262
9 Least-Squares Method
Durbin J, Watson J S (1971) Testing for serial correlation in least squares regression III. Biometrika
58:1–19
Fletcher R (1971) A modified Marquardt subroutine for non-linear least squares. AERE (UK)
Harwell Technical report n° R6799
Golub GH, Reinsch C (1970) Singular value decomposition and least squares solutions. Numer
Math 14:403–420
Groner P (2000) The quest for equilibrium structure of molecules. In: Durig JR(ed) Vibrational
spectra and molecular structure, vol 24. Elsevier, Amsterdam, pp 165–252
Hamilton L (1992) Regression with graphics: a second course in applied statistics. Wadsworth,
Belmont, CA
Hirose C (1974) The derivation of the r s structure by the use of a nondiagonal weight matrix for
rotational constants. Bull Chem Soc Japan 47:976–979
Ngari MS, Xu Y, Jäger W (1999) Rotational spectroscopic investigation of the weak interaction
between CO and N 2 O. J Mol Spectrosc 197:244–253
Kawashima Y, Endo Y, Hirota E (1989) Microwave spectrum, molecular structure, and force field
of HBO. J Mol Spectrosc 133:116–127
Kuchitsu K (1968) Comparison of molecular structures determined by electron diffraction and
spectroscopy. Ethane and diborane. J Chem Phys 49:4456–4466
Kyker Jr GC (1983) The range of data set: a quick estimator of the standard deviation. Am J Phys
51:852–852
Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Quart
Appl Math 2:164–168
Le Guennec M, Wlodarczak G, Demaison J, Bürger H, Litz M, Willner H (1993) Millimeterwave
and high-resolution infrared spectra of OCSe: determination of its structure. J Mol Spectrosc
157:419–446
Liévin J, Demaison J, Herman M, Fayt A, Puzzarini C (2011) Comparison of the experimental,
semi-experimental and ab initio equilibrium structures of acetylene: influence of relativisitic
effects and of the diagonal Born–Oppenheimer corrections. J Chem Phys 134:064119
Margulès L, Demaison J, Sreeja PB, Guillemin J-C (2006) Submillimeterwave spectrum of CH 2 PH
and equilibrium structures of CH 2 PH and CH 2 NH. J Mol Spectrosc 238:234–240
Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J
Appl Math 11:431–441
Mendolicchio M, Penocchio E, Licari D, Tasinato N, Barone V (2017) Development and implementation of advanced fitting methods for the calculation of accurate molecular structures. J Chem
Theory Comput 13:3060–3075
Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York
Rudolph HD (1991) Contribution to the systematics of r 0 -derived molecular structure determinations from rotational parameters. Struct Chem 2:581–588
Rudolph HD, Demaison J, Császár AG (2013) Accurate determination of the deformation of the
benzene ring upon substitution: equilibrium structures of benzonitrile and phenylacetylene. J
Phys Chem A 117:12969–12982
Sen A, Srivastava M (1990) Regression analysis: theory, methods, and applications. Springer, New
York
Tamassia F, Cané E, Fusina L, Di Lonardo G (2016) The experimental equilibrium structure of
acetylene. Phys Chem Chem Phys 18:1937–1944
Tikhonov AN, Arsenin VA (1977) Solution of Ill-posed problems. Wiley, New York
Vogt N, Vogt J, Demaison J (2011) Accuracy of rotational constants. J Mol Struct 988:119–127
Vogt N, Demaison J, Vogt J, Rudolph HD (2014) Why it is sometimes difficult to determine the
accurate position of a hydrogen atom by the semiexperimental method: structure of molecules
containing the OH or the CH 3 group. J Comput Chem 35:2333–2342
Vogt N, Demaison J, Vogt J, Rudolph HD, Perrin A (2015) Interplay of experiment and theory: high
resolution infrared spectrum and accurate equilibrium structure of BF 2 OH. Phys Chem Chem
Phys 17:30440–30449
9 Least-Squares Method
