Ab Initio Quantum Mechanical Calculations Research Articles

Self-association behavior of a novel nonproteinogenic β-strand-mimic in an organic solvent.

The self-association behavior of a newly characterized β-strand-mimic, presented by an achiral nonproteinogenic model system Boc-γ-Abz-NHMe (1: Boc = tert-butyloxycarbonyl; γ-Abz = γ-aminobenzoic acid; NHMe = N-methylamide), have been investigated using (1)H NMR and FT-IR absorption spectroscopy, in combination with computational ab initio calculations. The concentration dependence of (1)H NMR chemical shifts of the amide-NHs in CDCl3 exhibited noncooperative behavior of self-association, whereas the variable temperature (1)H NMR chemical shifts data of the amide-NHs, i.e., temperature-coefficient (Δδ/ΔT) values, could be accounted for by significant enhancement of self-association, i.e., aggregates higher than dimers. In the absence of N-H···O intramolecular H-bond in 1, the intense FT-IR absorption bands in informative amide-A region, i.e., N-H stretches at ∼3465 and 3438 cm(-1) in chloroform solution, could be interpreted in terms of intermolecular H-bonding. The ab initio quantum mechanical calculations performed on two discrete isolated antiparallel H-bonded duplexes with a face-to-face and an edge-to-edge aromatic-aromatic interaction provided strong support for their relative importance to stabilize favorable dimeric structures. The thermodynamic parameters deduced from van't Hoff plots, constructed from variable temperature (1)H NMR data of the amide-NHs in CDCl3, also substantiated the effectiveness of aromatic-aromatic interactions for dimer formation and higher-order self-association. In view of the enormous structural importance of β-strand-like building blocks in peptide design, we highlight intrinsic self-associating potentials of the readily available γ-Abz moiety, besides the fact that such planar secondary structural mimics are presumed to offer greater prospective for constructing peptidomimetics and therapeutically relevant small molecules.

Electronic structure, dielectric response, and surface charge distribution of RGD (1FUV) peptide.

Long and short range molecular interactions govern molecular recognition and self-assembly of biological macromolecules. Microscopic parameters in the theories of these molecular interactions are either phenomenological or need to be calculated within a microscopic theory. We report a unified methodology for the ab initio quantum mechanical (QM) calculation that yields all the microscopic parameters, namely the partial charges as well as the frequency-dependent dielectric response function, that can then be taken as input for macroscopic theories of electrostatic, polar, and van der Waals-London dispersion intermolecular forces. We apply this methodology to obtain the electronic structure of the cyclic tripeptide RGD-4C (1FUV). This ab initio unified methodology yields the relevant parameters entering the long range interactions of biological macromolecules, providing accurate data for the partial charge distribution and the frequency-dependent dielectric response function of this peptide. These microscopic parameters determine the range and strength of the intricate intermolecular interactions between potential docking sites of the RGD-4C ligand and its integrin receptor.

Low Symmetry Polymorph of Hydroxyapatite. Theoretical Equilibrium Morphology of the Monoclinic Ca5(OH)(PO4)3

The Hartman–Perdok analysis has been carried out on the monoclinic P21/c polymorph of Hydroxyapatite (HAp) in order to find the character of the main {hkl} forms and foresee the possible profiles of the related surfaces. Then, the corresponding specific surface energies have been calculated, at 0 K, by ab initio quantum-mechanical calculations, and the HAp equilibrium shape has been obtained: a striking pseudohexagonal prism comes out from the close similarity of the surface energy of the three pinacoids {001}, {100}, and {102}, all developing around the [010] zone axis which runs parallel to the OH channels of the structure bulk. The most stable form, the pinacoid {010}, truncates the pseudohexagonal prism perpendicularly to the OH channels, while the less morphologically important monoclinic prisms {012}, {110}, and {112} complete the HAp equilibrium shape. Preliminary considerations are exposed about the morphological path: monoclinic polymorph → twinning → hexagonal polymorph. Finally, a simple kine...

