applied research. Under such circumstances, a robust, flexible, and user‐friendly tool can allow for moving data analysis toward a proactive process of strategic decisions and actions. This chapter starts from these premises, and it proposes a perspective for a new virtual platform aimed at integrating past developments in theory, algorithms, and software with new workflow management and visualization tools. After a short review of the underlying theoretical framework, the features of the principal tools available in the current version of VMS for a selection of spectroscopic techniques are addressed in some details. Next, four case studies are presented, thus aiming to illustrate possible applications of VMS to systems of current interest for both fundamental and applied research. These applications convincingly show that even if several extensions of the software are planned or already under development, VMS represents a powerful and user‐friendly tool for both computational and experimentally oriented spectroscopists.
1.1 Introduction
Spectroscopic techniques provide a wealth of qualitative and quantitative information on the chemical and physical–chemical properties of molecular systems in a variety of environments. Nowadays, sophisticated experimental techniques, mainly based on vibrational, electronic, and resonance spectroscopies, allow studies under various environmental conditions and in a noninvasive fashion [1,2]. Particularly effective strategies are obtained when different spectroscopic techniques are combined together and further supported and/or integrated by computational approaches. Indeed, not only the spectral analysis is seldom straightforward, but also molecular spectra do not provide direct information on molecular structures, properties, and dynamics [3,4]. The challenges can be posed by the intrinsic properties and complexity of the system and/or caused by thermal or environmental effects, whose specific roles are not easy to separate and evaluate. In such a context, computational spectroscopy is undoubtedly a powerful and reliable tool to unravel the different contributions to the spectroscopic signal and understand the underlying physical phenomena [5,6]. However, direct vis‐à‐vis comparisons between experimental and computed spectroscopic data are still far from being standard. To fill this lack, a virtual multifrequency spectrometer (VMS) (http://dreamslab.sns.it/vms/) has been implemented with the aim of providing a user‐friendly access to the latest developments of computational spectroscopy, also to nonspecialists [7–11]. As it will be better explained in the following section, VMS integrates state‐of‐the‐art computational implementations of different spectroscopies with a powerful graphical user interface (GUI) [12], which offers an invaluable aid in preorganizing and displaying the computed spectroscopic information. For the sake of clarity, it should be noted that several codes incorporate implementation of spectroscopic properties at different levels of theory together with graphic engines. However, none of these tools offer the characteristics that should be considered mandatory for state‐of‐the‐art computational spectroscopy (e.g. rigorous treatment of anharmonicity, vibronic contributions, etc.) and/or for flexible user‐friendly graphical tools. In particular, it should emphasize the uniqueness of VMS in incorporating both general utilities needed by experimentally oriented scientists (e.g. conversion of theoretical quantities to experimental observables, manipulation of several spectra at the same time, etc.) and advanced tools for theoreticians and developers (e.g. resonance Raman [RR] spectra).
The aim of the present chapter is to provide an overview of the VMS software, thus focusing on its peculiarities and unique features. The chapter is organized as follows. In the following section, a brief summary of the general machinery of the VMS program and of the main technical aspects will be provided. This will be followed by a short introduction of the theoretical background for the selected spectroscopies (e.g. rotational, vibrational, vibronic, and magnetic) and of the corresponding quantum chemical (QC) requirements. Then, the current status of VMS will be presented in some detail with specific reference to rotational, vibrational, vibronic, and magnetic spectroscopy. Finally, applications will be illustrated with the help of four case studies, which will allow the capabilities of VMS to be demonstrated. Some general considerations will conclude the chapter.
1.2 The Virtual Multifrequency Spectrometer
VMS is a tool that integrates a wide range of computational and experimental spectroscopic techniques and aims at predicting and analyzing different types of molecular spectra as well as disclosing the static and dynamic physical–chemical information they contain [7]. VMS is mainly composed of two parts, namely, VMS‐Comp, which provides access to the latest developments in the field of computational spectroscopy, and VMS‐Draw, which provides a powerful GUI for an intuitive interpretation of theoretical outcomes and a direct prediction or comparison to experiment (http://dreamslab.sns.it/vms/) [7].
The spectroscopies supported by VMS are electron spin resonance (ESR), nuclear magnetic resonance (NMR), rotational (microwave [MW]), infrared (IR), vibrational circular dichroism (VCD), nonresonant Raman (nRR), resonance Raman, Raman optical activity (ROA), resonance Raman optical activity (RROA), electronic one‐photon absorption (OPA) (i.e. UV–vis) and one‐photon emission (OPE) (i.e. fluorescence), electronic circular dichroism (ECD), and circularly polarized luminescence (CPL).
