Theoretical Study on Gas—phase Pyrolytic Reactions of N—Ethyl,Isopropyl and N—t—Butyl Substituted 2—Aminopyrazine

Density functional theory (DFT) and ab initio methods were used to study gas‐phase pyrolytic reaction mechanisms of iV‐ethyl, N‐isopropyl and N‐t‐butyl substituted 2‐aminopyrazine at B3LYP/6–31G* and MP2/6–31G*, respectively. Single‐point energies of all optimized molecular geometries were calculated at B3LYP/6–311 + G(2d,p) level. Results show that the pyrolytic reactions were carried out through a unimolecular first‐order mechanism which were caused by the migration of atom H(17) via a six‐member ring transition state. The activation energies which were verified by vibrational analysis and correlated with zero‐point energies along the reaction channel at B3LYP/6–311 + G(2d,p) level were 252.02 kJ. mo^?1 (N‐ethyl substituted), 235.92 kJ‐mol^?1 (N‐t‐isopropyl substituted) and 234.27 kJ‐mol^?1 (N‐t‐butyl substituted), respectively. The results were in good agreement with available experimental data.     

The MC‐DFT approach including the SCS‐MP2 energies to the new minnesota‐type functionals

We have applied the multicoefficient density functional theory (MC‐DFT) to four recent Minnesota functionals, including M06‐2X, M08‐HX, M11, and MN12‐SX on the performance of thermochemical kinetics. The results indicated that the accuracy can be improved significantly using more than one basis set. We further included the SCS‐MP2 energies into MC‐DFT, and the resulting mean unsigned errors (MUEs) decreased by approximately 0.3 kcal/mol for the most accurate basis set combinations. The M06‐2X functional with the simple [6–311+G(d,p)/6–311+G(2d,2p)] combination gave the best performance/cost ratios for the MC‐DFT and MC‐SCS‐MP2|MC‐DFT methods with MUE of 1.58 and 1.22 kcal/mol, respectively. © 2014 Wiley Periodicals, Inc.     

A quantum mechanical approach to the kinetics of the hydrogen abstraction reaction H2O2 + •OH → HO2 + H2O

The kinetics of the hydrogen abstraction from H₂O₂ by ^?OH has been modeled with MP2/6‐31G*//MP2/6‐31G*, MP2‐SAC//MP2/6‐31G*, MP2/6‐31+G**//MP2/6‐31+G**, MP2‐SAC// MP2/6‐31+G**, MP4(SDTQ)/6‐311G**//MP2/6‐31G*, CCSD(T)/6‐31G*//CCSD(T)/6‐31G*, CCSD(T)/6‐31G**//CCSD(T)/6‐31G**, CCSD(T)/6‐311++G**//MP2/6‐31G* in the gas phase. MD simulations have been used to generate initial geometries for the stationary points along the potential energy surface for hydrogen abstraction from H₂O₂. The effective fragment potential (EFP) has been used to optimize the relevant structures in solution. Furthermore, the IEFPCM model has been used for the supermolecules generated via MD calculations. IEFPCM/MP2/6‐31G* and IEFPCM/CCSD(T)/6‐31G* calculations have also been performed for structures without explicit water molecules. Experimentally, the rate constant for hydrogen abstraction by ^?OH drops from 1.75 × 10^?12 cm³ molecule^?1 s^?1 in the gas phase to 4.48 × 10^?14 cm³ molecule^?1 s^?1 in solution. The same trend has been reproduced best with MP4 (SDTQ)/6‐311G**//MP2/6‐31G* in the gas phase (0.415 × 10^?12 cm³ molecule^?1 s^?1) and with EFP (UHF/6‐31G*) in solution (3.23 × 10^?14 cm³ molecule^?1 s^?1). © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 502–514, 2005     

Rearrangements in Model Peptide‐Type Radicals via Intramolecular Hydrogen‐Atom Transfer