Diffusion in mercury-argon gas mixtures

Ab initio quantum-mechanical calculations of potential of interactions U(R) are performed for Hg-Ar. Using equations from the molecular kinetic theory of rarefied gases, a new statistical correlation is found between data on the potential of interaction (molecular beams, molecular spectroscopy, and potential U(R)) and experimental data on the mutual diffusion coefficient (MDC) of mercury-argon gas mixtures. Calculated reference data on the MDC of mercury-argon gas mixtures in the temperature range of 300 to 600 K are offered as a possible standard for calibrating instruments that measure MDCs of liquid vapors and inert gases using the Stefan method.

Optical and Electrical Properties of Organic Conducting Polymers

Novel electrically conducting polymeric materials are prepared in this work. Polythiophene (PT) and poly (3-Methelthiophene) (P3MT) films were prepared by electro-polymerization method using cyclic voltammetry in acetonitrile as a solvent and lithium tetrafluoroborate as the electrolyte on a gold electrode. Electrical properties of P3MT have been examined in different environments using UV-Vis absorption spectroscopy and quantum mechanical ab initio calculations, The observed absorption peaks at 314 and 415 nm, were attributed to the n-π* and π-π* transitions, respectively in the conjugated polymer chain, in contrast, the observed absorbance peak at 649 nm, is responsible for electric conduction. The temperature dependence of the conductivity can be fitted to the Arrhenius and the VTF equations in different temperature ranges.

Highly accurate transport properties of helium-4, helium-3, and their binary mixtures by ab initio potential

A helium–helium interatomic potential determined from quantum–mechanical ab initio calculations by Przybytek et al. has been used in the framework of the classical kinetic theory to calculate the transport properties of helium. The viscosity, thermal conductivity, diffusion coefficient, and thermal diffusion factor were calculated for helium-4, helium-3, and their binary mixtures at low density between 100 and 10,000K. The predicted results of this work are listed in the Appendix, which are more accurate than the corresponding measured quantities over a wide temperature range.

Ab initio study on transition states of formohydroxamic acid tautomerization in the presence of water molecules

Keto-iminol transformation of formohydroxamic acid in the presence of water molecules is investigated using ab initio quantum mechanics calculations. Calculations revealed that the proton transfer energy barriers are significantly lowered in the presence of water molecules. The proton transfer in Z-keto form occurs via a pathway involving two transition states and a charge separated intermediate. The proton transfer in E-keto tautomer occurs via a single transition state. A third pathway, which is not feasible in the absence of water, becomes feasible when there are hydrogen bonded water molecules. The stability order of formohydroxamic acid tautomers was found to be E-keto>Z-keto>Z-iminol>E-iminol and remains the same even after hydrogen bonded to water.

Mode-specific vibrational relaxation of photoexcited guanosine 5′-monophosphate and its acid form: a femtosecond broadband mid-IR transient absorption and theoretical study

UV-pump/broadband-mid-IR-probe transient absorption (TA) experiments and ab initio quantum mechanical (QM) calculations were used to investigate the photophysics in heavy water of the neutral and acid forms of guanosine 5'-monophosphate (GMP and GMPD(+), respectively). Excited GMP undergoes ultrafast internal conversion (IC) and returns to the electronic ground state in less than one picosecond with a large amount of excess vibrational energy. The spectroscopic signals are dominated by vibrational cooling - a process in which the solute dissipates vibrational energy to the solvent. For neutral GMP, cooling proceeds with a time constant of 3 ps. Following IC, at least some medium-frequency modes such as the carbonyl stretch and an in-plane ring vibration are excited, suggesting that the vibrational energy distribution is non-statistical. This is consistent with predicted structural changes upon passage through the S1/S0 conical intersection. GMPD(+) differs from GMP by a single deuteron at the N7 position, but has a dramatically longer lifetime of 200 ps. Vibrational cooling of the S1 state of GMPD(+) was monitored via several medium-frequency modes that were assigned using QM calculations. These medium-frequency modes are also vibrationally excited in a non-statistical fashion. Excitation of these modes is in line with the change in geometry at the S1 minimum of GMPD(+) predicted by QM calculations. Furthermore, these modes relax at different rates, fully consistent with QM calculations, which predict that excited vibrational states of the carbonyl stretch couple strongly to the D2O solvent and thus deactivate via intermolecular energy transfer (IET). In contrast, the ring stretch couples strongly to other ring modes of the guanine chromophore and appears to decay via intramolecular vibrational energy redistribution (IVR).

