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Angela K Wilson - One of the best experts on this subject based on the ideXlab platform.
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vibrational frequency Scale Factors for density functional theory and the polarization consistent basis sets
Journal of Computational Chemistry, 2012Co-Authors: Marie L Laury, Matthew J Carlson, Angela K WilsonAbstract:Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a Scale factor. Scale Factors for: (i) harmonic vibrational frequencies [categorized into low ( 1000 cm−1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero-point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc-n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree-Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05-2X, M06-2X), a double hybrid functional with Moller-Plesset correlation (B2GP-PLYP), and a dispersion corrected functional (B97-D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the Scale Factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested Scale factor for each density functional when employing polarization consistent basis sets (pc-n, n = 1,2,3,4). A separate Scale factor is recommended when the un-polarized basis set, pc-0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.
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vibrational frequency Scale Factors for density functional theory and the polarization consistent basis sets
Journal of Computational Chemistry, 2012Co-Authors: Marie L Laury, Matthew J Carlson, Angela K WilsonAbstract:Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a Scale factor. Scale Factors for: (i) harmonic vibrational frequencies [categorized into low ( 1000 cm(-1))], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero-point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc-n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree-Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05-2X, M06-2X), a double hybrid functional with Moller-Plesset correlation (B2GP-PLYP), and a dispersion corrected functional (B97-D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the Scale Factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested Scale factor for each density functional when employing polarization consistent basis sets (pc-n, n = 1,2,3,4). A separate Scale factor is recommended when the un-polarized basis set, pc-0, is used in combination with the density functionals.
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harmonic vibrational frequencies Scale Factors for pure hybrid hybrid meta and double hybrid functionals in conjunction with correlation consistent basis sets
Journal of Computational Chemistry, 2011Co-Authors: Marie L Laury, Scott E Boesch, Ian Haken, Pankaj Sinha, Ralph A Wheeler, Angela K WilsonAbstract:Scale Factors for (a) low (<1000 cm−1) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy Scale Factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived Scale Factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011
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Harmonic vibrational frequencies: Scale Factors for pure, hybrid, hybrid meta, and double‐hybrid functionals in conjunction with correlation consistent basis sets
Journal of Computational Chemistry, 2011Co-Authors: Marie L Laury, Scott E Boesch, Ian Haken, Pankaj Sinha, Ralph A Wheeler, Angela K WilsonAbstract:Scale Factors for (a) low (
Rodolfo A. Frino - One of the best experts on this subject based on the ideXlab platform.
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On the Scale Factors of Energy Formulas
viXra, 2017Co-Authors: Rodolfo A. FrinoAbstract:This paper explores the Scale Factors of three laws: (a) the Einstein's relativistic energy law, (b) Newton's law of universal gravitation and (c) the special universal uncertainty principle. Two new concepts are defined: complete energy laws and incomplete energy laws. This investigation shows that the first two laws have Scale Factors of 1 while the third one has a Scale factor of -1. These results could be useful in the future to predict Scale Factors of new laws of nature.
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newton s law of universal gravitation and the Scale principle
viXra, 2014Co-Authors: Rodolfo A. FrinoAbstract:Earlier this year I wrote a paper entitled Scale Factors and the Scale Principle. In that paper I formulated a new law which describes a number of fundamental quantum mechanical laws and part of Einstein’s theory of relativity. The purpose of this article is to show that this theory also predicts Newton’s law of universal gravitation. Thus this new formulation can be extended to classical mechanics.
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Newton’s Law of Universal Gravitation and the Scale Principle
viXra, 2014Co-Authors: Rodolfo A. FrinoAbstract:Earlier this year I wrote a paper entitled Scale Factors and the Scale Principle. In that paper I formulated a new law which describes a number of fundamental quantum mechanical laws and part of Einstein’s theory of relativity. The purpose of this article is to show that this theory also predicts Newton’s law of universal gravitation. Thus this new formulation can be extended to classical mechanics.
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The Schwarzschild Radius and the Scale Principle
viXra, 2014Co-Authors: Rodolfo A. FrinoAbstract:Earlier this year I wrote a paper entitled Scale Factors and the Scale Principle. In that paper I formulated a new law which describes nature at both quantum and cosmic Scales. This article shows that the formula for the Schwarzschild radius (black hole radius) is a special case of the abovementioned formulation.
Leo Radom - One of the best experts on this subject based on the ideXlab platform.