Intramolecular H‐atom transfer in model peptide‐type radicals was investigated with high‐level quantum‐chemistry calculations. Examination of 1,2‐, 1,3‐, 1,5‐, and 1,6[C ? N]‐H shifts, 1,4‐ and 1,7[C ? C]‐H shifts, and 1,4[N ? N]‐H shifts (Scheme 1), was carried out with a number of theoretical methods. In the first place, the performance of UB3‐LYP (with the 6‐31G(d), 6‐31G(2df,p), and 6‐311+G(d,p) basis sets) and UMP2 (with the 6‐31G(d) basis set) was assessed for the determination of radical geometries. We found that there is only a small basis‐set dependence for the UB3‐LYP structures, and geometries optimized with UB3‐LYP/6‐31G(d) are generally sufficient for use in conjunction with high‐level composite methods in the determination of improved H‐transfer thermochemistry. Methods assessed in this regard include the high‐level composite methods, G3(MP2)‐RAD, CBS‐QB3, and G3//B3‐LYP, as well as the density‐functional methods B3‐LYP, MPWB1K, and BMK in association with the 6‐31+G(d,p) and 6‐311++G(3df,3pd) basis sets. The high‐level methods give results that are close to one another, while the recently developed functionals MPWB1K and BMK provide cost‐effective alternatives. For the systems considered, the transformation of an N‐centered radical to a C‐centered radical is always exothermic (by 25 kJ ? mol^?1 or more), and this can lead to quite modest barrier heights of less than 60 kJ ? mol^?1 (specifically for 1,5[C ? N]‐H and 1,6[C ? N]‐H shifts). H‐Migration barriers appear to decrease as the ring size in the transition structure (TS) increases, with a lowering of the barrier being found, for example when moving from a rearrangement proceeding via a four‐membered‐ring TS (e.g., the 1,3[C ? N]‐H shift, CH₃? C(O)? NH^. → ^.CH₂? C(O)? NH₂) to a rearrangement proceeding via a six‐membered‐ring TS (e.g., the 1,5[C ? N]‐H shift, ^.NH? CH₂? C(O)? NH? CH₃ → NH₂? CH₂? C(O)? NH? CH₂^.).     

Comparison of large basis set DFT and MP2 calculations in the study of the barrier for internal rotation of 2,3,5,6‐tetrafluoroanisole

The barrier for internal rotation around the ? OCH₃ bond in 2,3,5,6‐tetrafluoroanisole was calculated using the density functional theory (DFT) and second‐order Møller–Plesset (MP2) methods with Pople's basis sets up to 6‐311++G(3df,2p) and Jensen basis sets up to pc‐3. The results are converged only if fairly large basis sets are used (at least 6‐311++G(3df,2pd) or pc‐2). Both the DFT and MP2 potential energy curves show internal structure. Two minima and three maxima are observed on the curves, arising from the interplay between lone‐pair delocalization and changes in the hybridization around the oxygen atom, together with the attraction between the positively polarized hydrogens in the methyl group and the negatively polarized fluorine atom at the ortho position. These critical points are somehow ironed out by the addition of zero‐point and thermal corrections to the energy curves. At this level, the MP2 method can describe reasonably well the previously determined single‐well experimental rotational barrier, 2.7 ± 2.0 kcal/mol at 298 K, while all DFT methods yield a much smaller result. As observed experimentally, the ? OCH₃ group is perpendicular to the aryl ring in the equilibrium structure, although two very close minima with an intermediate hump at 90° are still observable. The theoretical free energy barrier of rotation at the MP2(full)/pc‐2 level is 2.0 ± 1.0 kcal/mol, in reasonable agreement with the experimental determination. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Are calculated enthalpies of formation sometimes more reliable than experimental? A test on alkyl substituted benzoic acids

Energies of 20 alkyl-substituted benzoic acids were calculated at the levels B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) and MP2/6-311+G(d,p)//MP2/6-311+G(d,p); the pertinent enthalpies at 298 K were calculated at the same levels. Comparison with experimental enthalpies of formation Delta(f)H degrees (g)(298) was carried out in terms of isodesmic reactions, that is, in the relative values. Of the four calculated quantities, the DFT enthalpies yielded best correlation with the standard deviation of 2.1 kJ mol(-1), near to the experimental uncertainty; the DFT energies are only slightly worse and the MP2 enthalpies or energies much worse. However, the DFT method overestimated systematically the substituent effects and had to be calibrated. Comparison with the experimental gas-phase acidities was less telling and the fit was worse because both methods overestimated the substituent effects. Extending the base in selected examples did not give better results. Although the systematic deviations are evidently due to the imperfections of the theoretical models, individual big deviations should be attributed to experimental errors or to the abnormal behavior of certain compounds at the experimental conditions. From this point of view, three examples of the so-called long-range effect claimed in the case of different benzoic acid derivatives, always for substituents in the meta position, must be refused as unproven because the experimental energies were not confirmed by calculations.     