Carbon Dioxide Hydrate Phase Equilibrium and Cage Occupancy Calculations Using Ab Initio Intermolecular Potentials

Gas hydrate deposits are receiving increased attention as potential locations for CO2 sequestration, with CO2 replacing the methane that is recovered as an energy source. In this scenario, it is very important to correctly characterize the cage occupancies of CO2 to correctly assess the sequestration potential as well as the methane recoverability. In order to predict accurate cage occupancies, the guest–host interaction potential must be represented properly. Earlier, these potential parameters were obtained by fitting to experimental equilibrium data and these fitted parameters do not match with those obtained by second virial coefficient or gas viscosity data. Ab initio quantum mechanical calculations provide an independent means to directly obtain accurate intermolecular potentials. A potential energy surface (PES) between H2O and CO2 was computed at the MP2/aug-cc-pVTZ level and corrected for basis set superposition error (BSSE), an error caused due to the lower basis set, by using the half counterpoise method. Intermolecular potentials were obtained by fitting Exponential-6 and Lennard-Jones 6-12 models to the ab initio PES, correcting for many-body interactions. We denoted this model as the “VAS” model. Reference parameters for structure I carbon dioxide hydrate were calculated using the VAS model (site–site ab initio intermolecular potentials) as Δμ(w)(0) = 1206 ± 2 J/mol and ΔH(w)(0) = 1260 ± 12 J/mol. With these reference parameters and the VAS model, pure CO2 hydrate equilibrium pressure was predicted with an average absolute deviation of less than 3.2% from the experimental data. Predictions of the small cage occupancy ranged from 32 to 51%, and the large cage is more than 98% occupied. The intermolecular potentials were also tested by calculating the pure CO2 density and diffusion of CO2 in water using molecular dynamics simulations.

Hydrogen storage on silicon, carbon, and silicon carbide nanotubes: A combined quantum mechanics and grand canonical Monte Carlo simulation study

Grand canonical Monte Carlo (GCMC) simulation combined with ab initio quantum mechanics calculations were employed to study hydrogen storage in homogeneous armchair open-ended single walled silicon nanotubes (SWSiNTs), single walled carbon nanotubes (SWCNTs), and single walled silicon carbide nanotubes (SWSiCNTs) in triangular arrays. Two different groups of nanotubes were studied: the first were (12,12) SiNTs, (19,19) CNTs, and (15,15) SiCNTs and the second were (7,7) SiNTs, (11,11) CNTs, and (9,9) SiCNTs with the diameters of ∼26 and ∼15 Å for the first and second groups, respectively. The simulations were carried out for different thermodynamic states. The potential energy functions (PEFs) were calculated using ab initio quantum mechanics and then fitted with (12,6) Lennard-Jones (LJ) potential model as a bridge between first principles calculations and GCMC simulations. The absolute, excess, and delivery adsorption isotherms of hydrogen were calculated for two groups of nanotubes. The isosteric heat of adsorption and the radial distribution functions (RDFs) for the adsorbed molecules on different nanotubes were also computed. Different isotherms were fitted with the simulation adsorption data and the model parameters were correlated. According to the results, the hydrogen uptake values in (19,19) CNT array exceeded the US DOE (Department of Energy) target of 6.0 wt% (FY 2010) at 77 K and 1.0 and 2.0 MPa for absolute and excess uptakes, respectively. The results also show that SiNTs and SiCNTs are not more useful materials compared with corresponding CNTs for hydrogen storage.

Syngonanthus nitens: Why it looks like spun gold

We report on the optical properties of Syngonanthus nitens, the golden grass, which is used to produce golden handicraft articles. The dry stems of the plant were analyzed with scanning electron microscopy, X-ray photoelectron spectroscopy, fluorescence microscopy; angle resolved optical reflectance and absorption/emission spectroscopy. The extract of the stems composed by 8 glucopyranosylflavones was also optically characterized. Electronic and geometric properties of the flavonoids were studied using ab initio and semi-empirical quantum mechanical calculations. The experimental and theoretical results explain the characteristic golden color of S. nitens dried stems.