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An Evaluation of Harmonic Vibrational Frequency Scale Factors
The journal of physical chemistry. A, 2007Co-Authors: Jeffrey P. Merrick, Damian Moran, Leo RadomAbstract:Scale Factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zeropoint vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory. Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP, PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency Scale Factors were determined by a comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing a standard set of 1066 individual vibrations. ZPVE Scale Factors were generally obtained from a comparison of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the Scale Factors for a wide range of levels of theory, we have also probed the effect on Scale Factors of varying the percentage of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has revealed a near-linear relationship between the magnitude of the Scale factor and the proportion of exact exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK Scale Factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.
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harmonic vibrational frequencies an evaluation of hartree fock moller plesset quadratic configuration interaction density functional theory and semiempirical Scale Factors
The Journal of Physical Chemistry, 1996Co-Authors: Anthony Scott P And, Leo RadomAbstract:Scaling Factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Moller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT: B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling Factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling Factors suitable for low-frequency vib...
Igor S. Ignatyev - One of the best experts on this subject based on the ideXlab platform.
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Theoretical prediction of vibrational spectra. The a priori Scaled quantum mechanical (SQM) force field and vibrational spectra of pyrimidine
Spectrochimica Acta Part A: Molecular Spectroscopy, 1992Co-Authors: Gábor Pongor, James E. Boggs, Géza Fogarasi, Ildiko Magdo, Gábor Keresztury, Igor S. IgnatyevAbstract:Abstract The complete harmonic force field of pyrimidine has been computed at the ab initio Hartree—Fock level using a 4–21 Gaussian basis set. In order to compensate the systematic overestimations of the force constants at the aforementioned level of quantum mechanical approximation, the theoretical force constants were empirically Scaled by using nine Scale Factors. (The values of all these Scale Factors were previously determined by fitting the theoretical force field of benzene to the observed vibrational spectra of benzene.) The resulting a priori Scaled quantum mechanical (SQM) force field is regarded as the most accurate and physically the most correct harmonic force field for pyrimidine. This force field was then used to predict the vibrational spectra of pyrimidine- h 4 and pyrimidine- d 4 . On the basis of these a priori vibrational spectra uncertain assignments have been confidently resolved. After a few reassignments, the mean deviations between the experimental and calculated frequencies are below 9 and 18 cm −1 for the non-CH stretching in-plane and the out-of-plane vibrations, respectively. Computed IR intensities are generally in agreement with experiments at a qualitative level.
Marie L Laury - One of the best experts on this subject based on the ideXlab platform.
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vibrational frequency Scale Factors for density functional theory and the polarization consistent basis sets
Journal of Computational Chemistry, 2012Co-Authors: Marie L Laury, Matthew J Carlson, Angela K WilsonAbstract:Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a Scale factor. Scale Factors for: (i) harmonic vibrational frequencies [categorized into low ( 1000 cm−1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero-point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc-n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree-Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05-2X, M06-2X), a double hybrid functional with Moller-Plesset correlation (B2GP-PLYP), and a dispersion corrected functional (B97-D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the Scale Factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested Scale factor for each density functional when employing polarization consistent basis sets (pc-n, n = 1,2,3,4). A separate Scale factor is recommended when the un-polarized basis set, pc-0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.
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vibrational frequency Scale Factors for density functional theory and the polarization consistent basis sets
Journal of Computational Chemistry, 2012Co-Authors: Marie L Laury, Matthew J Carlson, Angela K WilsonAbstract:Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a Scale factor. Scale Factors for: (i) harmonic vibrational frequencies [categorized into low ( 1000 cm(-1))], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero-point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc-n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree-Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05-2X, M06-2X), a double hybrid functional with Moller-Plesset correlation (B2GP-PLYP), and a dispersion corrected functional (B97-D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the Scale Factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested Scale factor for each density functional when employing polarization consistent basis sets (pc-n, n = 1,2,3,4). A separate Scale factor is recommended when the un-polarized basis set, pc-0, is used in combination with the density functionals.
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harmonic vibrational frequencies Scale Factors for pure hybrid hybrid meta and double hybrid functionals in conjunction with correlation consistent basis sets
Journal of Computational Chemistry, 2011Co-Authors: Marie L Laury, Scott E Boesch, Ian Haken, Pankaj Sinha, Ralph A Wheeler, Angela K WilsonAbstract:Scale Factors for (a) low (<1000 cm−1) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy Scale Factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived Scale Factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011
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Harmonic vibrational frequencies: Scale Factors for pure, hybrid, hybrid meta, and double‐hybrid functionals in conjunction with correlation consistent basis sets
Journal of Computational Chemistry, 2011Co-Authors: Marie L Laury, Scott E Boesch, Ian Haken, Pankaj Sinha, Ralph A Wheeler, Angela K WilsonAbstract:Scale Factors for (a) low (
