INFRARED AND RAMAN SPECTRA OF INORGANIC AND COORDINATION COMPOUNDS
CONTENTS CHAPTER 1 THEORY OF NORMAL VIBRATIONS 1 1 ORIGIN OF MOLECULAR SPECTRA / 1 2 ORIGIN OF INFRARED AND RAMAN SPECTRA / 1 3 VIBRATION OF A DIATOMIC MOLECULE / 1 4 NORMAL COORDINATES AND NORMAL VIBRATIONS / 1 5 SYMMETRY ELEMENTS AND POINT GROUPS / 1 6 SYMMETRY OF NORMAL VIBRATIONS AND SELECTION RULES / 1 7 INTRODUCTION TO GROUP THEORY / 1 8 THE NUMBER OF NORMAL VIBRATIONS FOR EACH SPECIES / 1 9 INTERNAL COORDINATES / 1 10 SELECTION RULES FOR INFRARED AND RAMAN SPECTRA / 1 11 STRUCTURE DETERMINATION / 1 12 PRINCIPLE OF THE GF MATRIX METHOD / 1 13 UTILIZATION OF SYMMETRY PROPERTIES / 1 14 POTENTIAL FIELDS AND FORCE CONSTANTS / 1 15 SOLUTION OF THE SECULAR EQUATION / 1 16 VIBRATIONAL FREQUENCIES OF ISOTOPIC MOLECULES / 1 17 METAL–ISOTOPE SPECTROSCOPY / 1 18 GROUP FREQUENCIES AND BAND ASSIGNMENTS / 1 19 INTENSITY OF INFRARED ABSORPTION / 1 20 DEPOLARIZATION OF RAMAN LINES / 1 21 INTENSITY OF RAMAN SCATTERING / 1 22 PRINCIPLE OF RESONANCE RAMAN SPECTROSCOPY / 1 23 RESONANCE RAMAN SPECTRA / 1 24 THEORETICAL CALCULATION OF VIBRATIONAL FREQUENCIES / 1 25 VIBRATIONAL SPECTRA IN GASEOUS PHASE AND INERT GAS MATRICES / 1 26 MATRIX COCONDENSATION REACTIONS / 1 27 SYMMETRY IN CRYSTALS / 1 28 VIBRATIONAL ANALYSIS OF CRYSTALS / 1 29 THE CORRELATION METHOD / 1 30 LATTICE VIBRATIONS / 1 31 POLARIZED SPECTRA OF SINGLE CRYSTALS / 1 32 VIBRATIONAL ANALYSIS OF CERAMIC SUPERCONDUCTORS / REFERENCES / CHAPTER 2 APPLICATIONS IN INORGANIC CHEMISTRY 2 1 DIATOMIC MOLECULES / 2 2 TRIATOMIC MOLECULES / 2 3 PYRAMIDAL FOUR-ATOM MOLECULES / 2 4 PLANAR FOUR-ATOM MOLECULES / 2 5 OTHER FOUR-ATOM MOLECULES / 2 6 TETRAHEDRAL AND SQUARE–PLANAR FIVE-ATOM MOLECULES / AND RELATED MOLECULES / 2 8 OCTAHEDRAL MOLECULES / 2 9 XY7 AND XY8 MOLECULES / 2 10 X2Y4 AND X2Y6 MOLECULES / 2 11 X2Y7, X2Y8, X2Y9, AND X2Y10 MOLECULES / 2 12 METAL CLUSTER COMPOUNDS / 2 13 COMPOUNDS OF BORON / 2 14 COMPOUNDS OF CARBON / 2 15 COMPOUNDS OF SILICON, GERMANIUM, AND OTHER GROUP IVB ELEMENTS / 2 16 COMPOUNDS OF NITROGEN / 2 17 COMPOUNDS OF PHOSPHORUS AND OTHER GROUP VB ELEMENTS / 2 18 COMPOUNDS OF SULFUR AND SELENIUM / CONTENTS 2 19 COMPOUNDS OF HALOGEN / THEORY OF NORMAL VIBRATIONS 1 1 ORIGIN OF MOLECULAR