Infrared spectroscopic properties of goethite: anharmonic broadening, long-range electrostatic effects and Al substitution

The infrared spectrum and its temperature dependence (20–320 K) were collected on a synthetic goethite sample (α-FeOOH). In addition, the infrared powder absorption spectrum of goethite and aluminum-substituted goethite was computed using ab initio quantum mechanical calculations based on density functional theory. This combined experimental and theoretical approach allows (1) the unequivocal assignment of absorption bands to the corresponding vibrational modes, (2) separate identification of the effects of the particle shape and of the aluminum substitution on the infrared spectrum, and (3) a discussion of the anharmonic properties and the origin of the line broadening in goethite. In particular, the two well-resolved OH bending absorption bands show different temperature evolution. Their detailed analysis suggests that the broadening of the band at ~800 cm−1 cannot be described solely by a usual three-phonon process. The strong anharmonic behavior of this mode implies the addition of a four-phonon process, such as a pure dephasing process. In our calculations, the effect of the Hubbard U correction is also investigated and found to be most visible on the OH stretching and bending modes, in relation to the associated structural relaxation. The OH stretching frequencies decrease, leading to a better agreement with experimental frequencies, while the OH bending frequencies increase.

Molecular origins of nonlinear optical activity in zinc tris(thiourea)sulfate revealed by high-resolution x-ray diffraction data andab initiocalculations

Structure-property relationships are established in the nonlinear optical (NLO) material, zinc tris(thiourea)sulfate (ZTS), via an experimental charge-density study, x-ray constrained wave-function refinement, and quantum-mechanical calculations. The molecular charge-transfer characteristics of ZTS, that are important for NLO activity, are topologically analyzed via a multipolar refinement of high-resolution x-ray diffraction data, which is supported by neutron diffraction measurements. The extent to which each chemical bond is ionic or covalent in nature is categorized by Laplacian-based bonding classifiers of the electron density; these include bond ellipticities, energy densities, and the local source function. Correspondingly, the NLO origins of ZTS are judged to best resemble those of organic NLO materials. The molecular dipole moment, ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, and (hyper)polarizability coefficients, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$ and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$, are calculated from the experimental diffraction data using the x-ray constrained wave-function method. Complementary gas-phase ab initio quantum-mechanical calculations of ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ offer a supporting comparison. When taken alone, the experimental charge-density analysis does not fare well in deriving ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, or ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$, which is not entirely surprising given that the associated calculations are only generally valid for organic molecules. However, by refining the x-ray data within the constrained wave-function method, the evaluations of ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$, ${\mathbit{\ensuremath{\alpha}}}_{\mathbf{ij}}$, and ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ are shown to agree very well with those from ab initio calculations and show remarkable normalization to experimental refractive index measurements. The small differences observed between ab initio and x-ray constrained wave-function refinement results can be related directly to gas- versus solid-state phase differences. ${\mathbit{\ensuremath{\mu}}}_{\mathbf{i}}$ is found to be 28.3 Debye (gas phase) and 29.7 Debye (solid state) while ${\mathbit{\ensuremath{\beta}}}_{\mathbf{ijk}}$ coefficients are not only significant but are also markedly three dimensional in form. Accordingly, substantial octupolar as well as dipolar NLO contributions in ZTS are indicated, which challenges the traditional focus on dipolar NLO molecules. This evaluation of NLO properties and their relation to the molecular structure offers several ways by which ZTS may be more widely functionalized as a NLO material. More generally, this case study on ZTS demonstrates how experimental and computational techniques can be combined to understand NLO structure-property relationships, an important tool for the quantum-tailored molecular design of next-generation metalorganic NLO materials.

Raman Spectrum of Pyrope Garnet. A Quantum Mechanical Simulation of Frequencies, Intensities, and Isotope Shifts

The Raman spectrum of pyrope garnet is simulated in ab initio quantum mechanical calculations, using an all-electron Gaussian-type basis set and the hybrid B3LYP functional. Frequencies calculated for the 25 Raman-active modes are in excellent agreement with the several sets of experimental data, with the mean absolute difference ranging from 4 to 8 cm(-1). Comparison of the computed and experimental spectrum shows excellent agreement for most of the intensities as well. Modes missing from experiment are shown to be characterized by low (computed) intensity. Spurious peaks in the experimental spectra are also identified. The isotopic effect has been simulated for (24)Mg → (26)Mg substitution and shows excellent agreement with shifts reported in one of the experiments. Agreement is excellent for all but one mode, which turns out to be attributed to the wrong symmetry in the experiment.