Complexation of Phenol and Thiophenol by Amine N‐Oxides: Isothermal Titration Calorimetry and ab Initio Calculations

To develop a new solvent‐impregnated resin (SIR) system for removal of phenols from water, the complex formation of dimethyldodecylamine N‐oxide (DMDAO), trioctylamine N‐oxide (TOAO), and tris(2‐ethylhexyl)amine N‐oxide (TEHAO) with phenol (PhOH) and thiophenol (PhSH) is studied. To this end we use isothermal titration calorimetry (ITC) and quantum chemical modeling (on B3LYP/6‐311G(d,p)‐optimized geometries: B3LYP/6‐311+G(d,p), B3LYP/6‐311++G(2d,2p), MP2/6‐311+G(d,p), and spin component scaled (SCS) MP2/6‐311+G(d,p); M06‐2X/6‐311+G(d,p)//M06‐2X/6‐311G(d,p), MP2 with an extrapolation to the complete basis set limit (MP2/CBS), as well as CBS‐Q). The complexes are analyzed in terms of structural (e.g., bond lengths) and electronic elements (e.g., charges). Furthermore, complexation and solvent effects (in benzene, toluene, and mesitylene) are investigated by ITC measurements, yielding binding constants K, enthalpies ΔH⁰, Gibbs fre energies ΔG⁰, and entropies ΔS⁰ of complex formation, and stoichiometry N. The ITC measurements revealed strong 1:1 complex formation between both DMDAO–PhOH and TOAO–PhOH. The binding constant (K=1.7–5.7×10⁴ M ^?1) drops markedly when water‐saturated toluene was used (K=5.8×10³ M ^?1), and π–π interaction with the solvent is shown to be relevant. Quantum mechanical modeling confirms formation of stable 1:1 complexes with linear hydrogen bonds that weaken on attachment of electron‐withdrawing groups to the amine N‐oxide moiety. Modeling also showed that complexes with PhSH are much weaker than those with PhOH, and in fact too weak for ITC determination. CBS‐Q incorrectly predicts equal or even higher binding enthalpies for PhSH than for PhOH, which invalidates it as a benchmark for other calculations. Data from the straightforward SCS‐MP2 method without counterpoise correction show very good agreement with the MP2/CBS values.     

Theoretical study of 1,2‐rearrangement in silylmethanethiol

The 1,2‐rearrangements in silylmethanethiol were studied by ab initio molecular orbital theory. The structures of reactants, transition states, and products were fully optimized at the MP2(full)/6‐31G(d) levels. Based on the MP2(full)/6‐31G(d) geometries, harmonic frequencies were obtained. Energies were computed at the G3 level of theory with MP2(full)/6‐31G(d) zero‐point corrections. The results indicate that the 1,2‐rearrangement in silylmethanethiol may occur via two pathways. Pathway A involves the 1,2‐migration of mercapto group from carbon to silicon via a double three‐membered ring transition state, forming methylsilanethiol. The barrier for reaction A is 275.0 kJ/mol. Pathway B involves the 1,2‐migration of silyl group from carbon to sulfur via a four‐membered ring transition state, forming methylthiosilane. The barrier for reaction B is 262.3 kJ/mol. Thermodynamic and kinetic properties of the reactions were analyzed over a temperature range of 300–1,300K. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The Rearrangement of 2,2‐Diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane to 3,4,4‐Triphenylcyclopent‐1‐ene: a DFT Analysis

A computational study on the rearrangement of 2,2‐diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane ( 1 ) is presented, using density functional theory (DFT), (U)B3LYP with the 6‐31G* basis set (DFT1) and (U)M05‐2X with the 6‐311+G** basis set (DFT2). In agreement with a biradical character of the transition structure (TS) or intermediate, the potential‐energy hypersurface is lowered by the influence of three conjugated Ph groups. Surprisingly, two conformations of the geminal diphenyl group (different twist angles) induce two different minimum‐energy pathways for the rearrangement. Independent of the functional used, the first hypersurface harbors true biradical intermediates, whereas the second energy surface is a flat, slightly ascending slope from the starting material to the TS. The functional (U)M05‐2X with the basis set 6‐311+G** provides realistic energies which seem to be close to experiment. The activation energy for racemization of enantiomers of 1 is lower than that of rearrangement by 2.5 kcal mol^?1, in agreement with experiment.     