1.2.1 The VMS Framework
The framework of the VMS program is graphically shown in Figure 1.1[7]. The key feature of VMS is to provide a user‐friendly access to computational spectroscopy tools also to nonspecialists. VMS integrates a powerful GUI, VMS‐Draw, which offers an invaluable aid in the pre‐ and post‐processing stages [12]. This permits a direct way to present the information produced by in vitro and in silico experiments, thus allowing the user to focus the attention on the underlying physical–chemical features without being concerned with technical details. VMS‐Draw is interfaced with VMS‐Comp [8,9,13], which takes care of QC computations of the required spectroscopic parameters and all high‐performance computing (HPC) aspects [7,12]. Both VMS‐Draw and VMS‐Comp modules are either fully embedded with the Gaussian package [] or loosely bound to other suites of QC programs, such as CFOUR [15]. In the last case, general input–output facilities as well as ad hoc scripts that permit effective interactions with other electronic structure codes than Gaussian have been developed or are still under development (see, for example, Ref. [10]). Overall, VMS has access to almost all computational models and to properties that are not yet available in the reference QC Gaussian suite. In addition to the large availability of QC methods and properties, VMS has the unique feature of allowing state‐of‐the‐art computational spectroscopy studies driven by a flexible user‐friendly graphical tool that furthermore includes those general utilities needed by experimentally oriented scientists (e.g. manipulations of several spectra at the same time, spectral normalization, etc.) and advanced tools for theoreticians and developers (e.g. resonance Raman spectroscopy). In the following sections, the theoretical background and the QC requirements for quantitative spectral prediction/analysis of selected spectroscopies are presented together with a description of the spectral simulation facilities and of the corresponding results.
Figure 1.1 The framework of the virtual multifrequency spectrometer.
1.2.2 The VMS Framework: Spectroscopies and Theoretical Background
The complete list of the spectroscopies available within the VMS software has been given above. In this chapter, we limit ourselves to the discussion of a selection of spectroscopies, namely, the rotational, vibrational, vibronic, and magnetic spectroscopies, for which we provide a short description of the theoretical background.
1.2.2.1 Rotational Spectroscopy
The terms of the effective rotational Hamiltonian are the pure rotational and centrifugal distortion contributions, which describe the rotational energy levels for a given vibrational state, with the ground state usually being the one of interest. While a complete treatment can be found in the literature (see, for example, Ref. [16]), here, we recall just the key aspects of interest.
The basic rotational Hamiltonian, within the semirigid rotor approximation, can be written as
where and are the quartic and sextic centrifugal terms, respectively. The dots refer to the possibility of including higher‐order centrifugal contributions. is the rigid rotor Hamiltonian:
where has been defined as follows:
where refers to the inertial axis. From a computational point of view, the equilibrium rotational constants are straightforwardly obtained from the geometry optimization.
Even if the equilibrium contribution to rotational constants is the most important, the effect of molecular vibrations cannot be neglected when aiming at a quantitative description of rotational spectra. Therefore, the term describing the dependence of the rotational constants on the vibrational quantum numbers should be incorporated in Eq. 1.3, and equilibrium rotational constants should be replaced by the effective rotational constants that contain the contributions beyond the rigid rotor harmonic oscillator (RRHO) approximation. Their effects on rotational motion can be conveniently described by means of vibrational perturbation theory (VPT), and we refer the reader to, for example, Refs. [16,17] for a detailed treatment. While there are no corrections at the first order in VPT, at the second order (VPT2), the expression becomes [18]:
where the superscript denotes a specific vibrational state and the sum runs on all fundamental vibrational modes , with being the corresponding quantum number and its degeneracy order. The values are the so‐called vibration–rotation interaction constants and contain three contributions: the first one is a corrective term related to the moment of inertia, the second one is due to the Coriolis interactions, and the last is an anharmonic correction. Therefore, from a computational point of view, anharmonic force field (FF) calculations are required to correct the equilibrium rotational constants for vibrational effects.
The quartic centrifugal distortion Hamiltonian is defined as
where the tensor depends only on the harmonic part of the potential energy surface (PES). To obtain the quartic centrifugal distortion parameters actually employed, further contact transformations with purely rotational operators (thus diagonal in the vibrational quantum numbers) are then required. An analogous expression can be written for the sextic centrifugal distortion term , and the computation of the corresponding sextic centrifugal distortion constants involves harmonic, anharmonic, and Coriolis perturbation terms. Therefore, from a computational point of view, anharmonic force field computations are needed for their determination. To relate the experimental parameters to combinations of ( in the case of sextics), it is necessary to further completely reduce the Hamiltonian. Different results are then obtained depending on the reduction chosen; see, for example, Refs. [16,17,19].
1.2.2.2 Vibrational Spectroscopy
For the simulation of vibrational spectra, a purely vibrational Hamiltonian () is commonly used. In the framework of VPT2, which is based on Taylor expansions of the harmonic potential (), vibrational () energies, and vibrational wavefunction, up to the second order [20], the vibrational Hamiltonian is defined as follows:
For asymmetric tops, at the VPT2 level, the energy (, in cm−1) of a given vibrational state is given by
where is the number of quanta associated with mode in state and the corresponding harmonic wavenumber. is the zero‐point vibrational energy, which is defined as follows:
In Eq. 1.7, is the anharmonicity contributions matrix, with its elements given by
where
Transition energies from the ground state are therefore straightforwardly obtained from Eqs. 1.7 and 1.8 as difference.