Effect of alloying elements on the properties of Zr and the Zr–H system

The effect of the alloying elements Sn, Fe, Cr, Ni, Nb, and O on hydrogen-containing alpha-zirconium and zirconium hydrides is investigated using ab initio quantum mechanical calculations and classical simulations. Cr, Fe, and Ni atoms attract interstitially dissolved H atoms whereas interstitial oxygen atoms show no pronounced interaction with H atoms. The alloying elements destabilize the hydride phases in the order Sn>Fe>Cr>Ni>Nb. Hence, substitutional Sn (if atomically dispersed), Cr and Fe atoms are likely to delay hydride precipitation, effectively increasing the hydrogen solubility. Nb and Sn influence the mobility of Zr self-interstitial atoms (SIA’s), which diffuse rapidly and preferentially parallel to the basal planes forming interstitial dislocations loops perpendicular to the basal planes (a-loops). Nb suppresses this diffusion of SIA’s, thereby reducing the rate of formation of interstitial a-loops. Sn atoms, if present on substitutional sites, have a similar, but smaller effect. If SIA’s approach substitutional Fe, Cr, and Ni atoms, the simulations indicate a spontaneous swap promoting the smaller transition metal atoms into interstitial atoms, which diffuse very rapidly with a preference in the c-direction, thereby facilitating their segregation to energetically more favorable sites such as vacancies, vacancy c-loops, grain boundaries, surfaces, and intermetallic precipitates.

Spectroscopic (FT-IR, FT-Raman and NMR) and computational studies on 3-methoxyaniline

In this work, the molecular structure, vibrational, UV and NMR spectra of 3-methoxyaniline (abbreviated as 3MOA, C7H9NO) were studied. The FT-IR and FT-Raman spectra were recorded. The ground-state molecular geometry and vibrational frequencies were calculated by using the Hartree–Fock (HF) and density functional theory (DFT)/B3LYP methods and 6-311++G(d,p) as a basis set. The fundamental vibrations were assigned on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanics (SQM) method and PQS program. Comparison of the observed fundamental vibrational frequencies of 3MOA with calculated results by HF and DFT methods indicates that B3LYP is superior to HF method for molecular vibrational problems. The difference between the observed and scaled wavenumber values is very small. The theoretically predicted FT-IR and FT-Raman spectra of the title molecule have been constructed. A study on the Mulliken atomic charges, the electronic properties were performed by time-dependent DFT (TD-DFT) approach, Frontier molecular orbitals (FMO), molecular electrostatic potential (MEP) and thermodynamic properties were performed and compared with methoxybenzene and aniline. The electric dipole moment (μ) and the first hyperpolarizability (β) values of the investigated molecule were computed using ab initio quantum mechanical calculations. The calculated results also show that the 3MOA molecule might have microscopic nonlinear optical (NLO) behavior with non-zero values. The 13C nuclear magnetic resonance (NMR) chemical shifts of the molecule were calculated by the gauge independent atomic orbital (GIAO) method and compared with experimental results.

Ab initio quantum mechanical calculation of the reaction probability for the [formula omitted] reaction

The SN2 substitution reactions at phosphorus play a key role in organic and biological processes. Quantum molecular dynamics simulations have been performed to study the prototype reaction Cl-+PH2Cl→ClPH2+Cl-, using one and two-dimensional models. A potential energy surface, showing an energy well for a transition complex, was generated using ab initio electronic structure calculations. The one-dimensional model is essentially reflection free, whereas the more realistic two-dimensional model displays involved resonance structures in the reaction probability. The reaction rate is almost two orders of magnitude smaller for the two-dimensional compared to the one-dimensional model. Energetic errors in the potential energy surface is estimated to affect the rate by only a factor of two. This shows that for these types of reactions it is more important to increase the dimensionality of the modeling than to increase the accuracy of the electronic structure calculation.