4- (4,6-二甲基嘧啶-2-基)-3-硫代脲酸甲酯的合成晶体结构及量子化学研究

4-（4,6-Dimethylpyrimidin-2-yl）-3-thio-allophanic acid methyl ester was synthesized with mixing 2-amino-4,6- dimethylpyrimidine, potassium thiocyanate and methyl chloroformate in ethyl acetate. Single crystals suitable for X-ray diffraction measurement were obtained by recrystallization from dimethylformamide at room temperature. The crystal belongs to monoclinic symmetry with space group C2/m, and crystal parameters of a= 1.7537（5） nm, b= 0.6759（2） nm, c=1.1148（3） nm, β=118.557（4）°, V=1.1605（6） nm^3, Z=4, De= 1.375 g/cm^3,μ=0.271 mm^-1, F（000）=504, and 1519 [1〉2σ（I）] observable independent reflections were used for the determination and refmement of the crystal structures with final R1 of 0.0372 and wR2 of 0.0992. The theoretical investigation of the title compound was carried out with DRT-B3LYP/6-311G, HF/6-311G and MP2/6-311G methods, and the atomic net charges and the population were discussed.     

Ligand‐Exchange Processes on Solvated Beryllium Cations. Part III

On the basis of DFT calculations (B3LYP/6‐311+G**), the possibility to include solvent effects is considered in the investigation of the H₂O‐exchange mechanism on [Be(H₂O)₄]²⁺ within the widely used cluster approach. The smallest system in the gas phase, [Be(H₂O)₄(H₂O)]²⁺, shows the highest activation barrier of +15.6 kcal/mol, whereas the explicit addition of five H‐bonded H₂O molecules in [{Be(H₂O)₄(H₂O)}(H₂O)₅]²⁺ reduces the barrier to +13.5 kcal/mol. Single‐point calculations applying CPCM (B3LYP(CPCM:H₂O)/6‐311+G**//B3LYP/6‐311+G**) on [Be(H₂O)₄(H₂O)]²⁺ lower the barrier to +9.6 kcal/mol. Optimization of the precursor and transition state of [Be(H₂O)₄(H₂O)]²⁺ within an implicit model (B3LYP(CPCM:H₂O)/6‐311+G** or B3LYP(PCM:H₂O)/6‐311+G**) reduces the activation energy further to +8.3 kcal/mol but does not lead to any local minimum for the precursor and is, therefore, unfavorable.     

Deactivation reactions in the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated free‐radical polymerization of styrene: A comparative study with the 2,2,6,6‐tetramethyl‐1‐piperidinyloxy/acrylonitrile system

The competitiveness of the combination and disproportionation reactions between a 1‐phenylpropyl radical, standing for a growing polystyryl macroradical, and a 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO) radical in the nitroxide‐mediated free‐radical polymerization of styrene was quantitatively evaluated by the study of the transition geometry and the potential energy profiles for the competing reactions with the use of quantum‐mechanical calculations at the density functional theory (DFT) UB3‐LYP/6‐311+G(3df, 2p)//(unrestricted) Austin Model 1 level of theory. The search for transition geometries resulted in six and two transition structures for the radical combination and disproportionation reactions, respectively. The former transition structures, mainly differing in the out‐of‐plane angle of the N? O bond in the transition structure TEMPO molecule, were correlated with the activation energy, which was determined to be in the range of 8.4–19.4 kcal mol^?1 from a single‐point calculation at the DFT UB3‐LYP/6‐311+G(3df, 2p)//unrestricted Austin Model 1 level. The calculated activation energy for the disproportionation reaction was less favorable by a value of more than 30 kcal mol^?1 in comparison with that for the combination reaction. The approximate barrier difference for the TEMPO addition and disproportionation reaction was slightly smaller for the styrene polymerization system than for the acrylonitrile polymerization system, thus indicating that a β‐proton abstraction through a TEMPO radical from the polymer backbone could diminish control over the radical polymerization of styrene with the nitroxide even more than in the latter system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 232–241, 2007     