The intensities for a broad range of spectroscopies at the VPT2 level can be obtained by referring to a generic property P, which can depend on either the normal coordinates (q) or their conjugate momenta (p):
where
In equations above, and are the creation and annihilation operators, respectively; , , and are constant factors; and corresponds to a sign (i.e. it represents the multiplication by +1 or ). The function of Eq. 1.12 is then used to obtain analytic formulas for the transition moments up to three quanta [21–25] and can be simply related to the property of interest by identifying the variables in Eqs. 1.12–1.15 with the actual quantities, as exemplified in Figure 1.2. The electric (μ) and magnetic (m) dipoles and the polarizability (α) are used in IR, VCD, and Raman intensities, respectively, whereas the electric dipole–magnetic dipole optical activity (G′) and the electric dipole–electric quadrupole (A) tensors also enter the ROA intensities [13].
Figure 1.2 Equivalence relations between the model property P and actual properties.
From a quick inspection of Eqs. 1.9 and 1.10, it is evident that for the VPT2 energies, the denominator might become exceedingly small. This situation leads to the so‐called Fermi resonances (FRs), which can be distinguished in type I () and type II (). Indeed, a near resonance can be sufficient to obtain unphysical results due to an excessive contribution from anharmonicity. This is a well‐known issue of VPT2, which has been extensively studied in the literature [1626–39] and needs to be correctly addressed for a successful application of this method. A major difficulty lies in the definition of the resonance conditions. In the literature, several efficient identification processes have been presented [2628–30,3336–40]. Then, those terms that have been identified as resonant should be removed from the perturbative treatment for the calculation of the energy. This approach is named deperturbed VPT2 (DVPT2). To take into account the missing terms, an ad hoc variational step, which reintroduces the previously discarded terms, can be performed using the DVPT2 vibrational energies as references. We refer to the overall resulting procedure as generalized VPT2 (GVPT2). An alternative approach has been proposed by Kuhler, Truhlar, and Isaacson and denoted degeneracy‐corrected PT2 (DCPT2); this is based on replacing the potentially resonant terms with nonresonant forms derived from a model system considering only the two states involved [29]. A shortcoming of this approach is a potential inaccuracy for each replaced terms far from resonance; this can be partially corrected by introducing a switch function that will mix the DCPT2 and VPT2 results for each potentially resonant term, thus leading to the so‐called hybrid DCPT2‐VPT2 (HDCPT2) [37]. Finally, other types of resonance should be mentioned; these are collectively denoted as Darling–Dennison resonances (DDRs) [26,30,3239–45] and are commonly treated through a variational procedure, analogous to that used for FRs. In the following, we always refer to GVPT2, and this includes corrections to both Fermi and DDRs.
The problem of resonances in intensity calculations has been more scarcely addressed in the literature, and limited is the number of programs supporting them [13,23,27,39,44]. Since they are related to the mechanical anharmonicity (wavefunction), it is possible to use the analysis for the energy shortly addressed above also for the transition moments. However, an important difference is the impact of DDRs, which can lead to incorrect intensities. Depending on the protocol applied for the definition of DDRs, it may be necessary to complement it with an ad hoc test targeted to handle the most critical cases (for instance, of near‐equal energies) [13,46]. The eigenvectors (LE) of the matrix diagonalized to introduce the variational contribution of resonances to energies are used to project the deperturbed transition moments on the variationally corrected states following the procedure described in Ref. [23]:
In the VMS framework, all the required strategies for a correct derivation of the intensities are implemented.
1.2.2.3 Vibronic Spectroscopy
A reliable description of molecular vibrations in ground and excited electronic states is at the heart of an accurate simulation of vibrational modulation (hereafter vibronic in a broad sense) effects in UV–vis spectra and their chiroptical (e.g. ECD) counterparts. Indeed, experimental spectra originate from the convolution of vibronic transitions, thus usually leading to highly asymmetric band‐shaped spectra at both low and high resolution. From a theoretical point of view, a rigorous inclusion of rovibrational effects beyond the standard rigid rotor harmonic oscillator approximation can be performed for small molecules, whereas for larger systems, feasible approaches are currently based on neglecting the rovibrational coupling and on the Franck–Condon (FC) principle at the harmonic level. Within this framework, a general sum‐over‐state expression for the vibronic contributions to the transition between two electronic states has been derived for OPA, OPE, ECD, and CPL [47,48], and it has been recently extended to resonance Raman, its chiroptical counterpart RROA, and also spin‐forbidden transitions [49], with the corresponding intensity being expressed by the following equation:
where the sums run over all possible initial and final vibronic states, with being the Boltzmann population; is the Dirac function, and the asterisk is used to denote the conjugate of the matrix element. In the equation above,