SPECTRA AS A FIRST APPROXIMATION, THE ENERGY OF THE MOLECULE CAN BE SEPARATED INTO THREE ADDITIVE COMPONENTS ASSOCIATED WITH (1) THE MOTION OF THE ELECTRONS IN THE MOLECULE,* (2) THE VIBRATIONS OF THE CONSTITUENT ATOMS, AND (3) THE ROTATION OF THE MOLECULE AS A WHOLE: ETOTAL ¼ EEL Þ EVIB Þ EROT Ð1:1Þ THE BASIS FOR THIS SEPARATION LIES IN THE FACT THAT ELECTRONIC TRANSITIONS OCCUR ON A MUCH SHORTER TIMESCALE, AND ROTATIONAL TRANSITIONS OCCUR ON A MUCH LONGER TIMESCALE, THAN 10 VIBRATIONAL TRANSITIONS THE TRANSLATIONAL ENERGY OF THE MOLECULE MAY BE IGNORED IN THIS DISCUSSION BECAUSE IT IS ESSENTIALLY NOT QUANTIZED IF A MOLECULE IS PLACED IN AN ELECTROMAGNETIC FIELD (E G , LIGHT), A TRANSFER OF ENERGY FROM THE FIELD TO THE MOLECULEWILL OCCUR WHEN BOHR’S FREQUENCY CONDITION IS SATISFIED: DE ¼ HN Ð1:2Þ WHERE DE IS THE DIFFERENCE IN ENERGY BETWEEN TWO QUANTIZED STATES, H IS PLANCK’S CONSTANT (6 625 1027 ERG S), AND N IS THE FREQUENCY OF THE LIGHT HERE, THE FREQUENCY IS THE NUMBER OF ELECTROMAGNETIC WAVES IN THE DISTANCE THAT LIGHT TRAVELS IN ONE SECOND: N ¼ C L Ð1:3Þ WHERE C IS THE VELOCITY OF LIGHT (3 1010 CM S1) AND L IS THE WAVELENGTH OF THE ELECTROMAGNETIC WAVE IF L HAS THE UNITS OF CM, N HAS DIMENSIONS OF (CM S1)/CM ¼ S1, WHICH IS ALSO CALLED “HERTZ (HZ) ” THE WAVENUMBER Ð~NÞ DEFINED BY ~N ¼ L Ð1:4Þ IS MOST COMMONLY USED IN VIBRATIONAL SPECTROSCOPY IT HAS THE DIMENSION OF CM1 BY COMBINING EQS 1 3 AND 1 4, WE OBTAIN ~N ¼ Ð1:7Þ WHERE E2 AND E1 ARE THE ENERGIES OF THE EXCITED AND GROUND STATES, RESPECTIVELY THEN, THE MOLECULE “ABSORBS” DE WHEN IT IS EXCITED FROM E1 TO E2 AND “EMITS” DE WHEN IT REVERTS FROM E2 TO E1 FIGURE 1 1 SHOWS THE REGIONS OF THE ELECTROMAGNETIC SPECTRUM WHERE DE IS INDICATED IN ~N, L, AND N IN THIS BOOK, WE ARE CONCERNED MAINLY WITH VIBRATIONAL TRANSITIONS WHICH ARE OBSERVED IN INFRARED (IR) OR RAMAN (R) SPECTRA *USE CONVERSION FACTORS SUCH AS AVOGADRO’S NUMBER N0 ¼ 6:023 1023ÐMOL 1Þ 1 ÐCALÞ ¼ 4:1846 107ÐERGÞ 1 ÐEVÞ ¼ 1:6021 10 12ÐERG MOLECULE 1Þ REGION (MICROWAVE REGION) BECAUSE ROTATIONAL LEVELS ARE RELATIVELY CLOSE TO EACH OTHER, WHEREAS ELECTRONIC TRANSITIONS ARE OBSERVED IN THE 104–106 CM1 REGION (UV–VISIBLE REGION) BECAUSE THEIR ENERGY LEVELS ARE FAR APART HOWEVER, SUCH DIVISION IS