复合物HNO···H2O2内N-H···O蓝移氢键的理论研究

A theoretical study on the blue-shifted H-bond N-H…O and red-shifted H-bond O-H…O in the complexHNO…H_2O_2 was conducted by employment of both standard and counterpoise-corrected methods to calculate thegeometric structures and vibrational frequencies at the MP2/6-31G(d),MP2/6-31 G(d,p),MP2/6-311 q G(d,p),B3LYP/6-31G(d),B3LYP/6-31 G(d,p) and B3LYP/6-311 G(d,p) levels.In the H-bond N-H…O,the calcu-lated blue shift of N-H stretching frequency is in the vicinity of 120 cm~(-1) and this is indeed the largest theoreticalestimate of a blue shift in the X-H…Y H-bond ever reported in the literature.From the natural bond orbital analy-sis,the red-shifted H-bond O-H…O can be explained on the basis of the dominant role of the hyperconjugation.For the blue-shifted H-bond N-H…O,the hyperconjugation was inhibited due to the existence of significant elec-tron density redistribution effect,and the large blue shift of the N-H stretching frequency was prominently due tothe rehybridization of sp~n N-H hybrid orbital.     

Transition states for deactivation reactions in the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated free‐radical polymerization of acrylonitrile

The geometries and energetics of transition states (TS) for radical deactivation reactions, including competitive combination and disproportionation reactions, have been studied for the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO)‐mediated free‐radical polymerization of acrylonitrile with quantum mechanical calculations at the DFT/UB3‐LYP/6‐311+G(3df,2p)//(U)AM1 level of theory (where DFT is density functional theory, AM1 is Austin model 1, and UAM1 is unrestricted Austin model 1). A method providing reasonable starting geometries for an effective search for TS between the TEMPO radical and 1‐cyanopropyl radical mimicking the growing polyacrylonitrile macroradical is shown. For the hydrogen atom abstraction reaction by the TEMPO radical from the 1‐cyanopropyl radical, practically one TS has been found, whereas for the combination reaction of the radicals, several TS have been found, mainly differing in out‐of‐plane angle α of the N? O bond in the TEMPO structure. α in the TS is correlated with the activation energy, ΔE, determined from the single‐point calculation at the DFT UB3‐LYP/6‐311+G(3df, 2p)//UAM1 level for the combination reaction of CH₃AN· with the TEMPO radical. The theoretical activation energy for the coupling reaction from DFT UB3‐LYP/6‐311+G(3df, 2p)//UAM1 calculations has been estimated to be 11.6 kcal mol^?1, that is, only about 4.5 times smaller than ΔE for the disproportionation reaction obtained with the DFT UB3‐LYP/6‐311+G(3df, 2p)//(U)AM1 approach. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 914–927, 2006     

Kinetic parameters for the reaction of hydroxyl radical with CH3OCH2F (HFE‐161) in the temperature range of 200–400 K: Transition state theory and Ab initio calculations

Rate coefficients for the reaction of the hydroxyl radical with CH₃OCH₂F (HFE‐161) were computed using transition state theory coupled with ab initio methods, viz., MP2, G3MP2, and G3B3 theories in the temperature range of 200–400 K. Structures of the reactants and transition states (TSs) were optimized at MP2(FULL) and B3LYP level of theories with 6‐31G* and 6‐311++G** basis sets. The potential energy surface was scanned at both the level of theories. Five different TSs were identified for each rotamer. Calculations of Intrinsic reaction coordinates were performed to confirm the existence of all the TSs. The kinetic parameters due to all different TSs are reported in this article. The rate coefficients for the title reaction were computed to be k = (9 ± 1.08) × 10^?13 exp [?(1,713 ± 33)/T] cm³ molecule^?1 s^?1 at MP2, k = (7.36 ± 0.42) × 10^?13 exp [?(198 ± 16)/T] cm³ molecule^?1 s^?1 at G3MP2 and k = (5.36 ± 1.57) × 10^?13 exp [?(412 ± 81)/T] cm³ molecule^?1 s^?1 at G3B3 theories. The atmospheric lifetimes of CH₃OCH₂F at MP2, G3MP2, and G3B3 level of theories were estimated to be 20, 0.1, and 0.3 years, respectively. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Conformations and rotational barriers of 2,2′‐bithiazole and 4,4′‐dimethyl‐2,2′‐bithiazole semiemperical,ab initio,and density functional theory calculations