Automated Force Field Parameterization for Nonpolarizable and Polarizable Atomic Models Based on Ab Initio Target Data

Classical molecular dynamics (MD) simulations based on atomistic models are increasingly used to study a wide range of biological systems. A prerequisite for meaningful results from such simulations is an accurate molecular mechanical force field. Most biomolecular simulations are currently based on the widely used AMBER and CHARMM force fields, which were parameterized and optimized to cover a small set of basic compounds corresponding to the natural amino acids and nucleic acid bases. Atomic models of additional compounds are commonly generated by analogy to the parameter set of a given force field. While this procedure yields models that are internally consistent, the accuracy of the resulting models can be limited. In this work, we propose a method, General Automated Atomic Model Parameterization (GAAMP), for generating automatically the parameters of atomic models of small molecules using the results from ab initio quantum mechanical (QM) calculations as target data. Force fields that were previously developed for a wide range of model compounds serve as initial guess, although any of the final parameter can be optimized. The electrostatic parameters (partial charges, polarizabilities and shielding) are optimized on the basis of QM electrostatic potential (ESP) and, if applicable, the interaction energies between the compound and water molecules. The soft dihedrals are automatically identified and parameterized by targeting QM dihedral scans as well as the energies of stable conformers. To validate the approach, the solvation free energy is calculated for more than 200 small molecules and MD simulations of 3 different proteins are carried out.

Experimental spectroscopic (FTIR, FT-Raman, FT-NMR, UV–Visible) and DFT studies of 1-ethyl-1,4-dihydro-7-methyl-4oxo-1,8 napthyridine-3-carboxylic acids

The solid phase FTIR and FT-Raman spectra of 1-ethyl-1,4-dihydro-7-methyl-4oxo-1,8 napthyridine-3-carboxylic acid (EDMONCA) have been recorded in the regions 4000–500 and 4000–400cm−1 respectively. The equilibrium geometry, harmonic vibrational frequencies have been investigated by DFT/B3LYP and B3PW91 methods with 6-311G (d,p) basis set. The different between the observed and scaled wave number values of most of the fundamental is very small. The assignments of the vibrational spectra have been carried out with the aid of normal coordinate analysis (NCA) following the scaled quantum mechanical force field methodology (SQMFFM). Stability of the molecule arising from hyper conjugative interactions, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. UV–Visible spectrum of the compound was recorded and the electronic properties HOMO and LOMO energies were measured. The electric dipole moment (μD) and first hyperpolarizability (βtot) values of the investigated molecule were computed using ab initio quantum mechanical calculations. The calculated results also show that the EDMONCA molecule may have microscopic nonlinear optics (NLO) behavior with non-zero values. 1H and 13C NMR spectra were recorded and 1H and 13C nuclear magnetic resonance chemical shift of the molecule were calculated using the gauge independent atomic orbital (GIAO) method. Thermal stability of EDMONCA was studied by thermogravimetric analysis (TGA). Next Fukui function was calculated to explain the chemical selectivity or reactivity site in EDMONCA. Finally molecular electrostatic potential (MEP) and other molecular properties were performed.

Ab initio simulation on the crystal structure and elastic properties of carbonated apatite

Ab initio quantum mechanical (QM) calculations were employed to study the crystal structure and elastic properties of carbonated apatite (CAp). Two locations for the carbonate ion in the apatite lattice were considered: carbonate substituting for OH− ion (type-A), and for PO43− ion (type-B) with possible charge compensation mechanisms. A combined type-AB substitution (two carbonate ions replacing one phosphate group and one hydroxyl group, respectively) was also investigated. The results show that the most energetically stable substitution is type-AB, followed by type-A and then type-B. The most stable configuration of type-A has its carbonate triangular plane almost parallel to c-axis at z=0.46. The lowest energy configuration of type-B is that with a sodium ion substituting for a calcium ion for charge balance and the carbonate lying on the b/c-plane of apatite. Lattice parameter changes after carbonate substitution in hydroxyapatite (HA) agree with reported experimental results qualitatively: for type-A, lattice parameter a increases but c decreases; and for type-B, lattice parameter a decreases but c increases. Using the calculated CAp stable structures, we also calculated the elastic properties of CAp and compared them with those of HA and biological apatites.