SOMEWHAT ARBITRARY, FOR PURE ROTATIONAL SPECTRA MAY APPEAR IN THE FAR-INFRARED REGION IF TRANSITIONS TO HIGHER EXCITED STATES ARE INVOLVED, AND PURE ELECTRONIC TRANSITIONS MAY APPEAR IN THE NEAR-INFRARED REGION IF ELECTRONIC LEVELS ARE CLOSELY SPACED FIGURE 1 2 ILLUSTRATES TRANSITIONS OF THE THREE TYPES MENTIONED FOR A DIATOMIC MOLECULE AS THE FIGURE SHOWS, ROTATIONAL INTERVALS TEND TO INCREASE AS THE ROTATIONAL QUANTUM NUMBER J INCREASES, WHEREAS VIBRATIONAL INTERVALS TEND TO DECREASE AS THE VIBRATIONAL QUANTUM NUMBER V INCREASES THE DASHED LINE BELOW EACH ELECTRONIC LEVEL INDICATES THE“ZERO-POINTENERGY” THAT MUST EXIST EVENAT ATEMPERATURE OFABSOLUTE ZERO AS A RESULT OF HEISENBERG’S UNCERTAINTY PRINCIPLE: E0 ¼ 2 HN Ð1:8Þ IT SHOULD BE EMPHASIZED THAT NOT ALL TRANSITIONS BETWEEN THESE LEVELS ARE POSSIBLE TO SEEWHETHER THE TRANSITION IS “ALLOWED” OR “FORBIDDEN,” THE RELEVANT SELECTION RULE MUST BE EXAMINED THIS, IN TURN, IS DETERMINED BY THE SYMMETRY OF THE MOLECULE AS EXPECTED FROM FIG 1 2, ELECTRONIC SPECTRA AREVERY COMPLICATED BECAUSE THEYARE ACCOMPANIED BY VIBRATIONAL AS WELL AS ROTATIONAL FINE STRUCTURE THE ROTATIONAL FINE STRUCTURE IN THE ELECTRONIC SPECTRUM CAN BE OBSERVED IF A MOLECULE IS SIMPLE AND THE SPECTRUM IS MEASURED IN THE GASEOUS STATE UNDER HIGH RESOLUTION THE VIBRATIONAL FINE STRUCTURE OF THE ELECTRONIC SPECTRUM IS EASIER TO OBSERVE THAN THE ROTATIONAL FINE STRUCTURE, AND CAN PROVIDE STRUCTURAL AND BONDING INFORMATION ABOUT MOLECULES IN ELECTRONIC EXCITED STATES VIBRATIONAL SPECTRA ARE ACCOMPANIED BY ROTATIONAL TRANSITIONS FIGURE 1 3 SHOWS THE ROTATIONAL FINE STRUCTURE OBSERVED FOR THE GASEOUS AMMONIA MOLECULE IN MOST POLYATOMIC MOLECULES, HOWEVER, SUCH A ROTATIONAL FINE STRUCTURE IS NOT OBSERVED FIG 1 1 REGIONS OF THE ELECTROMAGNETIC SPECTRUM AND ENERGY UNITS ORIGIN OF MOLECULAR SPECTRA FIG 1 3 ROTATIONAL ?NE STRUCTURE OF GASEOUS NH3 ELECTRONIC EXCITED STATE ZERO POINT ENERGY PURE ELECTRONIC TRANSITION PURE ROTATIONAL TRANSITION PURE VIBRATIONAL TRANSITION ELECTRONIC GROUND STATE ZERO POINT ENERGY J” = ?” = ?’ = FIG 1 2 ENERGY LEVEL OF A DIATOMIC MOLECULE (THE ACTUAL SPACINGS OF ELECTRONIC LEVELS ARE MUCH LARGER, AND THOSE OF ROTATIONAL LEVELS ARE MUCH SMALLER, THAN THAT SHOWN IN THE ?GURE)