Durbin J, Watson J S (1971) Testing for serial correlation in least squares regression III. Biometrika
58:1–19
Fletcher R (1971) A modified Marquardt subroutine for non-linear least squares. AERE (UK)
Harwell Technical report n° R6799
Golub GH, Reinsch C (1970) Singular value decomposition and least squares solutions. Numer
Math 14:403–420
Groner P (2000) The quest for equilibrium structure of molecules. In: Durig JR(ed) Vibrational
spectra and molecular structure, vol 24. Elsevier, Amsterdam, pp 165–252
Hamilton L (1992) Regression with graphics: a second course in applied statistics. Wadsworth,
Belmont, CA
Hirose C (1974) The derivation of the r s structure by the use of a nondiagonal weight matrix for
rotational constants. Bull Chem Soc Japan 47:976–979
Ngari MS, Xu Y, Jäger W (1999) Rotational spectroscopic investigation of the weak interaction
between CO and N 2 O. J Mol Spectrosc 197:244–253
Kawashima Y, Endo Y, Hirota E (1989) Microwave spectrum, molecular structure, and force field
of HBO. J Mol Spectrosc 133:116–127
Kuchitsu K (1968) Comparison of molecular structures determined by electron diffraction and
spectroscopy. Ethane and diborane. J Chem Phys 49:4456–4466
Kyker Jr GC (1983) The range of data set: a quick estimator of the standard deviation. Am J Phys
51:852–852
Levenberg K (1944) A method for the solution of certain non-linear problems in least squares. Quart
Appl Math 2:164–168
Le Guennec M, Wlodarczak G, Demaison J, Bürger H, Litz M, Willner H (1993) Millimeterwave
and high-resolution infrared spectra of OCSe: determination of its structure. J Mol Spectrosc
157:419–446
Liévin J, Demaison J, Herman M, Fayt A, Puzzarini C (2011) Comparison of the experimental,
semi-experimental and ab initio equilibrium structures of acetylene: influence of relativisitic
effects and of the diagonal Born–Oppenheimer corrections. J Chem Phys 134:064119
Margulès L, Demaison J, Sreeja PB, Guillemin J-C (2006) Submillimeterwave spectrum of CH 2 PH
and equilibrium structures of CH 2 PH and CH 2 NH. J Mol Spectrosc 238:234–240
Marquardt DW (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J
Appl Math 11:431–441
Mendolicchio M, Penocchio E, Licari D, Tasinato N, Barone V (2017) Development and implementation of advanced fitting methods for the calculation of accurate molecular structures. J Chem
Theory Comput 13:3060–3075
Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New York
Rudolph HD (1991) Contribution to the systematics of r 0 -derived molecular structure determinations from rotational parameters. Struct Chem 2:581–588
Rudolph HD, Demaison J, Császár AG (2013) Accurate determination of the deformation of the
benzene ring upon substitution: equilibrium structures of benzonitrile and phenylacetylene. J
Phys Chem A 117:12969–12982
Sen A, Srivastava M (1990) Regression analysis: theory, methods, and applications. Springer, New
York
Tamassia F, Cané E, Fusina L, Di Lonardo G (2016) The experimental equilibrium structure of
acetylene. Phys Chem Chem Phys 18:1937–1944
Tikhonov AN, Arsenin VA (1977) Solution of Ill-posed problems. Wiley, New York
Vogt N, Vogt J, Demaison J (2011) Accuracy of rotational constants. J Mol Struct 988:119–127
Vogt N, Demaison J, Vogt J, Rudolph HD (2014) Why it is sometimes difficult to determine the
accurate position of a hydrogen atom by the semiexperimental method: structure of molecules
containing the OH or the CH 3 group. J Comput Chem 35:2333–2342
Vogt N, Demaison J, Vogt J, Rudolph HD, Perrin A (2015) Interplay of experiment and theory: high
resolution infrared spectrum and accurate equilibrium structure of BF 2 OH. Phys Chem Chem
Phys 17:30440–30449