Conformational properties of 2,2′‐bithiazole and 4,4′‐dimethyl‐2,2′‐ bithiazole have been studied by using AM1 and PM3 semiemperical methods and ab initio HF/6‐311+G* and B3LYP/6‐311+G* calculations. All methods agree that the planar s‐trans conformation is the global minimum and the perpendicular conformation is the transition state. Additional local minima were found using the Hartree–Fock (HF) and B3LYP levels for 2,2′‐bithiazole while for 4,4′‐dimethyl derivative the minima was located only at the MP2//B3LYP level. The barrier heights for rotation are 1.72, 7.69, and 7.88 kcal/mol at the PM3, HF, and B3LYP levels, respectively, and methyl substitution did not affect appreciably this value. Fourier expansion terms and bond orders were used to explain the origins of the rotational barrier in terms of π conjugation, electrostatic interaction, and steric effects, which represent the main factors in the shape of the rotational barrier. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 367–377, 2000     

Infrared spectrum of potassium‐cationized triethylphosphate generated using tandem mass spectrometry and infrared multiple photon dissociation

Tandem mass spectrometry and wavelength‐selective infrared photodissociation were used to generate an infrared spectrum of gas‐phase triethylphosphate cationized by attachment of K⁺. Prominent absorptions were observed in the region of 900 to 1300 cm^?1 that are characteristic of phosphate P?O and P? O? R stretches. The relative positions and intensities of the IR absorptions were reproduced well by density functional theory (DFT) calculations performed using the B3LYP functional and the 6‐31+G(d), 6‐311+G(d,p) and 6‐311++G(3df,2pd) basis sets. Because of good correspondence between experiment and theory for the cation, DFT was then used to generate a theoretical spectrum for neutral triethylphosphate, which in turn accurately reproduces the IR spectrum of the neat liquid when solvent effects are included in the calculations. Copyright © 2009 John Wiley & Sons, Ltd.     

Mechanism for the gas‐phase reaction between OH and 3‐methylfuran: A theoretical study

The mechanism for the OH + 3‐methylfuran reaction has been studied via ab initio calculations to investigate various reaction pathways on the doublet potential energy surface. Optimizations of the reactants, products, intermediates, and transition structures are conducted using the MP2 level of theory with the 6‐311G(d,p) basis set. The single‐point electronic energy of each optimized geometry is refined with G3MP2 and G3MP2B3 calculations. The theoretical study suggests that the OH + 3‐methylfuran reaction is dominated by the formation of HC(O)CH?C(CH₃)CHOH (P7) and CH(OH)CH?C(CH₃)C(O)H (P9), formed from two low‐lying adducts, IM1 and IM2. The direct hydrogen abstraction pathways and the S_N2 reaction may play a minor or negligible role in the overall reaction of OH with 3‐methylfuran. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Investigation of (1R,2S)‐(−)‐Ephedrine by Cryogenic Terahertz Spectroscopy and Solid‐State Density Functional Theory

The terahertz (THz) spectrum of the pharmaceutical (1R,2S)‐(?)‐ephedrine from 8.0 to 100.0 cm^?1 is investigated at liquid‐nitrogen (78.4 K) temperature. The spectrum exhibits several distinct features in this range that are characteristic of the crystal form of the compound. A complete structural analysis and vibrational assignment of the experimental spectrum is performed using solid‐state density functional theory (DFT) and cryogenic single‐crystal X‐ray diffraction. Theoretical modeling of the compound includes an array of density functionals and basis sets with the final assignment of the THz spectrum performed at a PW91/6‐311G(d,p) level of theory, which provides excellent solid‐state simulation agreement with experiment. The solid‐state analysis indicates that the seven experimental spectral features observed at low temperature consist of 13 IR‐active vibrational modes. Of these modes, nine are external crystal vibrations and provide approximately 57 % of the predicted spectral intensity. This study demonstrates that the THz spectra of complex pharmaceuticals may be well reproduced by solid‐state DFT calculations and that inclusion of the crystalline environment is necessary for realistic and accurate simulations.